Patent Publication Number: US-9888255-B1

Title: Pull frame interpolation

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 13/853,354, filed on Mar. 29, 2013, which is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     This application relates to video frame interpolation. 
     BACKGROUND 
     Digital video can be used, for example, for remote business meetings via video conferencing, high definition video entertainment, video advertisements, or sharing of user-generated videos. Accordingly, it would be advantageous to provide temporal and spatial frame interpolation. 
     SUMMARY 
     This application relates to encoding and decoding of video stream data for transmission or storage. Disclosed herein are aspects of systems, methods, and apparatuses for pull frame interpolation. 
     An aspect is a method for pull frame interpolation which may include receiving an encoded bitstream including information representing a plurality of frames of video data, decoding, by a processor in response to instructions stored on a non-transitory computer readable medium, the plurality of frames. The decoding may include identifying a plurality of motion vectors indicating motion from a first frame of the plurality of video frames to a second frame of the plurality of video frames, identifying an interpolation point between the first frame and the second frame, identifying a plurality of candidate interpolation motion vectors indicating motion from the first frame to the interpolation point and from the second frame to the interpolation point based on the plurality of motion vectors, selecting an interpolation motion vector from the plurality of candidate interpolation motion vectors based on a metric, and generating an interpolated frame at the interpolation point based on the selected interpolation motion vector. Generating the interpolated frame may include correcting an artifact in the interpolated frame based on the interpolation motion vector by blending the interpolated frame with an average of the first frame and the second frame, the blending being based on a gradient of a motion field associated with the interpolation motion vector. 
     Another aspect is a decoder for processing a coded video stream that contains a plurality of frames. The decoder may include a processor and a memory, communicatively coupled to the processor, the memory storing a plurality of instructions that cause the processor to receive an encoded bitstream including information representing a plurality of frames of video data, and decode the plurality of frames, which may include identifying a plurality of motion vectors indicating motion from a first frame of the plurality of video frames to a second frame of the plurality of video frames, identifying an interpolation point between the first frame and the second frame, identifying a plurality of candidate interpolation motion vectors indicating motion from the first frame to the interpolation point and from the second frame to the interpolation point based on the plurality of motion vectors, selecting an interpolation motion vector from the plurality of candidate interpolation motion vectors based on a metric, and generating an interpolated frame at the interpolation point based on the selected interpolation motion vector. Generating the interpolated frame may include correcting an artifact in the interpolated frame based on the interpolation motion vector by blending the interpolated frame with an average of the first frame and the second frame, the blending being based on a gradient of a motion field associated with the interpolation motion vector. 
     Another aspect is a decoder for processing a coded video stream that contains a plurality of frames. The decoder may include a processor and a memory, communicatively coupled to the processor, the memory storing a plurality of instructions that cause the processor to receive an encoded bitstream including information representing a plurality of frames of video data, and decode the plurality of frames, which may include selecting an interpolation motion vector from a plurality of candidate interpolation motion vectors based on a metric, and generating an interpolated frame at an interpolation point between a first frame and a second frame based on the selected interpolation motion vector. Generating the interpolated frame may include correcting an artifact in the interpolated frame based on the interpolation motion vector by blending the interpolated frame with an average of the first frame and the second frame, the blending being based on a gradient of a motion field associated with the interpolation motion vector. 
     Variations in these and other aspects will be described in additional detail hereafter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The description herein makes reference to the accompanying drawings wherein like reference numerals refer to like parts throughout the several views, and wherein: 
         FIG. 1  is a diagram of a computing device in accordance with implementations of this disclosure; 
         FIG. 2  is a diagram of a computing and communications system in accordance with implementations of this disclosure; 
         FIG. 3  is a diagram of a video stream for use in frame interpolation in accordance with implementations of this disclosure; 
         FIG. 4  is a block diagram of an encoder in accordance with implementations of this disclosure; 
         FIG. 5  is a block diagram of a decoder  500  in accordance with implementations of this disclosure; 
         FIG. 6  shows examples of timelines for video frame rate conversion in accordance with implementations of this disclosure; 
         FIG. 7  shows a diagram of an example of pull frame interpolation in accordance with implementations of this disclosure; 
         FIG. 8  shows another diagram of an example of pull frame interpolation in accordance with implementations of this disclosure; 
         FIG. 9  shows a diagram of an example of proximate neighbours in a site grid in accordance with implementations of this disclosure; 
         FIG. 10  shows a diagram of an example of hit list generation in accordance with implementations of this disclosure; 
         FIG. 11  shows a diagram of an example of pull frame interpolation in accordance with implementations of this disclosure; and 
         FIG. 12  shows a simplified diagram of an example of pull frame interpolation in accordance with implementations of this disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Digital video may be used for various purposes including, for example, remote business meetings via video conferencing, high definition video entertainment, video advertisements, and sharing of user-generated videos. The generation and display of a video signal may be performed at different frame rates. Pull frame interpolation may be performed to convert from one frame rate to another or to generate temporal or spatial video effect, such as a slow motion effect. 
     Video signal generation may include generating a video signal in an analog or digital format. Some formats may include interlaced images of two fields each, wherein half of the lines available in each frame are sampled at each time instant (or frame sampling period). The number of frames per time unit (frame rate) may vary and conversion may be performed to convert from one frame rate to another. Non-motion compensated frame rate conversion, which may be based on dropping or repeating frames, may not preserve motion well. Motion compensated frame rate conversion, such as frame interpolation, which may better preserve motion, may include generating new, interpolated, frames using motion information from the video signal. 
     Pull frame interpolation may be used for frame rate conversion. In some implementations, pull frame interpolation may be used to generate temporal or spatial video effects. For example, pull frame interpolation may generate additional frames to transition into and out of a slow motion effect, or to interpolate frames between spatially proximate input frames to produce a space-move effect. 
     Pull frame interpolation may include generating interpolated frames using motion information pulled from consecutive existing frames. The motion information may be generated by any motion estimator. Interpolated motion may be generated independently of picture interpolation. Pull frame interpolation may include optimization based on candidate motion vector selection. Post-processing may be performed to, for example, improve handling of blur or low quality input data. In some implementations, pull frame interpolation may include using a multiresolution multipass scheme to improve performance of, for example, input including large amounts of motion. 
       FIG. 1  is a diagram of a computing device  100  in accordance with implementations of this disclosure. A computing device  100  can include a communication interface  110 , a communication unit  120 , a user interface (UI)  130 , a processor  140 , a memory  150 , instructions  160 , a power source  170 , or any combination thereof. As used herein, the term “computing device” includes any unit, or combination of units, capable of performing any method, or any portion or portions thereof, disclosed herein. 
     The computing device  100  may be a stationary computing device, such as a personal computer (PC), a server, a workstation, a minicomputer, or a mainframe computer; or a mobile computing device, such as a mobile telephone, a personal digital assistant (PDA), a laptop, or a tablet PC. Although shown as a single unit, any one or more element of the communication device  100  can be integrated into any number of separate physical units. For example, the UI  130  and processor  140  can be integrated in a first physical unit and the memory  150  can be integrated in a second physical unit. 
     The communication interface  110  can be a wireless antenna, as shown, a wired communication port, such as an Ethernet port, an infrared port, a serial port, or any other wired or wireless unit capable of interfacing with a wired or wireless electronic communication medium  180 . 
     The communication unit  120  can be configured to transmit or receive signals via a wired or wireless medium  180 . For example, as shown, the communication unit  120  is operatively connected to an antenna configured to communicate via wireless signals. Although not explicitly shown in  FIG. 1 , the communication unit  120  can be configured to transmit, receive, or both via any wired or wireless communication medium, such as radio frequency (RF), ultra violet (UV), visible light, fiber optic, wire line, or a combination thereof. Although  FIG. 1  shows a single communication unit  120  and a single communication interface  110 , any number of communication units and any number of communication interfaces can be used. 
     The UI  130  can include any unit capable of interfacing with a user, such as a virtual or physical keypad, a touchpad, a display, a touch display, a speaker, a microphone, a video camera, a sensor, or any combination thereof. The UI  130  can be operatively coupled with the processor, as shown, or with any other element of the communication device  100 , such as the power source  170 . Although shown as a single unit, the UI  130  may include one or more physical units. For example, the UI  130  may include an audio interface for performing audio communication with a user, and a touch display for performing visual and touch based communication with the user. Although shown as separate units, the communication interface  110 , the communication unit  120 , and the UI  130 , or portions thereof, may be configured as a combined unit. For example, the communication interface  110 , the communication unit  120 , and the UI  130  may be implemented as a communications port capable of interfacing with an external touchscreen device. 
     The processor  140  can include any device or system capable of manipulating or processing a signal or other information now-existing or hereafter developed, including optical processors, quantum processors, molecular processors, or a combination thereof. For example, the processor  140  can include a general purpose processor, a special purpose processor, a conventional processor, a digital signal processor (DSP), a plurality of microprocessors, one or more microprocessor in association with a DSP core, a controller, a microcontroller, an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), a programmable logic array, programmable logic controller, microcode, firmware, any type of integrated circuit (IC), a state machine, or any combination thereof. As used herein, the term “processor” includes a single processor or multiple processors. The processor can be operatively coupled with the communication interface  110 , communication unit  120 , the UI  130 , the memory  150 , the instructions  160 , the power source  170 , or any combination thereof. 
     The memory  150  can include any non-transitory computer-usable or computer-readable medium, such as any tangible device that can, for example, contain, store, communicate, or transport the instructions  160 , or any information associated therewith, for use by or in connection with the processor  140 . The non-transitory computer-usable or computer-readable medium can be, for example, a solid state drive, a memory card, removable media, a read only memory (ROM), a random access memory (RAM), any type of disk including a hard disk, a floppy disk, an optical disk, a magnetic or optical card, an application specific integrated circuits (ASICs), or any type of non-transitory media suitable for storing electronic information, or any combination thereof. The memory  150  can be connected to, for example, the processor  140  through, for example, a memory bus (not explicitly shown). 
     The instructions  160  can include directions for performing any method, or any portion or portions thereof, disclosed herein. The instructions  160  can be realized in hardware, software, or any combination thereof. For example, the instructions  160  may be implemented as information stored in the memory  150 , such as a computer program, that may be executed by the processor  140  to perform any of the respective methods, algorithms, aspects, or combinations thereof, as described herein. The instructions  160 , or a portion thereof, may be implemented as a special purpose processor, or circuitry, that can include specialized hardware for carrying out any of the methods, algorithms, aspects, or combinations thereof, as described herein. Portions of the instructions  160  can be distributed across multiple processors on the same machine or different machines or across a network such as a local area network, a wide area network, the Internet, or a combination thereof. 
     The power source  170  can be any suitable device for powering the communication device  110 . For example, the power source  170  can include a wired power source; one or more dry cell batteries, such as nickel-cadmium (NiCd), nickel-zinc (NiZn), nickel metal hydride (NiMH), lithium-ion (Li-ion); solar cells; fuel cells; or any other device capable of powering the communication device  110 . The communication interface  110 , the communication unit  120 , the UI  130 , the processor  140 , the instructions  160 , the memory  150 , or any combination thereof, can be operatively coupled with the power source  170 . 
     Although shown as separate elements, the communication interface  110 , the communication unit  120 , the UI  130 , the processor  140 , the instructions  160 , the power source  170 , the memory  150 , or any combination thereof can be integrated in one or more electronic units, circuits, or chips. 
       FIG. 2  is a diagram of a computing and communications system  200  in accordance with implementations of this disclosure. The computing and communications system  200  may include one or more computing and communication devices  100 A/ 100 B/ 100 C, one or more access points  210 A/ 210 B, one or more networks  220 , or a combination thereof. For example, the computing and communication system  200  can be a multiple access system that provides communication, such as voice, data, video, messaging, broadcast, or a combination thereof, to one or more wired or wireless communicating devices, such as the computing and communication devices  100 A/ 100 B/ 100 C. Although, for simplicity,  FIG. 2  shows three computing and communication devices  100 A/ 100 B/ 100 C, two access points  210 A/ 210 B, and one network  220 , any number of computing and communication devices, access points, and networks can be used. 
     A computing and communication device  100 A/ 100 B/ 100 C can be, for example, a computing device, such as the computing device  100  shown in  FIG. 1 . For example, as shown the computing and communication devices  100 A/ 100 B may be user devices, such as a mobile computing device, a laptop, a thin client, or a smartphone, and computing and the communication device  100 C may be a server, such as a mainframe or a cluster. Although the computing and communication devices  100 A/ 100 B are described as user devices, and the computing and communication device  100 C is described as a server, any computing and communication device may perform some or all of the functions of a server, some or all of the functions of a user device, or some or all of the functions of a server and a user device. 
     Each computing and communication device  100 A/ 100 B/ 100 C can be configured to perform wired or wireless communication. For example, a computing and communication device  100 A/ 100 B/ 100 C can be configured to transmit or receive wired or wireless communication signals and can include a user equipment (UE), a mobile station, a fixed or mobile subscriber unit, a cellular telephone, a personal computer, a tablet computer, a server, consumer electronics, or any similar device. Although each computing and communication device  100 A/ 100 B/ 100 C is shown as a single unit, a computing and communication device can include any number of interconnected elements. 
     Each access point  210 A/ 210 B can be any type of device configured to communicate with a computing and communication device  100 A/ 100 B/ 100 C, a network  220 , or both via wired or wireless communication links  180 A/ 180 B/ 180 C. For example, an access point  210 A/ 210 B can include a base station, a base transceiver station (BTS), a Node-B, an enhanced Node-B (eNode-B), a Home Node-B (HNode-B), a wireless router, a wired router, a hub, a relay, a switch, or any similar wired or wireless device. Although each access point  210 A/ 210 B is shown as a single unit, an access point can include any number of interconnected elements. 
     The network  220  can be any type of network configured to provide services, such as voice, data, applications, voice over internet protocol (VoIP), or any other communications protocol or combination of communications protocols, over a wired or wireless communication link. For example, the network  220  can be a local area network (LAN), wide area network (WAN), virtual private network (VPN), a mobile or cellular telephone network, the Internet, or any other means of electronic communication. The network can use a communication protocol, such as the transmission control protocol (TCP), the user datagram protocol (UDP), the internet protocol (IP), the real-time transport protocol (RTP) the Hyper Text Transport Protocol (HTTP), or a combination thereof. 
     The computing and communication devices  100 A/ 100 B/ 100 C can communicate with each other via the network  220  using one or more a wired or wireless communication links, or via a combination of wired and wireless communication links. For example, as shown the computing and communication devices  100 A/ 100 B can communicate via wireless communication links  180 A/ 180 B, and computing and communication device  100 C can communicate via a wired communication link  180 C. Any of the computing and communication devices  100 A/ 100 B/ 100 C may communicate using any wired or wireless communication link, or links. For example, a first computing and communication device  100 A can communicate via a first access point  210 A using a first type of communication link, a second computing and communication device  100 B can communicate via a second access point  210 B using a second type of communication link, and a third computing and communication device  100 C can communicate via a third access point (not shown) using a third type of communication link. Similarly, the access points  210 A/ 210 B can communicate with the network  220  via one or more types of wired or wireless communication links  230 A/ 230 B. Although  FIG. 2  shows the computing and communication devices  100 A/ 100 B/ 100 C in communication via the network  220 , the computing and communication devices  100 A/ 100 B/ 100 C can communicate with each other via any number of communication links, such as a direct wired or wireless communication link. 
     Other implementations of the computing and communications system  200  are possible. For example, in an implementation the network  220  can be an ad-hock network and can omit one or more of the access points  210 A/ 210 B. The computing and communications system  200  may include devices, units, or elements not shown in  FIG. 2 . For example, the computing and communications system  200  may include many more communicating devices, networks, and access points. 
       FIG. 3  is a diagram of a video stream  300  for use in encoding, decoding, frame interpolation, or any combination thereof, in accordance with implementations of this disclosure. A video stream  300 , such as a video stream captured by a video camera or a video stream generated by a computing device, may include a video sequence  310 . The video sequence  310  may include a sequence of adjacent frames  320 . Although three adjacent frames  320  are shown, the video sequence  310  can include any number of adjacent frames  320 . Each frame  330  from the adjacent frames  320  may represent a single image from the video stream. A frame  330  may include blocks  340 . Although not shown in  FIG. 3 , a block can include pixels. For example, a block can include a 16×16 group of pixels, an 8×8 group of pixels, an 8×16 group of pixels, or any other group of pixels. Unless otherwise indicated herein, the term ‘block’ can include a macroblock, a segment, a slice, or any other portion of a frame. A frame, a block, a pixel, or a combination thereof can include display information, such as luminance information, chrominance information, or any other information that can be used to store, modify, communicate, or display the video stream or a portion thereof. 
       FIG. 4  is a block diagram of an encoder  400  in accordance with implementations of this disclosure. Encoder  400  can be implemented in a device, such as the computing device  100  shown in  FIG. 1  or the computing and communication devices  100 A/ 100 B/ 100 C shown in  FIG. 2 , as, for example, a computer software program stored in a data storage unit, such as the memory  150  shown in  FIG. 1 . The computer software program can include machine instructions that may be executed by a processor, such as the processor  160  shown in  FIG. 1 , and may cause the device to encode video data as described herein. The encoder  400  can be implemented as specialized hardware included, for example, in computing device  100 . 
     The encoder  400  can encode an input video stream  402 , such as the video stream  300  shown in  FIG. 3  to generate an encoded (compressed) bitstream  404 . In some implementations, the encoder  400  may include a forward path for generating the compressed bitstream  404 . The forward path may include an intra/inter prediction unit  410 , a transform unit  420 , a quantization unit  430 , an entropy encoding unit  440 , or any combination thereof. In some implementations, the encoder  400  may include a reconstruction path (indicated by the broken connection lines) to reconstruct a frame for encoding of further blocks. The reconstruction path may include a dequantization unit  450 , an inverse transform unit  460 , a reconstruction unit  470 , a loop filtering unit  480 , or any combination thereof. Other structural variations of the encoder  400  can be used to encode the video stream  402 . 
     For encoding the video stream  402 , each frame within the video stream  402  can be processed in units of blocks. Thus, a current block may be identified from the blocks in a frame, and the current block may be encoded. 
     At the intra/inter prediction unit  410 , the current block can be encoded using either intra-frame prediction, which may be within a single frame, or inter-frame prediction, which may be from frame to frame. Intra-prediction may include generating a prediction block from samples in the current frame that have been previously encoded and reconstructed. Inter-prediction may include generating a prediction block from samples in one or more previously constructed reference frames. Generating a prediction block for a current block in a current frame may include performing motion estimation to generate a motion vector indicating an appropriate reference block in the reference frame. 
     The intra/inter prediction unit  410  may subtract the prediction block from the current block (raw block) to produce a residual block. The transform unit  420  may perform a block-based transform, which may include transforming the residual block into transform coefficients in, for example, the frequency domain. Examples of block-based transforms include the Karhunen-Loève Transform (KLT), the Discrete Cosine Transform (DCT), and the Singular Value Decomposition Transform (SVD). In an example, the DCT may include transforming a block into the frequency domain. The DCT may include using transform coefficient values based on spatial frequency, with the lowest frequency (i.e. DC) coefficient at the top-left of the matrix and the highest frequency coefficient at the bottom-right of the matrix. 
     The quantization unit  430  may convert the transform coefficients into discrete quantum values, which may be referred to as quantized transform coefficients or quantization levels. The quantized transform coefficients can be entropy encoded by the entropy encoding unit  440  to produce entropy-encoded coefficients. Entropy encoding can include using a probability distribution metric. The entropy-encoded coefficients and information used to decode the block, which may include the type of prediction used, motion vectors, and quantizer values, can be output to the compressed bitstream  404 . The compressed bitstream  404  can be formatted using various techniques, such as run-length encoding (RLE) and zero-run coding. 
     The reconstruction path can be used to maintain reference frame synchronization between the encoder  400  and a corresponding decoder, such as the decoder  500  shown in  FIG. 5 . The reconstruction path may be similar to the decoding process discussed below, and may include dequantizing the quantized transform coefficients at the dequantization unit  450  and inverse transforming the dequantized transform coefficients at the inverse transform unit  460  to produce a derivative residual block. The reconstruction unit  470  may add the prediction block generated by the intra/inter prediction unit  410  to the derivative residual block to create a reconstructed block. The loop filtering unit  480  can be applied to the reconstructed block to reduce distortion, such as blocking artifacts. 
     Other variations of the encoder  400  can be used to encode the compressed bitstream  404 . For example, a non-transform based encoder  400  can quantize the residual block directly without the transform unit  420 . In some implementations, the quantization unit  430  and the dequantization unit  450  may be combined into a single unit. 
       FIG. 5  is a block diagram of a decoder  500  in accordance with implementations of this disclosure. The decoder  500  can be implemented in a device, such as the computing device  100  shown in  FIG. 1  or the computing and communication devices  100 A/ 100 B/ 100 C shown in  FIG. 2 , as, for example, a computer software program stored in a data storage unit, such as the memory  150  shown in  FIG. 1 . The computer software program can include machine instructions that may be executed by a processor, such as the processor  160  shown in  FIG. 1 , and may cause the device to decode video data as described herein. The decoder  400  can be implemented as specialized hardware included, for example, in computing device  100 . 
     The decoder  500  may receive a compressed bitstream  502 , such as the compressed bitstream  404  shown in  FIG. 4 , and may decode the compressed bitstream  502  to generate an output video stream  504 . The decoder  500  may include an entropy decoding unit  510 , a dequantization unit  520 , an inverse transform unit  530 , an intra/inter prediction unit  540 , a reconstruction unit  550 , a loop filtering unit  560 , a deblocking filtering unit  570 , or any combination thereof. Other structural variations of the decoder  500  can be used to decode the compressed bitstream  502 . 
     The entropy decoding unit  510  may decode data elements within the compressed bitstream  502  using, for example, Context Adaptive Binary Arithmetic Decoding, to produce a set of quantized transform coefficients. The dequantization unit  520  can dequantize the quantized transform coefficients, and the inverse transform unit  530  can inverse transform the dequantized transform coefficients to produce a derivative residual block, which may correspond with the derivative residual block generated by the inverse transformation unit  460  shown in  FIG. 4 . Using header information decoded from the compressed bitstream  502 , the intra/inter prediction unit  540  may generate a prediction block corresponding to the prediction block created in the encoder  400 . At the reconstruction unit  550 , the prediction block can be added to the derivative residual block to create a reconstructed block. The loop filtering unit  560  can be applied to the reconstructed block to reduce blocking artifacts. The deblocking filtering unit  570  can be applied to the reconstructed block to reduce blocking distortion, and the result may be output as the output video stream  504 . 
     Other variations of the decoder  500  can be used to decode the compressed bitstream  502 . For example, the decoder  500  can produce the output video stream  504  without the deblocking filtering unit  570 . 
       FIG. 6  shows examples of timelines for video frame rate conversion in accordance with implementations of this disclosure. In some implementations, video frame rate conversion may be performed by a unit, such as the encoder  400  shown in  FIG. 4 , of a device, such as the computing device  100  shown in  FIG. 1 , to convert a frame rate of an input video stream, such as the video stream  300  shown in  FIG. 3 , to an output video stream. As shown, each frame  602  of an input video stream is indicated by a circle and each interpolated output frame  604  for a corresponding output video stream is indicated by a diamond. 
     The top timeline  610  shows an example of frame rate conversion wherein the output frame rate may be a multiple, such as three, of the input frame rate. For example, as shown, the input frame rate may be 25 frames per second (fps) and the output frame rate may be 75 fps. As shown, one third of the interpolated frames  604  coincide with the original frames  602  and the remaining two thirds of the interpolated frames  604  may be in-between the original frames  602 . The output may be presented at the input frame rate of 25 fps, which may produce a slow motion effect that may appear slowed down by a factor of three. A slow motion factor of three is described as an example; however, any other slow motion factor may be used. 
     The middle timeline  620  shows an example of frame rate conversion wherein the input frame rate may be 25 fps and the output frame rate may be 30 fps. As shown, the locations of the output frames  604  may not be evenly spaced relative to the input frames  602 . The location pattern of the output frames  604  may have a periodicity that can be used for the creation of the interpolated frames  604 . 
     The bottom timeline  630  shows an example of frame rate conversion wherein the input frame rate may be 25 fps and the output frame rate may be 50 fps, and wherein the output frame rate transitions linearly from 25 fps to 50 fps. For example, the output video sequence may show a deceleration in time, or a slow motion effect. In this last case there may not be a simple periodicity to the output frame location in time. 
     In some implementations, conversion between one frame or field rate and another may include non-motion compensating conversion, which may include repeating frames, as in zero-order hold conversion, or dropping frames, as in subsampling conversion. For example, converting 30 fps (60 fields per second) interlaced video to 25 fps (50 fields per second) interlaced video may include dropping 50 fields out of every 300 fields from the 30 fps source. Thus, one field may be dropped for every six fields from the source. Convert from 25 fps interlaced to 30 fps interlaced may include repeating one field in every six from the source. Dropping or repeating fields produce low quality converted pictures wherein one frame in every six may have a wrong field merged into a frame. That may result in poorly represented motion, which may be perceived like a stutter effect in the converted material. In some implementations, a missing field may be estimated by interpolating it from the given video data. For example, at a given time, an odd field may be estimated from an even field by averaging lines vertically. In a subsequent time, the estimated field may be repeated or an original field may be dropped. 
     Non-motion compensating conversion may not preserve motion well. For example, a large amount of motion, such as motion of five pixels per frame, may not be well preserved. Conversion to progressive formats or between progressive formats may not preserve motion well. In some implementations, conversion may include motion compensated techniques that use motion information derived from the video data. Motion compensated conversion may include interpolating new fields or frames by directing the interpolation along motion trajectories. Motion compensated conversion may include handling occlusion, wherein a portion of a frame is hidden in one frame and visible in another. A portion of a frame that is occluded, in one frame or another, may not be available for use in conversion. 
     In some implementations, motion compensation may be performed by dedicated motion compensation hardware, such as circuitry. For example, real time conversion may be implemented using motion compensation circuitry. Hardware based motion compensation may have relatively limited complexity compared to motion compensation implemented in software or in a combination of hardware and software. 
     In some implementations, motion compensation may be implemented in software, such as post-production software. For example, software based conversion may be used to create slow-motion effects in videos, such as movies and cinemas. Software based non-real-time conversion may include interpolating frames at arbitrary points in time or space. Thus, conversion may include decelerating a frame rate to create a slow-motion effect, and accelerate the frame rate to transition out of the slow-motion effect. 
     In some implementations, conversion may include interpolating among non-temporally sequential frames. For example, spatially sequential frames may be interpolated to create an effect, such as a smooth space-move effect. In some implementations, spatially sequential frames may be captured concurrently, or near concurrently. 
     In some implementations, image data from existing frames may be pushed into interpolated frames along contours of least gradient between relevant images. Push interpolation may include copying pixel values from existing frames into interpolated frames. Push interpolation may produce convincing frame interpolation, but may not be optimal along directions of motion. For example, the motion fidelity of the conversion may not be accurate when an input video sequence is viewed at the target frame rate. 
     In some implementations, frame interpolation may include recovering missing frames in archived motion picture film and video footage. Frame interpolation for frame recovery may include reconstructing a frame at an arbitrary time instant by recovering the motion field at that instant. 
       FIG. 7  shows a diagram of an example of pull frame interpolation in accordance with implementations of this disclosure. Input frames  710 / 720 / 730  capture an object  740 , indicated by a diamond shape, moving from the top left to the bottom right of a simplified scene. As shown in  FIG. 7 , scene includes a plain white background; however, the scene may include other content. An interpolated frame  750  between the first frame  710  and the second frame  720 , and an interpolated frame  760  between the second frame  720  and the third frame  730  are shown using broken lines. 
     For example, the first input frame  710  may capture the scene at a first point in time T 1 , the second input frame  720  may capture the scene at a second point in time T 2 , and the third input frame  730  may capture the scene at a third point in time T 3 . The first interpolated frame  750  may interpolate the scene at a point in time between the first point in time T 1  and the second point in time T 2 , and the second interpolated frame  760  may interpolate the scene at a point in time between the second point in time T 2  and the third point in time T 3 . 
     In some implementations, pull frame interpolation may include generating a time-stop or timeslice effect, wherein a camera may appear to move through space and wherein time may appear to slow or stop. For example, a time-stop effect may be generated using frames recorded concurrently by multiple cameras placed at multiple different spatial positions during a time period. The first input frame  710  may capture the scene at a first point in space T 1 , the second input frame  720  may capture the scene at a second point in space T 2 , and the third input frame  730  may capture the scene at a third point in space T 3 . The input frames  710 / 720 / 730  may be capture the scene at the same, or substantially the same point in time. The first interpolated frame  750  may interpolate the scene at a point in space between the first spatial point T 1  and the second spatial point T 2 , and the second interpolated frame  760  may interpolate the scene at a point in space between the second spatial point T 2  and the third spatial point T 3 . The interpolated frames  750 / 760  may be associated with the same, or substantially the same, point in time as the input frames  710 / 720 / 730 . 
     Occluded areas  770  of the scene, such as a background, that may be hidden by the object  740  in a frame and uncovered in a subsequent frame are shown using cross hatching. Uncovered areas  780  of the scene that may be shown in a frame and occluded in a subsequent frame are shown using stippling. A motion trajectory line  790  is also shown. In some implementations, pull frame interpolation may include preserving occluded areas  770 , uncovered areas  780 , and the motion trajectory  790 . 
     In some implementations, pull frame interpolation may include estimating pixel intensities in the interpolated frames  750 / 760  based on the data in the input frames  710 / 720 / 730 . Motion information may be used to copy pixel intensities from the input frames  710 / 720 / 730  into the locations interpolated along the direction of motion, thus building up the interpolated frames  750 / 760  pixel by pixel. Pixels in the occluded regions  770  may not be available for use in subsequent frames. Pixels in uncovered regions  780  may not be available for use in previous frames. 
       FIG. 8  shows another diagram of an example of pull frame interpolation in accordance with implementations of this disclosure. In some implementations, pull frame interpolation may include generating an interpolated frame  800 , which is shown using broken lines, between a first input frame  810  and a second input frame  812 . In some implementations, pull frame interpolation may include using four input frames  810 / 812 / 814 / 816  to create interpolated frames between two adjacent input frames. The interpolated frame  800  may be estimated at a time, or space, instant t+Δ. Although  FIG. 8  shows a single interpolated frame  800 , any number of interpolated frames may be generated between the first frame  810  and the second frame  812  based on the input frames. Although pull frame interpolation based on four input frames is described herein, pull frame interpolation may be performed based on any sequence of two or more frames. 
     The input frames  810 / 812 / 814 / 816  may include a scene captured as a spatial or temporal sequence. For example, the first input frame  810  may capture the scene at a first point in time t, the second input frame  812  may capture the scene at a subsequent point in time t+1, the third input frame  814  may capture the scene at another subsequent point in time t+2, and the fourth input frame  816  may capture the scene at a previous point in time t−1. In another example, the first input frame  810  may capture the scene at a first point in space t, the second input frame  812  may capture the scene at a subsequent point in space t+1, the third input frame  814  may capture the scene at another subsequent point in space t+2, and the fourth input frame  816  may capture the scene at a previous point in space t−1. The interpolated frame  800  may be generated at a point t+Δ between the first frame  810  at t and the second frame  812  at t+1. Although one interpolated frame is shown, any number of interpolated frames may be generated at points between the first frame  810  and the second frame  812 . 
     The interpolated frame  800  may be offset from the first input frame  810  at t by a time or space interval Δ, and from the second input frame  812  at t+1 by 1−Δ. An element of the captured scene, such as an object, is shown as a rectangle translating uniformly along the frames. For example, the object is shown at a first location  820  in the frame  816  at t−1, at a second location  822  in the frame  810  at t, at a third location  824  in the frame  812  at t+1, and at a fourth location  826  in the frame  814  at t+2. Although the object is shown as moving within the frames, the object may be stationary, or substantially stationary, within the frame and other elements of the scene, such as the background, may move relative to the object. An interpolated location  830  for the object is shown as a broken line rectangle at the interpolated frame  800  at t+Δ. 
     In some implementations, pull frame interpolation may include using motion estimation information, which may be generated independently of the pull frame interpolation. For example, any motion estimation technique may be used to generate motion estimation information prior to pull frame interpolation. Motion between the frame  810  at t and the frame  812  at t+1 at position x may be expressed as d t,t+1 (x)=[d 1 ; d 2 ] where d 1  and d 2  indicate the horizontal and vertical components of the motion. The intensity of a pixel at x in frame t may be expressed as I t (x). The location of the motion compensated pixel in the previous frame may be expressed as I t−1 (x+d t,t−1 (x)). 
     The motion of the object between the frame  814  at t−1 and the frame  810  at t, which may be expressed as d t,t−1 , is shown using an example motion vector  840 . The motion of the object between the frame  810  at t and the frame  812  at t+1, which may be expressed as d t,t+1 , is shown using another example motion vector  842 . Background motion between the frame  812  at t+1 and the frame  810  at t, which may be expressed as d t+1,t , is shown using an example zero motion vector  844 . Background motion between the frame  812  at t+1 and the frame  814  at t+2, which may be expressed as d t+1,t+2 , is shown using another example motion vector  846 . 
     The interpolated motion between the interpolated frame  800  at t+Δ and the frame  810  at t may be expressed as d t+Δ,t , and the interpolated motion between the interpolated frame  800  at t+Δ and the frame  812  at t+1 may be expressed as d t+Δ,t+1 . 
     In some implementations, pull frame interpolation may include using occlusion state information. The occlusion state information may include an occlusion state associated with each pixel in a frame. For example, the occlusion state associated with the pixel at position x of frame t may be expressed as s t (x)=[00; 01; 10], wherein s t (x)=00 indicates that the pixel is not occluded in the next and previous frames, s t (x)=01 indicates that the pixel is occluded in the next frame (forward occlusion), and s t (x)=10 indicates that the pixel is occluded in the previous frame (backward occlusion). The association of each position in the interpolated frame  800  at t+Δ with an occlusion state is indicated at t+Δ using crosshatching and stippling respectively. The occlusion state of the interpolated image data corresponding to content of the scene which exists in the frame  810  at t and the frame  812  at t+1 may be expressed as s=00. The occlusion state of the interpolated image data corresponding to the patch which does not exist, or is occluded, in the frame  810  at t and exists, or is uncovered, in the frame  812  at t+1 may be expressed as s=10. The occlusion state of the interpolated image data corresponding to the patch which exists in the frame  810  at t and does not exist, or is occluded, in the frame  812  at t+1 may be expressed as s=01. 
     In some implementations, a pull frame interpolation model may be expressed as the following: 
     
       
         
           
             
               
                 
                   
                     
                       I 
                       
                         t 
                         + 
                         Δ 
                       
                     
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               0.5 
                               ⁡ 
                               
                                 [ 
                                 
                                   
                                     
                                       I 
                                       
                                         t 
                                         - 
                                         1 
                                       
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         x 
                                         + 
                                         
                                           
                                             d 
                                             
                                               t 
                                               , 
                                               
                                                 t 
                                                 - 
                                                 1 
                                               
                                             
                                           
                                           ⁡ 
                                           
                                             ( 
                                             x 
                                             ) 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                   + 
                                   
                                     
                                       I 
                                       
                                         t 
                                         + 
                                         1 
                                       
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         x 
                                         + 
                                         
                                           
                                             d 
                                             
                                               
                                                 t 
                                                 + 
                                                 Δ 
                                               
                                               , 
                                               
                                                 t 
                                                 + 
                                                 1 
                                               
                                             
                                           
                                           ⁡ 
                                           
                                             ( 
                                             x 
                                             ) 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                           
                             
                               s 
                               = 
                               00 
                             
                           
                         
                         
                           
                             
                               
                                 I 
                                 
                                   t 
                                   - 
                                   1 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   + 
                                   
                                     
                                       d 
                                       
                                         
                                           t 
                                           + 
                                           Δ 
                                         
                                         , 
                                         
                                           t 
                                           - 
                                           1 
                                         
                                       
                                     
                                     ⁡ 
                                     
                                       ( 
                                       x 
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               s 
                               = 
                               01 
                             
                           
                         
                         
                           
                             
                               
                                 I 
                                 
                                   t 
                                   + 
                                   1 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   + 
                                   
                                     
                                       d 
                                       
                                         
                                           t 
                                           + 
                                           Δ 
                                         
                                         , 
                                         
                                           t 
                                           + 
                                           1 
                                         
                                       
                                     
                                     ⁡ 
                                     
                                       ( 
                                       x 
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               s 
                               + 
                               10 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     Pull frame interpolation may include estimating motion fields between the interpolated frame  800  at t+Δ and the input frame  810  at t, and between the interpolated frame  800  at t+Δ and the input frame  812  at t+1, and may include estimating the states of the pixels s t+Δ (x). Interpolating motion at t+Δ may be referred to as a pull process, and may include using the motion at the interpolated frame  800  at t+Δ to pull pixels from the input frame  810  at t and the input frame  812  at t+1 to create the image I t +Δ using Equation 2. 
     In some implementations, D, i may include existing motion estimates and image data, d_(x) may collect motion in the interpolated frame in proximity to a current site, and manipulating the posterior probability distribution p(d t+Δ;t+1 , d t+Δ,t ID, i) in a Bayesian fashion may be expressed as the following: 
     
       
         
           
             
               
                 
                   
                     p 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             d 
                             
                               
                                 t 
                                 + 
                                 Δ 
                               
                               , 
                               
                                 t 
                                 + 
                                 1 
                               
                             
                           
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                         , 
                         
                           
                             d 
                             
                               
                                 t 
                                 + 
                                 Δ 
                               
                               , 
                               t 
                             
                           
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                         , 
                         
                           
                             s 
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                           | 
                           D 
                         
                         , 
                         i 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           
                             i 
                             | 
                             
                               
                                 d 
                                 
                                   
                                     t 
                                     + 
                                     Δ 
                                   
                                   , 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 x 
                                 ) 
                               
                             
                           
                           , 
                           
                             
                               d 
                               
                                 
                                   t 
                                   + 
                                   Δ 
                                 
                                 , 
                                 t 
                               
                             
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                           , 
                           
                             s 
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                         ) 
                       
                     
                     × 
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               d 
                               
                                 
                                   t 
                                   + 
                                   Δ 
                                 
                                 , 
                                 
                                   t 
                                   + 
                                   1 
                                 
                               
                             
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                           , 
                           
                             
                               
                                 d 
                                 
                                   
                                     t 
                                     + 
                                     Δ 
                                   
                                   , 
                                   t 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 x 
                                 ) 
                               
                             
                             | 
                             D 
                           
                           , 
                           
                             s 
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                         ) 
                       
                     
                     × 
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               d 
                               
                                 
                                   t 
                                   + 
                                   Δ 
                                 
                                 , 
                                 t 
                               
                             
                             | 
                             
                               d 
                               
                                 - 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                             
                           
                           , 
                           
                             s 
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                         ) 
                       
                     
                     × 
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               d 
                               
                                 
                                   t 
                                   + 
                                   Δ 
                                 
                                 , 
                                 
                                   t 
                                   + 
                                   1 
                                 
                               
                             
                             | 
                             
                               d 
                               
                                 - 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                             
                           
                           , 
                           
                             s 
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                         ) 
                       
                     
                     × 
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
     The estimate for d t+δ , used as the interpolated motion, may maximize the posterior in Equation 2. 
     In some implementations, pull frame interpolation may include using image likelihood. Image likelihood may be used such that e I (x)=I t (x+d t+Δ,t )−I t+1 (x+d t+Δ,t+1 ) may indicate the motion compensated motion compensated pixel difference between the pixel in the next frame and the pixel in the previous frame. For example, an image may be a color image, and e I  may be is a vector of three differences corresponding to the three color planes. In some implementations, the interpolated motion may be accurate and the differences corresponding to the three color planes may be small unless occlusion occurs. 
     In some implementations, image data at t+Δ may not be known a-priori and, motion may be used to explicitly incorporate s(•), which may be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     p 
                     ⁡ 
                     
                       ( 
                       
                         
                           i 
                           | 
                           
                             
                               d 
                               
                                 
                                   t 
                                   + 
                                   Δ 
                                 
                                 , 
                                 
                                   t 
                                   + 
                                   1 
                                 
                               
                             
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                         , 
                         
                           
                             d 
                             
                               
                                 t 
                                 + 
                                 Δ 
                               
                               , 
                               t 
                             
                           
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   ∝ 
                   
                     { 
                     
                       
                         
                           
                             
                               exp 
                               - 
                               
                                 
                                   
                                     e 
                                     I 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     x 
                                     ) 
                                   
                                 
                                 
                                   2 
                                   ⁢ 
                                   
                                     σ 
                                     I 
                                     2 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 s 
                                 ⁡ 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                               = 
                               00 
                             
                           
                         
                         
                           
                             
                               exp 
                               - 
                               
                                 k 
                                 I 
                               
                             
                           
                           
                             
                               
                                 
                                   s 
                                   ⁡ 
                                   
                                     ( 
                                     x 
                                     ) 
                                   
                                 
                                 = 
                                 01 
                               
                               , 
                               10 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     In some implementations, k I  may equal 10×2.7 2  to allow for a strong bias away from occlusion in the image data. In color images e I   2  may be the scaled vector magnitude, such as the average of the square of the three difference components. In some implementations, σ I   2  can be measured from the pixel data or may be set to 1:0. 
     In some implementations, pull frame interpolation may include motion likelihood. Motion likelihood may be used such that the true interpolated motion may agree with the motion already estimated between the existing frames. Pull frame interpolation may include maximizing motion agreement by encouraging motion compensated motion differences to be small. Encouraging motion compensated motion differences to be small may include expressing the motion compensated motion differences as follows: 
     
       
         
           
             
               
                 
                   
                     e 
                     f 
                   
                   = 
                   
                      
                     
                       
                         d 
                         
                           
                             t 
                             + 
                             Δ 
                           
                           , 
                           
                             t 
                             + 
                             1 
                           
                         
                       
                       - 
                       
                         
                           ( 
                           
                             1 
                             - 
                             Δ 
                           
                           ) 
                         
                         ⁢ 
                         
                           
                             d 
                             
                               
                                 t 
                                 + 
                                 1 
                               
                               , 
                               
                                 t 
                                 + 
                                 2 
                               
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               + 
                               
                                 d 
                                 
                                   
                                     t 
                                     + 
                                     Δ 
                                   
                                   , 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                      
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     e 
                     b 
                   
                   = 
                   
                      
                     
                       
                         d 
                         
                           
                             t 
                             + 
                             Δ 
                           
                           , 
                           t 
                         
                       
                       - 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             d 
                             
                               t 
                               , 
                               
                                 t 
                                 - 
                                 1 
                               
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               + 
                               
                                 d 
                                 
                                   
                                     t 
                                     + 
                                     Δ 
                                   
                                   , 
                                   t 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                      
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     e 
                     fb 
                   
                   = 
                   
                      
                     
                       
                         d 
                         
                           
                             t 
                             + 
                             Δ 
                           
                           , 
                           
                             t 
                             + 
                             1 
                           
                         
                       
                       + 
                       
                         
                           ( 
                           
                             1 
                             - 
                             Δ 
                           
                           ) 
                         
                         ⁢ 
                         
                           
                             d 
                             
                               
                                 t 
                                 + 
                                 1 
                               
                               , 
                               t 
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               + 
                               
                                 d 
                                 
                                   
                                     t 
                                     + 
                                     Δ 
                                   
                                   , 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                      
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     e 
                     bf 
                   
                   = 
                   
                      
                     
                       
                         d 
                         
                           
                             t 
                             + 
                             Δ 
                           
                           , 
                           t 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             d 
                             
                               t 
                               , 
                               
                                 t 
                                 + 
                                 1 
                               
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               + 
                               
                                 d 
                                 
                                   
                                     t 
                                     + 
                                     Δ 
                                   
                                   , 
                                   t 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                      
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     e 
                     d 
                   
                   = 
                   
                      
                     
                       
                         
                           d 
                           
                             
                               t 
                               + 
                               Δ 
                             
                             , 
                             t 
                           
                         
                         
                           1 
                           - 
                           Δ 
                         
                       
                       + 
                       
                         
                           d 
                           
                             t 
                             , 
                             
                               t 
                               + 
                               1 
                             
                           
                         
                         Δ 
                       
                     
                      
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equations 4-8, the x argument in the interpolated motion fields d t+Δ  is omitted for clarity. 
     In some implementations, s(•) may be incorporated and the motion likelihood may be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     p 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             d 
                             
                               
                                 t 
                                 + 
                                 Δ 
                               
                               , 
                               
                                 t 
                                 + 
                                 1 
                               
                             
                           
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                         , 
                         
                           
                             
                               d 
                               
                                 
                                   t 
                                   + 
                                   Δ 
                                 
                                 , 
                                 t 
                               
                             
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                           ❘ 
                           D 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               exp 
                               - 
                               
                                 
                                   
                                     e 
                                     f 
                                     2 
                                   
                                   + 
                                   
                                     4 
                                     ⁢ 
                                     α 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     
                                       e 
                                       d 
                                       2 
                                     
                                   
                                 
                                 
                                   2 
                                   ⁢ 
                                   
                                     σ 
                                     d 
                                     2 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 s 
                                 ⁡ 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                               = 
                               10 
                             
                           
                         
                         
                           
                             
                               exp 
                               - 
                               
                                 
                                   
                                     e 
                                     b 
                                     2 
                                   
                                   + 
                                   
                                     4 
                                     ⁢ 
                                     α 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     
                                       e 
                                       d 
                                       2 
                                     
                                   
                                 
                                 
                                   2 
                                   ⁢ 
                                   
                                     σ 
                                     d 
                                     2 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 s 
                                 ⁡ 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                               = 
                               01 
                             
                           
                         
                         
                           
                             
                               exp 
                               - 
                               
                                 
                                   
                                     e 
                                     fb 
                                     2 
                                   
                                   + 
                                   
                                     e 
                                     bf 
                                     2 
                                   
                                   + 
                                   
                                     e 
                                     f 
                                     2 
                                   
                                   + 
                                   
                                     e 
                                     b 
                                     2 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     
                                       e 
                                       d 
                                       2 
                                     
                                   
                                 
                                 
                                   2 
                                   ⁢ 
                                   
                                     σ 
                                     d 
                                     2 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 s 
                                 ⁡ 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                               = 
                               00 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 9 α may represent penalty energies that may balance the loss of temporal continuity in occluded states 10, 01 and discourage the occurrence of occluded states. e d  may penalize motion vector pairs which show acceleration. The motion likelihood for state s(•)=00 may encourage the interpolated motion to align with existing motion between frames t,t−1; t,t+1; t+1, t+2. In the other states (01; 10) temporal smoothness may be encouraged with motion between t,t−1 and t=1,t+2 respectively. 
       FIG. 9  shows a diagram of an example of proximate (adjacent) neighbors in a site grid  900  in accordance with implementations of this disclosure. In a representation of a frame as a grid a current pixel  910  may have eight proximate neighbors  920 . 
     In some implementations, pull frame interpolation may include using motion priors. In an example, the motion fields may be Markov Random Fields. A motion prior may consists of two factors, p d (•) which may enforce spatial smoothness of the estimated motion field, and p g (•) which may penalize large deviations in the motion field from a pre-computed estimate for global motion. Spatial smoothness of the interpolated motion fields may be enforced using the usual Gibbs energy prior which may be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     
                       p 
                       d 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           d 
                           
                             
                               t 
                               + 
                               Δ 
                             
                             , 
                             t 
                           
                         
                         ❘ 
                         
                           d 
                           
                             - 
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                   
                   ∝ 
                   
                     exp 
                     - 
                     
                       
                         Λ 
                         d 
                       
                       ⁢ 
                       
                         { 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               K 
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               λ 
                               d 
                             
                             ⁢ 
                             
                               
                                 f 
                                 ( 
                                 
                                    
                                   
                                     
                                       
                                         d 
                                         
                                           
                                             t 
                                             + 
                                             Δ 
                                           
                                           , 
                                           t 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         x 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         d 
                                         
                                           
                                             t 
                                             + 
                                             Δ 
                                           
                                           , 
                                           t 
                                         
                                       
                                       ( 
                                       
                                         x 
                                         - 
                                         
                                           v 
                                           k 
                                         
                                       
                                        
                                     
                                   
                                   ) 
                                 
                                 } 
                               
                               . 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ] 
                 
               
             
           
         
       
     
     Motion in the opposite direction may be expressed similarly. In Equation 10, Λ d  may control the strength of the smoothness. For example, Λ d =2.0 may be used. The contribution from each of the clique terms may be weighted with λ k  inversely with their distance from x. For example, λ k =1/|v k | may be used. In some implementations, K may be eight, such that the eight pixels proximate to the current pixel may be indexed with v k . 
     As shown in  FIG. 9 , the offset vectors may have unit values in the horizontal and vertical directions. In some implementations, f(•) may be a robust function which may be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁡ 
                     
                       ( 
                       a 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             a 
                           
                           
                             
                               
                                  
                                 a 
                                  
                               
                               &lt; 
                               10.0 
                             
                           
                         
                         
                           
                             10.0 
                           
                           
                             Otherwise 
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ] 
                 
               
             
           
         
       
     
     In some implementations, d g  may be a pre-computed estimate for the global (or camera) motion of the interpolated frames, f(•) may be a robust function, such as the function expressed in Equation 11, and p g (•) may be expressed as follows:
 
 p   g ( d   t+Δ,t   |d   g )∝exp−Λ g   f ( d   t+Δ,t ( x )− d   g ).   [Equation 12]
 
     In some implementations, the motion in the current frame may be encouraged to ‘snap’ to the global motion of the camera when sensible. In some implementations, a low strength constraint, such as Λg=01, may be employed. In some implementations, the constraint may be turned off for robustness, such as Λg=0. 
     In some implementations, pull frame interpolation may include using occlusion priors. A prior for occlusion p(s(•)) may encourage spatial smoothness in the estimated states and may be expressed as the following: 
     
       
         
           
             
               
                 
                   
                     
                       p 
                       s 
                     
                     ⁡ 
                     
                       ( 
                       
                         s 
                         | 
                         
                           s 
                           
                             - 
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                   
                   ∝ 
                   
                     exp 
                     - 
                     
                       
                         Λ 
                         o 
                       
                       ⁢ 
                       
                         
                           { 
                           
                             
                               ∑ 
                               
                                 k 
                                 = 
                                 0 
                               
                               
                                 K 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 λ 
                                 k 
                               
                               ⁢ 
                               
                                 h 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     s 
                                     , 
                                     
                                       s 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           x 
                                           + 
                                           
                                             v 
                                             k 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           } 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     13 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 13, h(s 1 ; s 2 ) may be an energy function that assigns energies according to the state pairs (s 1 ; s 2 ) which may be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     h 
                     ⁡ 
                     
                       ( 
                       
                         
                           s 
                           1 
                         
                         , 
                         
                           s 
                           2 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               0.5 
                               ⁡ 
                               
                                 [ 
                                 
                                   
                                     
                                       I 
                                       
                                         t 
                                         - 
                                         1 
                                       
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         x 
                                         + 
                                         
                                           
                                             d 
                                             
                                               t 
                                               , 
                                               
                                                 t 
                                                 - 
                                                 1 
                                               
                                             
                                           
                                           ⁡ 
                                           
                                             ( 
                                             x 
                                             ) 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                   + 
                                   
                                     
                                       I 
                                       
                                         t 
                                         + 
                                         1 
                                       
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         x 
                                         + 
                                         
                                           
                                             d 
                                             
                                               
                                                 t 
                                                 + 
                                                 Δ 
                                               
                                               , 
                                               
                                                 t 
                                                 + 
                                                 1 
                                               
                                             
                                           
                                           ⁡ 
                                           
                                             ( 
                                             x 
                                             ) 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                           
                             
                               s 
                               = 
                               00 
                             
                           
                         
                         
                           
                             
                               
                                 I 
                                 
                                   t 
                                   - 
                                   1 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   + 
                                   
                                     
                                       d 
                                       
                                         
                                           t 
                                           + 
                                           Δ 
                                         
                                         , 
                                         
                                           t 
                                           - 
                                           1 
                                         
                                       
                                     
                                     ⁡ 
                                     
                                       ( 
                                       x 
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               s 
                               = 
                               01 
                             
                           
                         
                         
                           
                             
                               
                                 I 
                                 
                                   t 
                                   + 
                                   1 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   + 
                                   
                                     
                                       d 
                                       
                                         
                                           t 
                                           + 
                                           Δ 
                                         
                                         , 
                                         
                                           t 
                                           + 
                                           1 
                                         
                                       
                                     
                                     ⁡ 
                                     
                                       ( 
                                       x 
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               s 
                               + 
                               10 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ] 
                 
               
             
           
         
       
     
     The energy function expressed in Equation 13 may discourage occlusion states 01 and 10 from sharing a boundary and may encourage the states to be the same in proximity. The energy function may encourage spatial smoothness in the occlusion states, such as in a group of proximate pixels. For example, the states of the eight pixels proximate to a current pixel are 01, the energy function may encourage the state at the current site to be the 01. In another example, the states of five sites around a current site may be 00, and the energy function may encourage the current site to be 00, which may produce in the smoothest configuration in the local area. 
     The energy function also serves to prevent 01 and 10 from being close together in that 8 nearest neighbourhood. 
     The energy function expressed in Equation 13 may be used to identify the unknown motion d t+Δ , which may include optimizing Equation 2 using, for example, Graph Cuts, Belief Propagation or any other local update scheme. 
     In some implementations, pull frame interpolation may include optimization. The computational load of pull frame interpolation may be reduced by proposing local candidates for the interpolated motion using temporal motion prediction techniques, and using the energy function expressed in Equation 13 to select an optimized candidates at each site. Motion and occlusion may be jointly estimated, rather than estimating for each in turn. The optimization process may be iterated until conclusion. In some implementations, the optimization may include Iterated Conditional Modes (ICM) optimization combined with local importance sampling. In some implementations, to facilitate candidate generation, optimization may include motion estimation, temporal hit list generation, initial estimate generation, or any combination thereof. Although described herein as elements of pull frame interpolation motion estimation, temporal hit list generation, and initial estimate generation may be performed independently prior to pull frame interpolation. 
       FIG. 10  shows a diagram of an example of generating a list of candidate interpolation motion vectors (hit list) in accordance with implementations of this disclosure. Generating the hit list may include identifying temporal and spatial candidates at each site in the interpolation frame. The computational load may be reduced by generating a list of temporal or spatial motion candidates prior to pull frame interpolation. In some implementations, such as in temporal motion prediction, the candidates may be estimated based on predicting the motion at interpolated locations by copying the motion between existing frames along their motion directions into the pixel locations at t+Δ. Each motion vector between frames t, t+1 may be used to predict candidate vectors for the interpolated field d t+Δ, t+1 . Similarly, d t+1, t  may be used to predict possible vectors for d t+1, t+Δ . 
     As shown in  FIG. 10 , the hit list for the interpolated frame  800  at t+Δ may be generated using motion fields d t , d t+1;• . Sites in t+Δ at which there are hits from both sides  1010  are shown as black squares, and an example of a site showing one hit  1020  (in the t+1, t direction) is shown as a stippled square. The backward vector from D→E may yield a candidate for d t+Δ, t  and the vector from F→G may yield a similar hit in the opposite direction, which may be a candidate for d t+Δ, t+1 . Similar hits may be identified for JK and HI. The vector AB may yield a hit in the backward direction (white square) and there may not be a vector BA that would yield a hit. The vectors starting at B may map to C. This may be an indication of an occluded region. 
     In some implementations, generating a hit list may include identifying forward hits by scanning every vector d t,t+1 (x) for all x in the frame  810  at t, and, at each site x+Δd t,t+1 (x) in the frame  800  at t+Δ, storing an indication, such as a record, of d t,t+1 (x), which may indicate a hit at that site. 
     In some implementations, generating a hit list may include identifying backward hits by scanning every vector d t+1,t (x) for each x in the frame  820  at t+1, and, at each site x+(1−Δ)d t+1,t (x) in the frame  800  at t+Δ, storing an indication, such as a record, of d t+1,t (x), which may indicate a hit at that site. 
     The forward hits and the backward hits may be two co-located lists, 
               C   ⁢     b   T       ,     C   ⁢     f   T       ,         
of candidate interpolation motion vectors (pointing in the forward and backward temporal directions) for every site in the interpolated frame at t+Δ. In some implementations, the motion fields may include inaccuracies, the handling occlusion may be difficult, and the hit list generation may include sites at which there is more than one hit in each list, or no hits.
 
       FIG. 11  shows a diagram of an example of pull frame interpolation in accordance with implementations of this disclosure. In some implementations, pull frame interpolation may include identifying input frames at  1100 , generating input motion vectors at  1110 , determine motion smoothness at  1120 , generating candidate interpolation motion vectors at  1130 , initializing output information at  1140 , performing local site updates at  1150 , determining whether to build the interpolated frame at  1160 , building an interpolated frame at  1170 , post processing at  1180 , outputting the interpolated frame at  1190 , or any combination thereof. In some implementations, estimating motion at  1110 , measuring smoothness at  1120 , generating a hit list at  1130 , or any combination thereof may be considered pre-processing and may be performed independently of the interpolation. 
     In some implementations, input frames, such as the input frames  810 / 812 / 814 / 816  shown in  FIG. 8  may be identified at  1100 . The sequence of frames may include a frame at position t−1, a frame at position t, a frame at position t+1, and a frame at position t+2. In some implementations, identifying the input frames may include identifying a temporal or spatial location Δ for each interpolated frame, such that the location of the interpolated frames Δ is between t and t+1. 
     In some implementations, motion may be generated for input frames at  1110 . For example, motion fields may be computed between frame pairs t, t−1; t, t+1; t+1, t; t+1, t+2. Any motion estimation (prediction) process can be used, such as block matching or optic flow motion estimation. The motion fields may be used to initialize d t;t−1 ; d t;t+1 ; d t+1; t−1 ; d t+1; t+2  respectively. The motion fields may remain constant during interpolation. 
     In some implementations, motion smoothness may be determined at  1120 . Determining motion smoothness may include determining whether the motion smoothness is low at  1122 , repeating an input frame as the interpolated frame at  1124 , or both. The motion fields between the existing frames of some scenes, such as badly illuminated scenes or scenes shot with a low original frame rate that include high motion content, may not be temporally or spatially consistent (low motion smoothness) and generation of a high quality interpolated frame may be unlikely. For frames exhibiting low motion smoothness an input frame, such as the frame at t or the frame at t+1, may be repeated as the interpolated frame. 
     Identifying temporal or spatial inconsistency (low motion smoothness) at  1122  may include determining the motion compensated motion difference between frames t and t+1 in blocks that tile the frame evenly. A grid of three blocks horizontally and two blocks vertically may be used with the block sizes scaled to tile the image frame accordingly. Each block may include B 1 ×B 2  sites, B may include the sites x in block b, and calculating the motion compensated motion differences in a block b, e m   b  may be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         m 
                         f 
                       
                       ⁡ 
                       
                         ( 
                         x 
                         ) 
                       
                     
                     = 
                     
                        
                       
                         
                           d 
                           
                             t 
                             , 
                             
                               t 
                               + 
                               1 
                             
                           
                         
                         + 
                         
                           
                             d 
                             
                               
                                 t 
                                 + 
                                 1 
                               
                               , 
                               1 
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               + 
                               
                                 d 
                                 
                                   t 
                                   , 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                        
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         m 
                         b 
                       
                       ⁡ 
                       
                         ( 
                         x 
                         ) 
                       
                     
                     = 
                     
                        
                       
                         
                           d 
                           
                             
                               t 
                               + 
                               1 
                             
                             , 
                             t 
                           
                         
                         + 
                         
                           
                             d 
                             
                               t 
                               , 
                               
                                 t 
                                 + 
                                 1 
                               
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               + 
                               
                                 d 
                                 
                                   
                                     t 
                                     + 
                                     1 
                                   
                                   , 
                                   t 
                                 
                               
                             
                             ) 
                           
                         
                       
                        
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       d 
                       m 
                       b 
                     
                     = 
                     
                       
                         1 
                         
                           
                             B 
                             1 
                           
                           ⁢ 
                           
                             B 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             x 
                             ∈ 
                             B 
                           
                         
                         ⁢ 
                         
                           
                             max 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     m 
                                     f 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     x 
                                     ) 
                                   
                                 
                                 , 
                                 
                                   
                                     m 
                                     b 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     x 
                                     ) 
                                   
                                 
                               
                               ) 
                             
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     15 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 15, the x in d t,t+1 (x) is omitted for simplicity. The motion compensated motion differences may be above a smoothness constraint or threshold and an input frame such as the frame at t or the frame at t+1, may be repeated as the interpolated frame at  1124 . 
     A motion compensated motion difference e m   b  that exceeds a threshold (constraint) δ b  may indicate that the motion information is unreliable and an input frame such as the frame at t or the frame at t+1, may be repeated as the interpolated frame at  1124 . In some implementations, the repeated input frame may be identified based on proximity to the interpolated frame Δ. For example, Δ may be less than or equal to 0.5 and the frame at t may be repeated. In another example, Δ may be greater than 0.5 and the frame at t+1 may be repeated. In some implementations, Δ may be greater than or equal to 0.5 and the frame at t+1 may be repeated. 
     In some implementations, identification of motion as consistent motion may change smoothly with the size of the frames in the video sequence. For example, a large threshold may be used for high definition pictures and a low threshold may be used for low resolution pictures. In some implementations, the threshold δ b  may be proportional to the horizontal size of the image in pixels N h . For example, the threshold δ b  may be 50×N h/ 1920. 
     In some implementations, candidate interpolation motion vectors (hits) may be generated at  1130 . A list of candidate interpolation motion vectors (hit list) for the interpolated frame may be based on the motion identified for the input frames. For example, the hit list may be generated as shown in  FIG. 10 . 
     In some implementations, output information may be initialized at  1140 . For example, initializing the output information may include using random assignment, hit list based assignment, or a combination thereof. In some implementations, a quick initial estimate of the interpolated motion field may be generated using the hit list. In some implementations, N T   b (x) may indicate the number of temporal candidates (hits) in the backward direction and N T   f (x) may indicate the number of temporal candidates (hits) in the forward direction. The initial estimation may include scanning the sites in t+Δ. The number of hits may be such that N T   b (x)==1) &amp;&amp; (N T   f (x)==1), the motion in the lists may be assigned to the interpolated motion, and s may be set to 00. The number of hits may be such that N T   b (x)≧1) &amp;&amp; (N T   f (x)==0), a first motion hit in the backward direction may be assigned to both directions of interpolated motion, and s may be set to 10. The number of hits may be such that N T   b (x)==0) &amp;&amp; (N T   f (x)≧1), a first motion hit in the forward direction may be assigned to both directions of interpolated motion, and s may be set to 01. Otherwise the interpolated motion may be set to 0 and s may be set to 00. Initializing the output information may include setting an iteration counter to zero. 
     In some implementations, local site updates may be performed at  1150 . Performing local site updates may include selecting and updating an interpolation motion vector for each site in the interpolation frame. Local site updates may be performed iteratively for each site in the interpolated frame. 
     In some implementations, performing local site updates may include identifying candidate interpolation motion vectors in the forward and backward directions using the hit list generated at  1130 . The hit list may be empty and no forward or backwards hits may be identified. Motion at the eight proximate neighbors of the current site, as shown in  FIG. 9 , may be identified as motion candidates for forward and backward directions. Current motion information at the current site may be included as a candidate. The length of the forward and backward motion candidate lists may be reduced by removing vectors which are the same or similar. For example, motion vectors that have a difference that is less than a threshold, such as 0.25 pixels, may be removed. The reduced length candidate list of vectors may be referred to as d k   f ,d k   b  for the kth forward and backward candidate. For example, the reduced length candidate list of vectors may include K candidate pairs. For each pair of motion candidates, three possible motion/occlusion candidates may be generated by augmenting each pair with the three possible states s=00, 01, or 10. The augmented candidate set may be referred to as m k   1 =[d k   f ,d k   b ,s=00], m k   2 =[d k   f ,d k   b ,s=01], m k   3 =[d k   f ,d k   b ,s=10]. For example, the augmented candidate set may include 3×K motion candidates. For each of the 3K motion candidates, using e f , e b , e fb , e bf , e d  as indicated in Equations 4-8, Λ o =10.0, Λ d =2.0, and λ k =1/|v k |, energies may be calculated, which may be expressed as the following: 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       E 
                       s 
                       b 
                     
                     = 
                     
                       
                         Λ 
                         d 
                       
                       ⁢ 
                       
                         { 
                         
                           
                             
                               ∑ 
                               
                                 k 
                                 = 
                                 0 
                               
                               
                                 K 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 λ 
                                 k 
                               
                               ⁢ 
                               
                                 f 
                                 ( 
                                 
                                    
                                   
                                     
                                       
                                         d 
                                         k 
                                         b 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         x 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         d 
                                         
                                           
                                             t 
                                             + 
                                             Δ 
                                           
                                           , 
                                           t 
                                         
                                       
                                       ( 
                                       
                                         x 
                                         + 
                                         
                                           v 
                                           k 
                                         
                                       
                                        
                                     
                                   
                                   ) 
                                 
                                 } 
                               
                               ⁢ 
                               
                                 
 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 E 
                                 s 
                                 f 
                               
                             
                           
                           = 
                           
                             
                               Λ 
                               d 
                             
                             ⁢ 
                             
                               { 
                               
                                 
                                   
                                     ∑ 
                                     
                                       k 
                                       = 
                                       0 
                                     
                                     
                                       K 
                                       - 
                                       1 
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       λ 
                                       k 
                                     
                                     ⁢ 
                                     
                                       f 
                                       ( 
                                       
                                          
                                         
                                           
                                             
                                               d 
                                               k 
                                               f 
                                             
                                             ⁡ 
                                             
                                               ( 
                                               x 
                                               ) 
                                             
                                           
                                           - 
                                           
                                             
                                               d 
                                               
                                                 
                                                   t 
                                                   + 
                                                   Δ 
                                                 
                                                 , 
                                                 
                                                   t 
                                                   + 
                                                   1 
                                                 
                                               
                                             
                                             ( 
                                             
                                               x 
                                               + 
                                               
                                                 v 
                                                 k 
                                               
                                             
                                              
                                           
                                         
                                         ) 
                                       
                                       } 
                                     
                                     ⁢ 
                                     
                                       
 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       E 
                                       i 
                                     
                                   
                                 
                                 = 
                                 
                                   
                                     
                                       
                                         ( 
                                         
                                           
                                             
                                               I 
                                               t 
                                             
                                             ⁡ 
                                             
                                               ( 
                                               
                                                 x 
                                                 + 
                                                 
                                                   
                                                     d 
                                                     k 
                                                     b 
                                                   
                                                   ⁡ 
                                                   
                                                     ( 
                                                     x 
                                                     ) 
                                                   
                                                 
                                               
                                               ) 
                                             
                                           
                                           - 
                                           
                                             
                                               I 
                                               
                                                 t 
                                                 + 
                                                 1 
                                               
                                             
                                             ⁡ 
                                             
                                               ( 
                                               
                                                 x 
                                                 + 
                                                 
                                                   
                                                     d 
                                                     k 
                                                     f 
                                                   
                                                   ⁡ 
                                                   
                                                     ( 
                                                     x 
                                                     ) 
                                                   
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         ) 
                                       
                                       / 
                                       
                                         ( 
                                         
                                           2 
                                           ⁢ 
                                           
                                             σ 
                                             I 
                                             2 
                                           
                                         
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       E 
                                       g 
                                     
                                   
                                   = 
                                   
                                     
                                       
                                         Λ 
                                         g 
                                       
                                       ⁢ 
                                       
                                         f 
                                         ⁡ 
                                         
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                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     16 
                   
                   ] 
                 
               
             
           
         
       
     
     In some implementations, performing local site updates may include assigning the motion candidate pair having the lowest energy to the interpolated motion field, which may include replacing values currently in that field. For that candidate the state value s may be indicated by the minimal energy. For example, if E 00  has minimal energy, then s=00. 
     In some implementations, performing local site updates may include removing isolated occlusion states at  1152 , estimating global motion at  1154 , or both. 
     Removing isolated occlusion states at  1152  may include detecting occurrences of sites at which s(x) is not equal to s(v k +x) and s(v k +x) are all the same, and replacing s(•) with the value of the neighbors. The motion at the site may be replaced with the average motion of its neighbors. Removing isolated occlusion states may reduce the occurrence of impulsive single site artifacts. 
     Estimating global motion at  1154  may be performed if all sites have been visited. Estimating global motion of the new estimate for the interpolated motion field may include using a global motion estimation method based on using dense motion flow. For example, the most frequently occurring motion vector, the average of all the vectors, or a polynomial fit to the vector field, may be used as the global motion of the scene. 
     In some implementations, whether to build the interpolated frame may be determined at  1160 . Performing local site updates at  1150  may include iterating the iterations counter. If the iterations counter exceeds a threshold, such as five, the interpolated frame may be built at  1170 . In some implementations, if there has been no change in any estimated motion, the interpolated frame may be built at  1170 . If the iterations counter is within the threshold, there has been a change in estimated motion, or both, initializing output information at  1140 , performing local site updates at  1150 , and determining whether to build the interpolated frame at  1160  may be iteratively performed. 
     In some implementations, an interpolated frame may be built at  1170 . Building the interpolated frame may include using the estimated motion and may be based on Equation 2. 
     In some implementations, post processing may be performed at  1180 . Due to difficulty in estimating motion when that motion is fast, or the recording was taken in low light, post-processing may be performed to reduce or correct the appearance of image artifacts. These artifacts may appear as holes in the image I t+Δ , or strange warping of the image near large occluded or uncovered regions. Low confidence image estimates may be identified and may be blended seamlessly with the average of the future and past frames. A gradient of the motion field may be used, which may include choosing forward or backward direction depending on which is greater, as the measure of confidence in the interpolation. 
     Post-processing may include generating a conservative estimate for the interpolated frame using averaging I*(x)=(1−Δ)I t (x)+ΔI t+1 (x). For simplicity, the backward interpolated motion d t+Δ,t−1 (x) may be expressed as [{circumflex over (d)} 1   b (h, k), {circumflex over (d)} 2   b (h, k)] and the forward interpolated motion d t+Δ,t (x) may be expressed as [{circumflex over (d)} 1   f (h, k), {circumflex over (d)} 2   f (h, k)] where x=[h,k]. Measuring the motion gradient g m (x) at each site x and blending weight w(x) may be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     
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                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
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                     17 
                   
                   ] 
                 
               
             
           
         
       
     
     For example, δ t =4 may be used. 
     A final output picture may be calculated using Î(x)=w(x)I*(x)+(1−w(x))I t+Δ (x), which may be a weighted blend between the non-motion compensated average picture I* and the output picture from the previous stage I t+Δ . In some implementations, an interpolated frame may be output at  1190 . 
     Equation 1 is shown as an example and other reconstruction methods may be used, such as a median (or other order statistic) operation on a volume of pixels extracted around them motion compensated sites in the previous and next frames. 
     Although not shown in  FIG. 11 , in some implementations, pull frame interpolation may include using a multiresolution scheme. For example, a scene may include large motion and a multiresolution scheme may be used. Using a multiresolution scheme may include performing pull frame interpolation as shown in  FIG. 11  to a coarse block based motion field. Each site may be processed as a block of B×B pixels (B=3,4,8,16,4 depending on the size of the picture). Site image differences may become the average pixel intensity difference. The interpolated block motion field at the coarse level may be used to initialize iterations at a next, finer, level. For example, processing a high definition video sequence (1920×1080) may include generating images of size 960×540, 480×270, 240×135, 120×72, 60×36, or any combination thereof, and using block size B=4 at all levels of the image pyramid. At the highest scale, when the iterations are complete, the block based vector field may be used as the final interpolated motion field. 
       FIG. 12  shows a simplified diagram of an example of pull frame interpolation in accordance with implementations of this disclosure. In some implementations, pull frame interpolation may include identifying input frames at  1210 , generating motion vectors at  1220 , identifying an interpolation point at  1230 , generating candidate interpolation motion vectors at  1240 , selecting an interpolation motion vector at  1250 , generating an interpolated frame at  1260 , or any combination thereof. 
     In some implementations, input frames may be identified at  1210 . Identifying input frames may identifying frames, such as the input frames  810 / 812 / 814 / 816  shown in  FIG. 8 , such that an identified sequence of frames includes a frame at position t−1, a frame at position t, a frame at position t+1, and a frame at position t+2. 
     In some implementations, motion vectors may be generated at  1220 , which may be similar to estimating motion at  1110  in  FIG. 11 . Generating the motion vectors may include additional processing, such as measuring motion smoothness as shown in  FIG. 11  at  1120 , determining whether the motion smoothness is low as shown in  FIG. 11  at  1122 , repeating an input frame as the interpolated frame at as shown in  FIG. 11  at  1124 , or any combination thereof. 
     In some implementations, an interpolation point may be identified at  1230 . Identifying an interpolation point may include identifying a temporal or spatial location Δ for each interpolated frame, such that the location of the interpolated frames Δ is between t and t+1. 
     In some implementations, candidate interpolation motion vectors may be generated at  1240 . Generating candidate interpolation motion vectors may include generating a hit list as shown in  FIG. 11  at  1130 . 
     In some implementations, an interpolation motion vector may be selected at  1250 . Selecting an interpolation motion vector may include initializing output information as shown in  FIG. 11  at  1140 , performing local site updates as shown in  FIG. 11  at  1150 , determining whether to build the interpolated frame as shown in  FIG. 11  at  1160 , or any combination thereof. 
     In some implementations, an interpolated frame may be generated at  1260 . Generating the interpolated frame may include building an interpolated frame as shown in  FIG. 11  at  1170 , post processing as shown in  FIG. 11  at  1180 , outputting the interpolated frame as shown in  FIG. 11  at  1190 , or any combination thereof. 
     Other implementations of the diagram of pull frame interpolation as shown in  FIG. 12  are available. In implementations, additional elements of pull frame interpolation can be added, certain elements can be combined, and/or certain elements can be removed. For example, in an implementation, a first pass pull frame interpolation may be performed on a course block based motion field and a second pass pull frame interpolation may be performed using the output of the first pass to generate an interpolated frame. 
     Pull frame interpolation, or any portion thereof, can be implemented in a device, such as the computing device  100  shown in  FIG. 1 . For example, an encoder, such as the encoder  400  shown in  FIG. 4 , can implement pull frame interpolation, or any portion thereof, using instruction stored on a tangible, non-transitory, computer readable media, such as memory  150  shown in  FIG. 1 . 
     The words “example” or “exemplary” are used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “example” or “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects or designs. Rather, use of the words “example” or “exemplary” is intended to present concepts in a concrete fashion. As used in this application, the term “or” is intended to mean an inclusive “or” rather than an exclusive “or”. That is, unless specified otherwise, or clear from context, “X includes A or B” is intended to mean any of the natural inclusive permutations. That is, if X includes A; X includes B; or X includes both A and B, then “X includes A or B” is satisfied under any of the foregoing instances. In addition, the articles “a” and “an” as used in this application and the appended claims should generally be construed to mean “one or more” unless specified otherwise or clear from context to be directed to a singular form. Moreover, use of the term “an embodiment” or “one embodiment” or “an implementation” or “one implementation” throughout is not intended to mean the same embodiment or implementation unless described as such. As used herein, the terms “determine” and “identify”, or any variations thereof, includes selecting, ascertaining, computing, looking up, receiving, determining, establishing, obtaining, or otherwise identifying or determining in any manner whatsoever using one or more of the devices shown in  FIG. 1 . 
     Further, for simplicity of explanation, although the figures and descriptions herein may include sequences or series of steps or stages, elements of the methods disclosed herein can occur in various orders and/or concurrently. Additionally, elements of the methods disclosed herein may occur with other elements not explicitly presented and described herein. Furthermore, not all elements of the methods described herein may be required to implement a method in accordance with the disclosed subject matter. 
     The implementations of encoding, decoding, and frame interpolation described herein illustrate some exemplary frame interpolation techniques. However, it is to be understood that encoding and decoding, as those terms are used herein may include compression, decompression, transformation, or any other processing or change of data, and that the terms frame interpolation and pull frame interpolation, as those terms are used herein, may include generating one or more new frames between two original frames, such that the new frame depicts content at a time or space not captured by the original frames. 
     The implementations of the transmitting station  100 A and/or the receiving station  100 B (and the algorithms, methods, instructions, etc. stored thereon and/or executed thereby) can be realized in hardware, software, or any combination thereof. The hardware can include, for example, computers, intellectual property (IP) cores, application-specific integrated circuits (ASICs), programmable logic arrays, optical processors, programmable logic controllers, microcode, microcontrollers, servers, microprocessors, digital signal processors or any other suitable circuit. In the claims, the term “processor” should be understood as encompassing any of the foregoing hardware, either singly or in combination. The terms “signal” and “data” are used interchangeably. Further, portions of the transmitting station  100 A and the receiving station  100 B do not necessarily have to be implemented in the same manner. 
     Further, in one implementation, for example, the transmitting station  100 A or the receiving station  100 B can be implemented using a general purpose computer or general purpose/processor with a computer program that, when executed, carries out any of the respective methods, algorithms and/or instructions described herein. In addition or alternatively, for example, a special purpose computer/processor can be utilized which can contain specialized hardware for carrying out any of the methods, algorithms, or instructions described herein. 
     The transmitting station  100 A and receiving station  100 B can, for example, be implemented on computers in a real-time video system. Alternatively, the transmitting station  100 A can be implemented on a server and the receiving station  100 B can be implemented on a device separate from the server, such as a hand-held communications device. In this instance, the transmitting station  100 A can encode content using an encoder  400  into an encoded video signal and transmit the encoded video signal to the communications device. In turn, the communications device can then decode the encoded video signal using a decoder  500 . Alternatively, the communications device can decode content stored locally on the communications device, for example, content that was not transmitted by the transmitting station  100 A. Other suitable transmitting station  100 A and receiving station  100 B implementation schemes are available. For example, the receiving station  100 B can be a generally stationary personal computer rather than a portable communications device and/or a device including an encoder  400  may also include a decoder  500 . 
     Further, all or a portion of implementations can take the form of a computer program product accessible from, for example, a tangible computer-usable or computer-readable medium. A computer-usable or computer-readable medium can be any device that can, for example, tangibly contain, store, communicate, or transport the program for use by or in connection with any processor. The medium can be, for example, an electronic, magnetic, optical, electromagnetic, or a semiconductor device. Other suitable mediums are also available. 
     The above-described implementations have been described in order to allow easy understanding of the application are not limiting. On the contrary, the application covers various modifications and equivalent arrangements included within the scope of the appended claims, which scope is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structure as is permitted under the law.