Patent Publication Number: US-11025907-B2

Title: Receptive-field-conforming convolution models for video coding

Description:
BACKGROUND 
     Digital video streams may represent video using a sequence of frames or still images. Digital video can be used for various applications, including, for example, video conferencing, high-definition video entertainment, video advertisements, or sharing of user-generated videos. A digital video stream can contain a large amount of data and consume a significant amount of computing or communication resources of a computing device for processing, transmission, or storage of the video data. Various approaches have been proposed to reduce the amount of data in video streams, including compression and other encoding techniques. 
     Over the years, the coding efficiency of video encoders has improved. Coding efficiency can mean encoding a video at the lowest possible bit rate while minimizing distortion (i.e., while maintaining a certain level of video quality). However, the improved coding efficiency has resulted in increased computational complexity. That is, more computation time is required by an encoder to achieve the improved coding efficiency. As such, it is desirable to obtain improved coding efficiencies with less computation time (i.e., reduced computational complexity). 
     SUMMARY 
     One aspect of the disclosed implementations is a convolutional neural network (CNN) for determining a mode decision for encoding a block in video coding. The CNN includes feature extraction layers for extracting features of the block for determining the mode decision. A non-overlapping convolution operation is performed on input at at least one of the feature extraction layers by setting a stride value equal to a kernel size, the mode decision comprises a block partitioning of the block, the block has a N×N size, and a smallest partition output for the block has a S×S size. The CNN also includes multiple classifiers. Each classifier comprises classification layers, each classification layer of the classification layers receiving respective feature maps having a respective feature dimension. Each classifier is configured to infer partition decisions for sub-blocks of size (αS)×(αS) of the block, wherein α is a power of 2 and α=2, . . . , N/S, by applying, at some of successive classification layers of the classification layers, a kernel of size 1×1 to reduce the respective feature dimension, and outputting by a final layer of the classification layers an output corresponding to a N/(αS)×N/(αS)×1 output map. An initial classification layer of each classifier can receive the feature maps as an output of a final feature extraction layer of the feature extraction layers. The output map can indicate one or more mode decisions for the block. For example, the output map can indicate a partition decision. The output map may be used to encode the block. 
     Another aspect is a method of determining a mode decision for encoding a block in video coding using a convolutional neural network (CNN). The method includes extracting, using feature extraction layers of the CNN, features of the block for determining the mode decision, wherein a non-overlapping convolution operation is performed on input at at least one of the feature extraction layers by setting a stride value equal to a kernel size, the mode decision comprises a block partitioning of the block, the block has a N×N size, and a smallest partition output for the block has a S×S size. The method also includes inferring, by multiple classifiers of the CNN that each include classification layers, the mode decision. Inferring the mode decision includes receiving, by each classification layer, respective feature maps having a respective feature dimension, and inferring, by a respective classifier of the multiple classifiers, partition decisions for sub-blocks of size (αS)×(αS) of the block, wherein α is a power of 2 and α=2, . . . , N/S. Inferring the mode decisions includes applying, at some of successive classification layers of the classification layers, a kernel of size 1×1 to reduce the respective feature dimension in half, and outputting by a last layer of the classification layers an output corresponding to a N/(αS)×N/(αS)×1 output map. An initial classification layer of each classifier may receive the feature maps as an output of a final feature extraction layer of the feature extraction layers. The mode decision, as indicated by the output, may be used to encode the block. 
     Another aspect is an apparatus for decoding an image block. The apparatus includes a processor configured to execute a method including receiving, in a compressed bitstream, an indication of a partitioning of the image block into sub-blocks. An encoder determined the partitioning of the image block using a convolutional neural network (CNN) that includes feature extraction layers for extracting features of the block for determining the partitioning, wherein a non-overlapping convolution operation is performed on input at at least one of the feature extraction layers by setting a stride value equal to a kernel size, the block has a N×N size, and a smallest partition output for the block has a S×S size. The CNN also includes multiple classifiers, wherein each classifier comprises classification layers, each classification layer of the classification layers receiving respective feature maps having a respective feature dimension. Each classifier is configured to infer partition decisions for sub-blocks of size (αS)×(αS) of the block, wherein α is a power of 2 and α=2, . . . , N/S, by applying, at some of successive classification layers of the classification layers, a kernel of size 1×1 to reduce the respective feature dimension, and outputting by a last layer of the classification layers an output corresponding to a N/(αS)×N/(αS)×1 output map. An initial classification layer of each classifier can receive the feature maps as an output of a final feature extraction layer of the feature extraction layers. The method also includes decoding the image block using the indication of the partitioning of the image block. 
     These and other aspects of the present disclosure are disclosed in the following detailed description of the embodiments, the appended claims, and the accompanying figures. 
    
    
     
       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. 
         FIG. 1  is a schematic of a video encoding and decoding system. 
         FIG. 2  is a block diagram of an example of a computing device that can implement a transmitting station or a receiving station. 
         FIG. 3  is a diagram of a video stream to be encoded and subsequently decoded. 
         FIG. 4  is a block diagram of an encoder according to implementations of this disclosure. 
         FIG. 5  is a block diagram of a decoder according to implementations of this disclosure. 
         FIG. 6  is a block diagram of a representation of a portion of a frame according to implementations of this disclosure. 
         FIG. 7  is a block diagram of an example of a quad-tree representation of a block according to implementations of this disclosure. 
         FIG. 8  is a flowchart of a process for searching for a best mode to code a block. 
         FIG. 9  is a block diagram of a first example of a convolutional neural network (CNN) for a mode decision according to implementations of this disclosure. 
         FIG. 10  is an example of convolution operations according to implementations of this disclosure. 
         FIG. 11  is an example of receptive fields according to implementations of this disclosure. 
         FIG. 12  is a block diagram of a second example of a CNN for a mode decision according to implementations of this disclosure. 
         FIG. 13  is a block diagram of a third example of a CNN for a mode decision according to implementations of this disclosure. 
         FIG. 14  is a block diagram of a fourth example of a CNN for a mode decision according to implementations of this disclosure. 
         FIG. 15  is a block diagram of a fifth example of a CNN for a mode decision according to implementations of this disclosure. 
         FIG. 16  is a flowchart of a process for encoding, by an encoder, an image block according to implementations of this disclosure. 
         FIG. 17  is an example of non-square partitions of a block. 
     
    
    
     DETAILED DESCRIPTION 
     Encoding techniques may be designed to maximize coding efficiency. Coding efficiency can mean encoding a video at the lowest possible bit rate while minimizing distortion (e.g., while maintaining a certain level of video quality). Coding efficiency is typically measured in terms of both rate and distortion. Rate refers to the number of bits required for encoding (such as encoding a block, a frame, etc.). Distortion measures the quality loss between, for example, a source video block and a reconstructed version of the source video block. For example, the distortion may be calculated as a mean-square error between pixel values of the source block and those of the reconstructed block. By performing a rate-distortion optimization process, a video codec optimizes the amount of distortion against the rate required to encode the video. 
     Modern video codecs (e.g., H.264, which is also known as MPEG-4 AVC; VP9; H.265, which is also known as HEVC; AVS2; and AV1) define and use a large number of tools and configurations (e.g., parameters) to improve coding efficiency. A video encoder can use a mode decision to examine (e.g., test, evaluate, etc.) at least some of the valid combinations of parameters to select a combination that results in a relatively low rate-distortion value. An example of a mode decision is an intra-prediction mode decision, which determines the best intra-prediction mode for coding a block. Another example of a mode decision is a partition decision, which determines an optimal partitioning of a coding unit (also known as a coding unit or CU). Another example of a mode decision includes a decision as to a transform type and/or size to use in transforming a block (such as a residual or an image block) from the pixel domain to the frequency domain to form a transform block that includes transform coefficients. 
     To evaluate whether one combination is better than another, a metric can be computed for each of the examined combinations and the respective metrics compared. In an example, the metric can combine the rate and distortion described above to produce a rate-distortion (RD) value or cost. The RD value or cost may be a single scalar value. 
     As mentioned, a best mode can be selected from many possible combinations. For example, the RD cost associated with a specific mode (or a specific combination of tools) may be determined by performing at least a subset of the encoding steps of the encoder. The subset of the encoding steps can include, depending on the mode for which a RD cost is to be determined, at least one of determining a prediction block, determining a residual block, determining a transform type, determining an interpolation filter, quantizing a transform block, entropy encoding, and so on. Note that these encoding steps are neither intended to be an exhaustive list of encoding steps that a typical encoder may perform nor presented in any particular order (that is, an encoder does not necessarily perform these steps, as listed, sequentially). As the number of possible tools and parameters increases, the number of combinations also increases, which, in turn, increases the time required to determine the best mode. 
     Instead of an exhaustive search, an encoder may terminate a mode search as soon as it finds a mode with a RD cost that is less than a set threshold. This means, however, that a better mode may have been found later on if the encoder had continued in mode search. In some cases, an exhaustive search may or may not be performed, but the entire RD cost calculation is replaced by a coarse estimation. This can further degrade decision making by an encoder. 
     Techniques such as machine learning may be exploited to reduce the time required to determine a best mode, such as a partition mode. For example, instead of performing all of the encoding steps (i.e., a brute-force or exhaustive approach) for determining the rate and distortion for various partitioning modes to compare those modes and select a best mode, a machine-learning model can be used to estimate or infer the best mode. 
     The machine-learning model may be trained using the vast amount of training data that is available from an encoder performing standard encoding techniques, such as those described below. More specifically, the training data can be used during the learning phase of machine learning to derive (e.g., learn, infer, etc.) the machine-learning model that is (e.g., defines, constitutes, etc.) a mapping from the input data (e.g., block data) to an output. 
     Once a machine-learning model is trained, the model computes the output as a deterministic function of its input. In an example, the machine-learning model can be a neural network model, which can be implemented by a convolutional neural network (CNN). A well-trained machine-learning model can be expected to closely match the brute-force approach in coding efficiency but at a significantly lower computational cost or with a regular or dataflow-oriented computational cost. 
     In addition to using appropriate training data and inputs to the machine-learning model, the architecture of the machine-learning model can also be critical to the performance and/or prediction capability of the model. The models described herein comprise convolution layers of a CNN with filter designs that respect boundaries for recursive partitioning. That is, when analyzing an image region, such as for determining a quad-tree partitioning, the features extracted (e.g., calculated, inferred, etc.) for the image region are confined to the image region itself, and not for other image regions. Further, the models described herein allow the models to have a small size (i.e., those with a reduced number of parameters as compared to models using fully connected layers). The inference accuracy for mode decision in video encoding can be significantly improved while reducing the computational complexity. 
     Further details of the inventive CNN architectures according to the teachings herein will be discussed below first with reference to a block-based codec with the teachings may be incorporated. Although a block-based codec is described as an example, other codecs may be used with the present teachings, including a feature-based codec. 
       FIG. 1  is a schematic of a video encoding and decoding system  100 . A transmitting station  102  can be, for example, a computer having an internal configuration of hardware, such as that described with respect to  FIG. 2 . However, other suitable implementations of the transmitting station  102  are possible. For example, the processing of the transmitting station  102  can be distributed among multiple devices. 
     A network  104  can connect the transmitting station  102  and a receiving station  106  for encoding and decoding of the video stream. Specifically, the video stream can be encoded in the transmitting station  102 , and the encoded video stream can be decoded in the receiving station  106 . The network  104  can be, for example, the Internet. The network  104  can also be a local area network (LAN), wide area network (WAN), virtual private network (VPN), cellular telephone network, or any other means of transferring the video stream from the transmitting station  102  to, in this example, the receiving station  106 . 
     In one example, the receiving station  106  can be a computer having an internal configuration of hardware, such as that described with respect to  FIG. 2 . However, other suitable implementations of the receiving station  106  are possible. For example, the processing of the receiving station  106  can be distributed among multiple devices. 
     Other implementations of the video encoding and decoding system  100  are possible. For example, an implementation can omit the network  104 . In another implementation, a video stream can be encoded and then stored for transmission at a later time to the receiving station  106  or any other device having memory. In one implementation, the receiving station  106  receives (e.g., via the network  104 , a computer bus, and/or some communication pathway) the encoded video stream and stores the video stream for later decoding. In an example implementation, a real-time transport protocol (RTP) is used for transmission of the encoded video over the network  104 . In another implementation, a transport protocol other than RTP (e.g., an HTTP-based video streaming protocol) may be used. 
     When used in a video conferencing system, for example, the transmitting station  102  and/or the receiving station  106  may include the ability to both encode and decode a video stream as described below. For example, the receiving station  106  could be a video conference participant who receives an encoded video bitstream from a video conference server (e.g., the transmitting station  102 ) to decode and view and further encodes and transmits its own video bitstream to the video conference server for decoding and viewing by other participants. 
       FIG. 2  is a block diagram of an example of a computing device  200  that can implement a transmitting station or a receiving station. For example, the computing device  200  can implement one or both of the transmitting station  102  and the receiving station  106  of FIG.  1 . The computing device  200  can be in the form of a computing system including multiple computing devices, or in the form of a single computing device, for example, a mobile phone, a tablet computer, a laptop computer, a notebook computer, a desktop computer, and the like. 
     A CPU  202  in the computing device  200  can be a central processing unit. Alternatively, the CPU  202  can be any other type of device, or multiple devices, now-existing or hereafter developed, capable of manipulating or processing information. Although the disclosed implementations can be practiced with a single processor as shown (e.g., the CPU  202 ), advantages in speed and efficiency can be achieved by using more than one processor. 
     In an implementation, a memory  204  in the computing device  200  can be a read-only memory (ROM) device or a random-access memory (RAM) device. Any other suitable type of storage device can be used as the memory  204 . The memory  204  can include code and data  206  that is accessed by the CPU  202  using a bus  212 . The memory  204  can further include an operating system  208  and application programs  210 , the application programs  210  including at least one program that permits the CPU  202  to perform the methods described herein. For example, the application programs  210  can include applications 1 through N, which further include a video coding application that performs the methods described herein. The computing device  200  can also include a secondary storage  214 , which can, for example, be a memory card used with a computing device  200  that is mobile. Because the video communication sessions may contain a significant amount of information, they can be stored in whole or in part in the secondary storage  214  and loaded into the memory  204  as needed for processing. 
     The computing device  200  can also include one or more output devices, such as a display  218 . The display  218  may be, in one example, a touch-sensitive display that combines a display with a touch-sensitive element that is operable to sense touch inputs. The display  218  can be coupled to the CPU  202  via the bus  212 . Other output devices that permit a user to program or otherwise use the computing device  200  can be provided in addition to or as an alternative to the display  218 . When the output device is or includes a display, the display can be implemented in various ways, including as a liquid crystal display (LCD); a cathode-ray tube (CRT) display; or a light-emitting diode (LED) display, such as an organic LED (OLED) display. 
     The computing device  200  can also include or be in communication with an image-sensing device  220 , for example, a camera, or any other image-sensing device, now existing or hereafter developed, that can sense an image, such as the image of a user operating the computing device  200 . The image-sensing device  220  can be positioned such that it is directed toward the user operating the computing device  200 . In an example, the position and optical axis of the image-sensing device  220  can be configured such that the field of vision includes an area that is directly adjacent to the display  218  and from which the display  218  is visible. 
     The computing device  200  can also include or be in communication with a sound-sensing device  222 , for example, a microphone, or any other sound-sensing device, now existing or hereafter developed, that can sense sounds near the computing device  200 . The sound-sensing device  222  can be positioned such that it is directed toward the user operating the computing device  200  and can be configured to receive sounds, for example, speech or other utterances, made by the user while the user operates the computing device  200 . 
     Although  FIG. 2  depicts the CPU  202  and the memory  204  of the computing device  200  as being integrated into a single unit, other configurations can be utilized. The operations of the CPU  202  can be distributed across multiple machines (each machine having one or more processors) that can be coupled directly or across a local area or other network. The memory  204  can be distributed across multiple machines, such as a network-based memory or memory in multiple machines performing the operations of the computing device  200 . Although depicted here as a single bus, the bus  212  of the computing device  200  can be composed of multiple buses. Further, the secondary storage  214  can be directly coupled to the other components of the computing device  200  or can be accessed via a network and can comprise a single integrated unit, such as a memory card, or multiple units, such as multiple memory cards. The computing device  200  can thus be implemented in a wide variety of configurations. 
       FIG. 3  is a diagram of an example of a video stream  300  to be encoded and subsequently decoded. The video stream  300  includes a video sequence  302 . At the next level, the video sequence  302  includes a number of adjacent frames  304 . While three frames are depicted as the adjacent frames  304 , the video sequence  302  can include any number of adjacent frames  304 . The adjacent frames  304  can then be further subdivided into individual frames, for example, a frame  306 . At the next level, the frame  306  can be divided into a series of segments  308  or planes. The segments  308  can be subsets of frames that permit parallel processing, for example. The segments  308  can also be subsets of frames that can separate the video data into separate colors. For example, the frame  306  of color video data can include a luminance (or luma) plane and two chrominance (or chroma) planes. The segments  308  may be sampled at different resolutions. 
     Whether or not the frame  306  is divided into the segments  308 , the frame  306  may be further subdivided into blocks  310 , which can contain data corresponding to, for example, 16×16 pixels in the frame  306 . The blocks  310  can also be arranged to include data from one or more segments  308  of pixel data. The blocks  310  can also be of any other suitable size, such as 4×4 pixels, 8×8 pixels, 16×8 pixels, 8×16 pixels, 16×16 pixels, or larger. For example, and as described below with regards to  FIG. 6 , a block may comprise luma pixels from the luma plane, or chroma pixels from the chroma plane. 
       FIG. 4  is a block diagram of an encoder  400  in accordance with implementations of this disclosure. The encoder  400  can be implemented, as described above, in the transmitting station  102 , such as by providing a computer software program stored in memory, for example, the memory  204 . The computer software program can include machine instructions that, when executed by a processor, such as the CPU  202 , cause the transmitting station  102  to encode video data in manners described herein. The encoder  400  can also be implemented as specialized hardware included in, for example, the transmitting station  102 . The encoder  400  has the following stages to perform the various functions in a forward path (shown by the solid connection lines) to produce an encoded or compressed bitstream  420  using the video stream  300  as input: an intra/inter-prediction stage  402 , a transform stage  404 , a quantization stage  406 , and an entropy encoding stage  408 . The encoder  400  may also include a reconstruction path (shown by the dotted connection lines) to reconstruct a frame for encoding of future blocks. In  FIG. 4 , the encoder  400  has the following stages to perform the various functions in the reconstruction path: a dequantization stage  410 , an inverse transform stage  412 , a reconstruction stage  414 , and a loop filtering stage  416 . Other structural variations of the encoder  400  can be used to encode the video stream  300 . 
     When the video stream  300  is presented for encoding, the frame  306  can be processed in units of blocks. At the intra/inter-prediction stage  402 , a block can be encoded using intra-frame prediction (also called intra-prediction) or inter-frame prediction (also called inter-prediction), or a combination of both. In any case, a prediction block can be formed. In the case of intra-prediction, all or part of a prediction block may be formed from samples in the current frame that have been previously encoded and reconstructed. In the case of inter-prediction, all or part of a prediction block may be formed from samples in one or more previously constructed reference frames determined using motion vectors. 
     Next, still referring to  FIG. 4 , the prediction block can be subtracted from the current block at the intra/inter-prediction stage  402  to produce a residual block (also called a residual). The transform stage  404  transforms the residual into transform coefficients in, for example, the frequency domain using block-based transforms. Such block-based transforms (i.e., transform types) include, for example, the Discrete Cosine Transform (DCT) and the Asymmetric Discrete Sine Transform (ADST). Other block-based transforms are possible. Further, combinations of different transforms may be applied to a single residual. In one example of application of a transform, the DCT transforms the residual block into the frequency domain where the transform coefficient values are based on spatial frequency. The lowest frequency (DC) coefficient is at the top-left of the matrix, and the highest frequency coefficient is at the bottom-right of the matrix. It is worth noting that the size of a prediction block, and hence the resulting residual block, may be different from the size of the transform block. For example, the prediction block may be split into smaller blocks to which separate transforms are applied. 
     The quantization stage  406  converts the transform coefficients into discrete quantum values, which are referred to as quantized transform coefficients, using a quantizer value or a quantization level. For example, the transform coefficients may be divided by the quantizer value and truncated. The quantized transform coefficients are then entropy encoded by the entropy encoding stage  408 . Entropy coding may be performed using any number of techniques, including token and binary trees. The entropy-encoded coefficients, together with other information used to decode the block (which may include, for example, the type of prediction used, transform type, motion vectors, and quantizer value), are then output to the compressed bitstream  420 . The information to decode the block may be entropy coded into block, frame, slice, and/or section headers within the compressed bitstream  420 . The compressed bitstream  420  can also be referred to as an encoded video stream or encoded video bitstream; these terms will be used interchangeably herein. 
     The reconstruction path in  FIG. 4  (shown by the dotted connection lines) can be used to ensure that both the encoder  400  and a decoder  500  (described below) use the same reference frames and blocks to decode the compressed bitstream  420 . The reconstruction path performs functions that are similar to functions that take place during the decoding process and that are discussed in more detail below, including dequantizing the quantized transform coefficients at the dequantization stage  410  and inverse transforming the dequantized transform coefficients at the inverse transform stage  412  to produce a derivative residual block (also called a derivative residual). At the reconstruction stage  414 , the prediction block that was predicted at the intra/inter-prediction stage  402  can be added to the derivative residual to create a reconstructed block. The loop filtering stage  416  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  420 . For example, a non-transform based encoder  400  can quantize the residual signal directly without the transform stage  404  for certain blocks or frames. In another implementation, an encoder  400  can have the quantization stage  406  and the dequantization stage  410  combined into a single stage. 
       FIG. 5  is a block diagram of a decoder  500  in accordance with implementations of this disclosure. The decoder  500  can be implemented in the receiving station  106 , for example, by providing a computer software program stored in the memory  204 . The computer software program can include machine instructions that, when executed by a processor, such as the CPU  202 , cause the receiving station  106  to decode video data in the manners described below. The decoder  500  can also be implemented in hardware included in, for example, the transmitting station  102  or the receiving station  106 . 
     The decoder  500 , similar to the reconstruction path of the encoder  400  discussed above, includes in one example the following stages to perform various functions to produce an output video stream  516  from the compressed bitstream  420 : an entropy decoding stage  502 , a dequantization stage  504 , an inverse transform stage  506 , an intra/inter-prediction stage  508 , a reconstruction stage  510 , a loop filtering stage  512 , and a post filtering stage  514 . Other structural variations of the decoder  500  can be used to decode the compressed bitstream  420 . 
     When the compressed bitstream  420  is presented for decoding, the data elements within the compressed bitstream  420  can be decoded by the entropy decoding stage  502  to produce a set of quantized transform coefficients. The dequantization stage  504  dequantizes the quantized transform coefficients (e.g., by multiplying the quantized transform coefficients by the quantizer value), and the inverse transform stage  506  inverse transforms the dequantized transform coefficients using the selected transform type to produce a derivative residual that can be identical to that created by the inverse transform stage  412  in the encoder  400 . Using header information decoded from the compressed bitstream  420 , the decoder  500  can use the intra/inter-prediction stage  508  to create the same prediction block as was created in the encoder  400 , for example, at the intra/inter-prediction stage  402 . At the reconstruction stage  510 , the prediction block can be added to the derivative residual to create a reconstructed block. The loop filtering stage  512  can be applied to the reconstructed block to reduce blocking artifacts. Other filtering can be applied to the reconstructed block. In an example, the post filtering stage  514  is applied to the reconstructed block to reduce blocking distortion, and the result is output as an output video stream  516 . The output video stream  516  can also be referred to as a decoded video stream; these terms will be used interchangeably herein. 
     Other variations of the decoder  500  can be used to decode the compressed bitstream  420 . For example, the decoder  500  can produce the output video stream  516  without the post filtering stage  514 . In some implementations of the decoder  500 , the post filtering stage  514  is applied after the loop filtering stage  512 . The loop filtering stage  512  can include an optional deblocking filtering stage. Additionally, or alternatively, the encoder  400  includes an optional deblocking filtering stage in the loop filtering stage  416 . 
       FIG. 6  is a block diagram of a representation of a portion  600  of a frame, such as the frame  306  of  FIG. 3 , according to implementations of this disclosure. As shown, the portion  600  of the frame includes four 64×64 blocks  610 , which may be referred to as superblocks, in two rows and two columns in a matrix or Cartesian plane. A superblock can have a larger or a smaller size. While  FIG. 6  is explained with respect to a superblock of size 64×64, the description is easily extendable to larger (e.g., 128×128) or smaller superblock sizes. 
     In an example, and without loss of generality, a superblock can be a basic or maximum coding unit (CU). Each superblock can include four 32×32 blocks  620 . Each 32×32 block  620  can include four 16×16 blocks  630 . Each 16×16 block  630  can include four 8×8 blocks  640 . Each 8×8 block  640  can include four 4×4 blocks  650 . Each 4×4 block  650  can include 16 pixels, which can be represented in four rows and four columns in each respective block in the Cartesian plane or matrix. The pixels can include information representing an image captured in the frame, such as luminance information, color information, and location information. In an example, a block, such as a 16×16-pixel block as shown, can include a luminance block  660 , which can include luminance pixels  662 ; and two chrominance blocks  670 / 680 , such as a U or Cb chrominance block  670 , and a V or Cr chrominance block  680 . The chrominance blocks  670 / 680  can include chrominance pixels  690 . For example, the luminance block  660  can include 16×16 luminance pixels  662 , and each chrominance block  670 / 680  can include 8×8 chrominance pixels  690 , as shown. Although one arrangement of blocks is shown, any arrangement can be used. Although  FIG. 6  shows N×N blocks, in some implementations, N×M, where N≠M, blocks can be used. For example, 32×64 blocks, 64×32 blocks, 16×32 blocks, 32×16 blocks, or any other size blocks can be used. In some implementations, N×2N blocks, 2N×N blocks, or a combination thereof can be used. 
     In some implementations, video coding can include ordered block-level coding. Ordered block-level coding can include coding blocks of a frame in an order, such as raster-scan order, wherein blocks can be identified and processed starting with a block in the upper left corner of the frame, or a portion of the frame, and proceeding along rows from left to right and from the top row to the bottom row, identifying each block in turn for processing. For example, the superblock in the top row and left column of a frame can be the first block coded, and the superblock immediately to the right of the first block can be the second block coded. The second row from the top can be the second row coded, such that the superblock in the left column of the second row can be coded after the superblock in the rightmost column of the first row. 
     In an example, coding a block can include using quad-tree coding, which can include coding smaller block units with a block in raster-scan order. The 64×64 superblock shown in the bottom-left corner of the portion of the frame shown in  FIG. 6 , for example, can be coded using quad-tree coding in which the top-left 32×32 block can be coded, then the top-right 32×32 block can be coded, then the bottom-left 32×32 block can be coded, and then the bottom-right 32×32 block can be coded. Each 32×32 block can be coded using quad-tree coding in which the top-left 16×16 block can be coded, then the top-right 16×16 block can be coded, then the bottom-left 16×16 block can be coded, and then the bottom-right 16×16 block can be coded. Each 16×16 block can be coded using quad-tree coding in which the top-left 8×8 block can be coded, then the top-right 8×8 block can be coded, then the bottom-left 8×8 block can be coded, and then the bottom-right 8×8 block can be coded. Each 8×8 block can be coded using quad-tree coding in which the top-left 4×4 block can be coded, then the top-right 4×4 block can be coded, then the bottom-left 4×4 block can be coded, and then the bottom-right 4×4 block can be coded. In some implementations, 8×8 blocks can be omitted for a 16×16 block, and the 16×16 block can be coded using quad-tree coding in which the top-left 4×4 block can be coded, and then the other 4×4 blocks in the 16×16 block can be coded in raster-scan order. 
     In an example, video coding can include compressing the information included in an original, or input, frame by omitting some of the information in the original frame from a corresponding encoded frame. For example, coding can include reducing spectral redundancy, reducing spatial redundancy, reducing temporal redundancy, or a combination thereof. 
     In an example, reducing spectral redundancy can include using a color model based on a luminance component (Y) and two chrominance components (U and V or Cb and Cr), which can be referred to as the YUV or YCbCr color model or color space. Using the YUV color model can include using a relatively large amount of information to represent the luminance component of a portion of a frame and using a relatively small amount of information to represent each corresponding chrominance component for the portion of the frame. For example, a portion of a frame can be represented by a high-resolution luminance component, which can include a 16×16 block of pixels, and by two lower resolution chrominance components, each of which representing the portion of the frame as an 8×8 block of pixels. A pixel can indicate a value (e.g., a value in the range from 0 to 255) and can be stored or transmitted using, for example, eight bits. Although this disclosure is described with reference to the YUV color model, any color model can be used. 
     Reducing spatial redundancy can include transforming a block into the frequency domain as described above. For example, a unit of an encoder, such as the entropy encoding stage  408  of  FIG. 4 , can perform a DCT using transform coefficient values based on spatial frequency. 
     Reducing temporal redundancy can include using similarities between frames to encode a frame using a relatively small amount of data based on one or more reference frames, which can be previously encoded, decoded, and reconstructed frames of the video stream. For example, a block or a pixel of a current frame can be similar to a spatially corresponding block or pixel of a reference frame. A block or a pixel of a current frame can be similar to a block or a pixel of a reference frame at a different spatial location. As such, reducing temporal redundancy can include generating motion information indicating the spatial difference (e.g., a translation between the location of the block or the pixel in the current frame and the corresponding location of the block or the pixel in the reference frame). 
     Reducing temporal redundancy can include identifying a block or a pixel in a reference frame, or a portion of the reference frame, that corresponds with a current block or pixel of a current frame. For example, a reference frame, or a portion of a reference frame, which can be stored in memory, can be searched for the best block or pixel to use for encoding a current block or pixel of the current frame. For example, the search may identify the block of the reference frame for which the difference in pixel values between the reference block and the current block is minimized, and can be referred to as motion searching. The portion of the reference frame searched can be limited. For example, the portion of the reference frame searched, which can be referred to as the search area, can include a limited number of rows of the reference frame. In an example, identifying the reference block can include calculating a cost function, such as a sum of absolute differences (SAD), between the pixels of the blocks in the search area and the pixels of the current block. 
     The spatial difference between the location of the reference block in the reference frame and the current block in the current frame can be represented as a motion vector. The difference in pixel values between the reference block and the current block can be referred to as differential data, residual data, or as a residual block. In some implementations, generating motion vectors can be referred to as motion estimation, and a pixel of a current block can be indicated based on location using Cartesian coordinates such as ƒ x,y . Similarly, a pixel of the search area of the reference frame can be indicated based on a location using Cartesian coordinates such as r x,y . A motion vector (MV) for the current block can be determined based on, for example, a SAD between the pixels of the current frame and the corresponding pixels of the reference frame. 
     Although other partitions are possible, as described above in regards to  FIG. 6 , a CU or block may be coded using quad-tree partitioning or coding as shown in the example of  FIG. 7 . The example shows quad-tree partitioning of a block  700 . However, the block  700  can be partitioned differently, such as by an encoder (e.g., the encoder  400  of  FIG. 4 ) or a machine-learning model as described below. 
     The block  700  is partitioned into four blocks, namely, the blocks  700 - 1 ,  700 - 2 ,  700 - 3 , and  700 - 4 . The block  700 - 2  is further partitioned into the blocks  702 - 1 ,  702 - 2 ,  702 - 3 , and  702 - 4 . As such, if, for example, the size of the block  700  is N×N (e.g., 128×128), then the blocks  700 - 1 ,  700 - 2 ,  700 - 3 , and  700 - 4  are each of size N/2×N/2 (e.g., 64×64), and the blocks  702 - 1 ,  702 - 2 ,  702 - 3 , and  702 - 4  are each of size N/4×N/4 (e.g., 32×32). If a block is partitioned, it is partitioned into four equally sized, non-overlapping square sub-blocks. 
     A quad-tree data representation is used to describe how the block  700  is partitioned into sub-blocks, such as blocks  700 - 1 ,  700 - 2 ,  700 - 3 ,  700 - 4 ,  702 - 1 ,  702 - 2 ,  702 - 3 , and  702 - 4 . A quadtree  704  of the partition of the block  700  is shown. Each node of the quadtree  704  is assigned a flag of “1” if the node is further split into four sub-nodes and assigned a flag of “0” if the node is not split. The flag can be referred to as a split bit (e.g., 1) or a stop bit (e.g., 0) and is coded in a compressed bitstream. In a quadtree, a node either has four child nodes or has no child nodes. A node that has no child nodes corresponds to a block that is not split further. Each of the child nodes of a split block corresponds to a sub-block. 
     In the quadtree  704 , each node corresponds to a sub-block of the block  700 . The corresponding sub-block is shown between parentheses. For example, a node  704 - 1 , which has a value of 0, corresponds to the block  700 - 1 . 
     A root node  704 - 0  corresponds to the block  700 . As the block  700  is split into four sub-blocks, the value of the root node  704 - 0  is the split bit (e.g., 1). At an intermediate level, the flags indicate whether a sub-block of the block  700  is further split into four sub-sub-blocks. In this case, a node  704 - 2  includes a flag of “1” because the block  700 - 2  is split into the blocks  702 - 1 ,  702 - 2 ,  702 - 3 , and  702 - 4 . Each of nodes  704 - 1 ,  704 - 3 , and  704 - 4  includes a flag of “0” because the corresponding blocks are not split. As nodes  704 - 5 ,  704 - 6 ,  704 - 7 , and  704 - 8  are at a bottom level of the quadtree, no flag of “0” or “1” is necessary for these nodes. That the blocks  702 - 5 ,  702 - 6 ,  702 - 7 , and  702 - 8  are not split further can be inferred from the absence of additional flags corresponding to these blocks. In this example, the smallest sub-block is 32×32 pixels, but further partitioning is possible. 
     The quad-tree data for the quadtree  704  can be represented by the binary data of “10100,” where each bit represents a node of the quadtree  704 . The binary data indicates the partitioning of the block  700  to the encoder and decoder. The encoder can encode the binary data in a compressed bitstream, such as the compressed bitstream  420  of  FIG. 4 , in a case where the encoder needs to communicate the binary data to a decoder, such as the decoder  500  of  FIG. 5 . 
     The blocks corresponding to the leaf nodes of the quadtree  704  can be used as the bases for prediction. That is, prediction can be performed for each of the blocks  700 - 1 ,  702 - 1 ,  702 - 2 ,  702 - 3 ,  702 - 4 ,  700 - 3 , and  700 - 4 , referred to herein as coding blocks. As mentioned with respect to  FIG. 6 , the coding block can be a luminance block or a chrominance block. It is noted that, in an example, the block partitioning can be determined with respect to luminance blocks. The same partition, or a different partition, can be used with the chrominance blocks. 
     A prediction type (e.g., intra- or inter-prediction) is determined at the coding block. That is, a coding block is the decision point for prediction. 
     A mode decision process (e.g., partition decision process) determines the partitioning of a coding block, such as the block  700 . The partition decision process calculates the RD costs of different combinations of coding parameters. That is, for example, different combinations of prediction blocks and predictions (e.g., intra-prediction, inter-prediction, etc.) are examined to determine an optimal partitioning. 
     As a person skilled in the art recognizes, many mode decision processes can be performed by an encoder. 
       FIG. 8  is a flowchart of a process  800  for searching for a best mode to code a block. The process  800  is an illustrative, high level process of a mode decision process that determines a best mode. For ease of description, the process  800  is described with respect to selecting an intra-prediction mode for encoding a prediction block. Other examples of best modes that can be determined by processes similar to the process  800  include determining a transform type and determining a transform size. The process  800  can be implemented by an encoder, such as the encoder  400  of  FIG. 4 , using a brute-force approach to mode decision. 
     At  802 , the process  800  receives an image block. As the process  800  is described with respect to determining an intra-prediction mode, the image block can be a prediction unit. As described with respect to  FIG. 7 , each of the leaf node coding blocks (e.g., a block  700 - 1 ,  702 - 1 ,  702 - 2 ,  702 - 3 ,  702 - 4 ,  700 - 3 , or  700 - 4 ) can be partitioned into one or more prediction units until a smallest prediction unit/block size is reached such that further partitioning is not possible. The image block can be one such prediction unit. 
     At  804 , the process  800  determines (e.g., selects, calculates, chooses, etc.) a list of modes. The list of modes can include K modes, where K is an integer number. The list of modes can be denoted {m 1 , m 2 , . . . , m k }. The encoder can have available a list of intra-prediction modes. For example, the list of available intra-prediction modes can be {DC_PRED, V_PRED, H_PRED, D45_PRED, D135_PRED, D117_PRED, D153_PRED, D207_PRED, D63_PRED, SMOOTH_PRED, SMOOTH_V_PRED, and SMOOTH_H_PRED, PAETH_PRED}. A description of these intra-prediction modes is omitted as the description is not pertinent to the understanding of this disclosure. The list of modes determined at  804  can be any subset of the list of available intra-prediction modes. 
     At  806 , the process  800  initializes a BEST_COST variable to a high value (e.g., INT_MAX, which may be equal to 2,147,483,647) and initializes a loop variable i to 1, which corresponds to the first mode to be examined. 
     At  808 , the process  800  computes (e.g., calculates) an RD_COST i  for the mode i . At  810 , the process  800  tests whether the RD cost, RD_COST i , of the current mode under examination, mode i , is less than the current best cost, BEST_COST. If the test at  810  is positive, then at  812 , the process  800  updates the best cost to be the cost of the current mode (i.e., BEST_COST=RD_COST i ) and sets the current best mode index (BEST_MODE) to the loop variable i (BEST_MODE=i). The process  800  then proceeds to  814  to increment the loop variable i (i.e., i=i+1) to prepare for examining the next mode (if any). If the test at  810  is negative, then the process  800  proceeds to  814 . 
     At  816 , if there are more modes to examine (i.e., if i≤K), the process  800  proceeds back to  808 ; otherwise the process  800  proceeds to  818 . At  818 , the process  800  outputs the index of the best mode, BEST_MODE. Outputting the best mode can mean returning the best mode to a caller of the process  800 . Outputting the best mode can mean encoding the image using the best mode. Outputting the best mode can have other semantics. The process  800  terminates after outputting the best mode at  818 . 
       FIG. 8  illustrates that a brute-force approach to mode decision is largely a serial process that essentially codes an image block X by using candidate modes to determine the mode with the best cost. Machine learning can be used to reduce the computational complexity in mode decisions. 
     At a high level, and without loss of generality, a machine-learning model, such as a classification deep-learning model, includes two main portions: a feature-extraction portion and a classification portion. The feature-extraction portion detects features of the model. The classification portion attempts to classify the detected features into a desired response. Each of the portions can include one or more layers and/or one or more operations. 
     As mentioned above, a CNN is an example of a machine-learning model. In a CNN, the feature extraction portion can include a set of convolutional operations, which is typically a series of filters that are used to filter an input image based on a filter (e.g., a square of size k). For example, and in the context of machine vision, these filters can be used to find features in an input image. The features can include, for example, edges, corners, endpoints, and so on. As the number of stacked convolutional operations increases, later convolutional operations can find higher-level features. 
     In a CNN, the classification portion may be a set of fully connected layers. The fully connected layers can be thought of as looking at all the input features of an image in order to generate a high-level classifier. Several stages (e.g., a series) of high-level classifiers eventually generate the desired classification output. 
     As can be discerned from this description, a CNN network is often composed of a number of convolutional operations (e.g., the convolution layers of the feature-extraction portion) followed by a number of fully connected layers (also called Dense layers) forming the classification portion. The number of operations of each type and their respective sizes are typically determined during the training phase of the machine learning. As a person skilled in the art recognizes, additional layers and/or operations can be included in each portion. For example, combinations of Pooling, MaxPooling, Dropout, Activation, Normalization, BatchNormalization, and other operations can be grouped with convolution operations (i.e., in the features-extraction portion) and/or the fully connected operation (i.e., in the layers of the classification portion). A convolution operation can use a SeparableConvolution2D or Convolution2D operation. For example, a convolution layer can be a group of operations starting with a Convolution2D or SeparableConvolution2D operation followed by zero or more operations (e.g., Pooling, Dropout, Activation, Normalization, BatchNormalization, other operations, or a combination thereof), until another convolution layer, Dense layer, or the output of the CNN is reached. 
     Similarly, a Dense layer can be a group of operations or layers starting with a Dense operation (i.e., a fully connected layer) followed by zero or more operations (e.g., Pooling, Dropout, Activation, Normalization, BatchNormalization, other operations, or a combination thereof) until another convolution layer, another Dense layer, or the output of the network is reached. The boundary between feature extraction based on convolutional networks and a feature classification using Dense operations can be marked by a Flatten operation, which flattens the multidimensional matrix from the feature extraction into a vector. 
     Each of the convolution layers may consist of a set of filters. While a filter is applied to a subset of the input data at a time, the filter is applied across the full input, such as by sweeping over the input. The operations performed by this layer may be linear/matrix multiplications. An example of a convolution filter is described below. The output of the convolution filter may be further filtered using an activation function. The activation function may be a linear function or non-linear function (e.g., a sigmoid function, an arcTan function, a tan H function, a ReLu function, or the like). 
     Each of the fully connected operations is a linear operation in which every input is connected to every output by a weight. As such, a fully connected layer with N number of inputs and M outputs can have a total of N×M weights. A Dense operation may be generally followed by a non-linear activation function to generate an output of that layer. 
     Some CNN network architectures may include several feature extraction portions that extract features at different granularities (e.g., at different sub-block sizes of a superblock) and a flattening layer (which may be referred to as a concatenation layer) that receives the output(s) of the last convolution layer of each of the extraction portions. The flattening layer aggregates all the features extracted by the different feature extractions portions into one input set. The output of the flattening layer may be fed into (i.e., used as input to) the fully connected layers of the classification portion. As such, the number of parameters of the entire network may be dominated (e.g., defined, set) by the number of parameters at the interface between the feature extraction portion (i.e., the convolution layers) and the classification portion (i.e., the fully connected layers). That is, the number of parameters of the network is dominated by the parameters of the flattening layer. This is one disadvantage of the above-described architectures. 
     Other disadvantages of the CNN architectures described above, which include a flattening layer whose output is fed into fully connected layers, exist. First, models with fully connected layers tend to have a large number of parameters and operations. In some situations, the machine-learning model may include over 1 million parameters. Such large models may not be effectively or efficiently used, if at all, to infer classifications on devices (e.g., mobile devices) that may be constrained (e.g., computationally constrained, energy constrained, and/or memory constrained). That is, some devices may not have sufficient computational capabilities (for example, in terms of speed) or memory storage (e.g., RAM) to handle (e.g., execute) such large models. 
     Second, the fully connected layers of such network architectures are said to have a global view of all the features that are extracted by the feature extraction portions. As such, the fully connected layers may, for example, lose a correlation between a feature and the location of the feature in the input image. As such, receptive fields of the convolution operations can become mixed by the fully connected layers. A receptive field can be defined as the region in the input space that a particular feature is looking at and/or is affected by. An example of a receptive field is described below. Presently, however, the problem wherein the receptive fields become mixed may be illustrated briefly in regards to  FIG. 7   
     Namely, when a CNN as described above (e.g., a CNN that includes a flattening layer and fully connected layers) may be used to determine a partition of a block  700  of  FIG. 7 . The CNN may extract features corresponding to different regions and/or sub-block sizes of the block  700 . As such, for example, features extracted from blocks  700 - 1 ,  700 - 2 ,  700 - 3 , and  700 - 4  of the block  700  are flattened into one input vector to the fully connected layers. In inferring whether to partition the sub-block  700 - 2  into blocks  702 - 1 ,  702 - 2 ,  702 - 3 , and  702 - 4 , by the fully connected layers, features of at least one of the blocks  700 - 1 ,  700 - 3 , and  700 - 4  may be used by the fully connected layers. As such, features of sub-blocks (e.g., the blocks  700 - 1 ,  700 - 3 , and  700 - 4 ), which are unrelated to the sub-block  700 - 2  for which a partition decision is to be inferred, may be used in the inference. This may lead to erroneous inferences and/or inferences that are based on irrelevant information. 
     In contrast, the CNN architectures according to the present teachings herein analyze frames and blocks of frames in a way that the receptive field of a cascade of convolutional layers respect quad-tree boundaries. That is, when analyzing an image region, such as for determining a quad-tree partitioning, the receptive fields of any features extracted (e.g., calculated, inferred, etc.) for the image region are confined to the image region itself. This may be achieved by using an all-convolution network, and carefully designing the filter sizes of the convolutional operations to yield a matrix representation of the analysis region, whether a 64×64 region, a 32×32 region, or a 16×16 region, for example. Implementations according to this disclosure can ensure that machine-learning models (generated during training and used during inference) for determining, e.g., block partitioning, are not erroneously based on irrelevant or extraneous features, such as pixels from outside the image region. 
     One example of such a receptive-field-conforming convolution model for video coding is shown in  FIG. 9 . Specifically,  FIG. 9  is a block diagram of an example of a convolutional neural network (CNN)  900  for a mode decision according to implementations of this disclosure. The CNN  900  can be used for determining a block partition of an image block. The block can be a superblock. For example, the CNN  900  can be used to determine the block size used in the intra/inter-prediction stage  402  of  FIG. 4 . The partition can be a quad-tree partition, such as described with respect to  FIG. 7 . The CNN  900  can be used to determine a partition for an intra-coded block or an inter-coded block of a frame, such as the frame  304  of  FIG. 3 . The CNN  900  can be used by an encoder where the smallest possible block partition is an 8×8 partition. As such, determinations of whether to split a block need be made for blocks (i.e., sub-blocks of the superblock) that are 16×16 or larger. 
     As further described below, the number of parallel branches of the feature extraction portion of the CNN  900  can be parameterizable (e.g., configurable). For example, in a configuration, only one branch (e.g., a linear branch) can be used. This is possible as long as the receptive field conformance property, as further described below, is maintained. Except for the top and left rows of the block, the receptive field conformance property means that the receptive field boundary of the block does not cross the boundaries of the block. 
     A block  902  (i.e., an image block) to be encoded is presented to the CNN  900 . The block  902  can be a one color-plane block. As such, the block  902  can be a luminance block. That the block is a one color-plane block is illustrated by the “×1” in “64×64×1” in  FIG. 9 . As mentioned, the block  902  can be a superblock. While a superblock of size 64×64 is shown and used to describe the CNN  900 , the block  902  can be of any size. For example, the block  902  can be 128×128, 32×32, or any size block for which a, e.g., quad-tree, partitioning has been determined by an encoder, such as an encoder  400  of  FIG. 4 . In another example, and since prediction modes can depend on adjacent (i.e., peripheral) pixels to a block that is to be partitioned, the block  902  (i.e., the block that is used as input to the CNN  900 ) can include pixels that are outside of the block for which a partitioning is to be determined. For example, if a partitioning of a 64×64 block is to be determined, then a block of size 65×65×1 can be used as input to the CNN  900 . That is, for example, the left and top neighboring pixels of the block for which a partitioning is to determined can be included in the input block to the CNN  900 . An example of such as configuration is described below. 
     One or more feature extraction layers  903  form three branches as shown; namely a branch  903 -A, a branch  903 -B, and a branch  903 -C. The number of branches in the feature extraction layer can be configurable to include more or fewer branches. Each of the branches can include one or more layers. At each layer, respective feature maps is extracted. In the description below, features maps, such as feature maps  904 , is referred to as having a dimension of A×B×C. For example, the feature maps  904  is of size 8×8×256. This is to be interpreted as follows: the feature maps  904  includes 256 feature maps and each of the 256 feature maps is of size 8×8 pixels (or features). In other words, the feature maps  904  can be thought of as a set of 256 matrices where each matrix is of size 8×8. In one configuration of the CNN  900 , the feature extraction of each partition type can be separated, instead of sharing the feature extraction as in  FIG. 9 . Architectures using such a configuration are described in more detail below. 
     The number of features at a feature map can be configurable. For example, while the feature maps  904  is shown to be 8×8×256, it can be 8×8×N, where N is any desired number of features. Other sizes are possible in different implementations, such as those described with respect to  FIG. 12 , below. In some examples, a feature compression rate can be applied to a machine-learning model to expand or reduce the number of features in the model. For example, the feature compression rate can be multiplied by all feature maps for feature expansion (or reduction). 
     The branch  903 -A extracts, in a first layer of the branch  903 -A, features corresponding to 8×8 blocks of the block  902 . The branch  903 -A convolves, with the block  902 , 256 filters (also referred to as kernels).  FIG. 10  is an example  1000  of convolution operations according to implementations of this disclosure. The convolution operations can be used to generate any of the feature maps described herein. 
     The example  1000  includes a region  1002  of an image. The region  1002  is shown as a 6×6 region for the purposes of this example. However, it is to be understood that convolution filters can be applied to any size block, superblock, region of image, or an image. 
     A filter  1004  of size 3×3 is used in this example. However, filters can have different sizes. The example  1000  uses a non-overlapping convolution operation with a stride that is equal to the filter size. As such, the stride size, in each of the horizontal and vertical directions is 3. The filter  1004  is shown as including binary (i.e., zero and one) values. However, the values of a filter can be any value (e.g., positive and/or negative real values). As mentioned above, the values of a filter can be determined, by the machine-learning model, during the training phase of the machine-learning model. Feature map  1014  is the output of convolving the region  1002  and the filter  1004 . 
     The filter  1004  is first convolved (e.g., using a matrix multiplication operation) with a sub-region  1006 . As a result, a pixel  1016  of the feature map  1014  can be calculated as (0×0+9×1+3×0+9×0+4×1+8×1+5×0+1×0+2×1)=23. The filter  1004  is then convolved with a sub-region  1008 . As a result, a pixel  1018  can be calculated as (4×0+8×1+3×0+0×0+0×1+0×1+9×0+9×0+10×1)=18. The filter  1004  is then convolved with a sub-region  1010 . As a result, a pixel  1020  can be calculated as (9×0+5×1+1×0+5×0+9×1+3×1+8×0+3×0+6×1)=23. The filter  1004  is then convolved with a sub-region  1012 . As a result, a pixel  1022  can be calculated as (5×0+1×1+6×0+2×0+7×1+7×1+8×0+10×0+3×1)=18. 
     Referring again to  FIG. 9 , the branch  903 -A convolves, with the block  902 , 256 filters, each having a size 8×8. A stride that is equal to the size of the filters (i.e., a stride that is equal to 8) is used. As a result, 256 feature maps (i.e., the feature maps  904 ), each of size 8×8, are extracted. A filter of size 8×8 is defined by a kernel of the same size where each entry in the kernel can be a real number. In an example, the entries can be non-negative integers that are greater than 1. Filtering an 8×8 block may thus be achieved by computing the inner product between the block and a filter kernel of the same size. In machine learning, filter kernels (i.e., the real numbers which constitute the values of the kernels) can be learned in the training process. 
     The branch  903 -B extracts 256 feature maps (i.e., feature maps  908 ), each of size 8×8. The branch  903 -B first extracts, at a first layer of the branch  903 -B, feature maps  906  by convolving the block  902  with 128 filters, each of size 4×4, and using a stride of 4 (i.e., a stride that is equal to the filter size). At a second layer of the branch  903 -B, each of the 128 feature maps of the feature maps  906  is convolved with two 2×2 filters, using a stride of 2, thereby resulting in the feature maps  908 . 
     The branch  903 -C extracts 256 feature maps (i.e., feature maps  914 ), each of size 8×8. The branch  903 -C first extracts, at a first layer of the branch  903 -C, feature maps  910  by convolving the block  902  with 64 filters, each of size 2×2, and using a stride of 2. At a second layer of the branch  903 -B, each of the 64 feature maps of the feature maps  910  is convolved with two 2×2 filters, using a stride of 2, thereby resulting in 128 feature maps (i.e., feature maps  912 ). At a third layer of the branch  903 -C, each of the 128 features maps of the feature maps  912  is convolved with two 2×2 filters, using a stride of 2, thereby resulting in the feature maps  914 . 
     It is to be noted that, each time a filter is applied to a unit (e.g., the region  1002  or a feature map), the unit is downsized (i.e., down-sampled), in each dimension, by the size of the filter. 
     The feature maps  910  are feature maps of the 32×32 blocks of the block  902 . The feature maps  906  are feature maps of the 16×16 blocks of the block  902 . The feature maps  904  are feature maps of the 8×8 blocks of the block  902 . The feature maps  908  normalizes the feature maps  906  to be, like the feature maps  904 , of size 8×8. Likewise, the feature maps  912  followed by the feature maps  914  normalize the feature maps  910  to be, similarly, of size 8×8. 
     In an example, the feature maps can be normalized, via successive convolutions, to be feature maps of the smallest possible partition that can be used by the encoder. As such, the size 8×8 corresponding to the smallest possible partition type that can be used by the encoder when the CNN  900  of  FIG. 9  is used. Similarly, if the smallest possible partition were 4×4, then the feature extraction layers  903  can normalize the feature maps to be of size 4×4. In an example, the feature extraction layers  903  can include an additional branch and each of the branches would generate, via successive convolutions, feature maps that are each of size 4×4. In another example, the feature maps can be normalized to a size that does not necessarily correspond to the smallest partition size. For example, the features maps can be normalized to any size that is larger than or equal 8×8. 
     A concatenation layer  916  receives the feature maps  904 ,  908 , and  914 . Additionally, when the CNN  900  is used to determine (e.g., infer, provide, etc.) a partition for the block  902  that is to be intra-predicted, at least some samples of the neighboring blocks can also be used as input to the concatenation layer  916 . This is because intra-prediction uses at least some samples (i.e., pixels) of neighboring blocks. While samples from the top neighboring block (indicated with TOP in  FIG. 9 ) and samples from the left neighboring block (indicated with LEFT in  FIG. 9 ) are shown for illustrative purposes, other neighboring blocks may be used, depending on the scan order used to process blocks of a video frame. For example, LEFT and TOP are used in the case of a raster scan order. In an implementation, all the samples of the top and left neighboring blocks are used as inputs to the concatenation layer  916 . However, and as mentioned above, samples of the top and left neighboring blocks can be included in the input block (e.g., the block  902  of  FIG. 9 ). Additionally, in a CNN that is used to determine other mode decision parameters (e.g., an inter-prediction parameter or transform parameter), samples from neighboring blocks may or may not be used as inputs to the CNN. 
     In an implementation, and as a person skilled in the art appreciates, TOP can be a row of previously reconstructed pixels that are peripheral to the top edge of the block  902 ; and LEFT can be a column of previously reconstructed pixels that are peripheral to the left edge of the block  902 . There can be up to 64 samples corresponding to TOP and up to 64 samples corresponding to LEFT. As mentioned above, TOP and LEFT can be added, instead or in addition, to the input block that is presented to the CNN. 
     A non-linear function of a quantization parameter (QP, q, or Q) may optionally be used as an input to the CNN. A QP in video codecs can be used to control the tradeoff between rate and distortion. Usually, a larger QP means higher quantization (e.g., of transform coefficients) resulting in a lower rate but higher distortion; and a smaller QP means lower quantization resulting in a higher rate but a lower distortion. 
     The value of the QP can be fixed. For example, an encoder can use one QP value to encode all frames and/or all blocks of a video. In other examples, the QP can change, for example, from frame to frame. For example, in the case of a video conference application, the encoder can change the QP value based on fluctuations in network bandwidth. 
     As the QP can be used to control the tradeoff between rate and distortion, the QP can be used to calculate the RD cost associated with each combination of parameters in an exhaustive search as described above with regard to  FIG. 8 . In an example, the QP can be used to derive a multiplier that is used to combine the rate and distortion values into one metric. Some codecs may refer to the multiplier as the Lagrange multiplier (denoted λ mode ); other codecs may use a similar multiplier that is referred as rdmult. Each codec may have a different method of calculating the multiplier. Unless the context makes clear, the multiplier is referred to herein, regardless of the codec, as the Lagrange multiplier or Lagrange parameter. 
     To reiterate, the Lagrange multiplier can be used to evaluate the RD costs of competing modes (i.e., competing combinations of parameters). Specifically, let r m  denote the rate (in bits) resulting from using a mode m and let d m  denote the resulting distortion. The RD cost of selecting the mode m can be computed as a scalar value d m +λ mode r m . By using the Lagrange parameter λ mode , it is then possible to compare the cost of two modes and select one with the lower combined RD cost. This technique of evaluating RD cost is a basis of mode decision processes in at least some video codecs. 
     Different video codecs may use different techniques to compute the Lagrange multipliers from the QPs. This is due in part to the fact that the different codecs may have different meanings (e.g., definitions, semantics, etc.) for, and method of use of, QPs. For example, codecs that implement the H.264 standard may derive the Lagrange multiplier λ mode  according to λ mode =0.85×2 (QP−12)/3 . Codecs that implement the HEVC standard may use a formula that is similar. Codecs that implement the H.263 standard may derive the Lagrange multiplier λ mode  according to λ mode =0.85·Q H263   2 : Codecs that implement the VP9 standard may derive the multiplier rdmult according to rdmult=88·q 2 /24. Codecs that implement the AV1 standard may derive the Lagrange multiplier λ mode  according to λ mode =0.12·Q AV1   2 /256. 
     As can be seen in the above cases, the multiplier has a non-linear (e.g., exponential or quadratic) relationship to the QP. Note that the multipliers may undergo further changes before being used in the respective codecs to account for additional side information included in a compressed bitstream by the encoder. Examples of side information include picture type (e.g., intra vs. inter predicted frame), color components (e.g., luminance or chrominance), and/or region of interest. In an example, such additional changes can be linear changes to the multipliers. 
     Given the above, if the value of the QP itself is used as an input to a machine-learning model, a disconnect may result between how the QP is used in evaluating the RD cost and how the QP is used in training machine-learning models. For codecs that use QP in the determination of RD cost, better performance can be achieved by using non-linear (e.g., exponential, quadratic, etc.) forms of the QPs as input to machine-learning models as compared to using linear (e.g., scalar) forms of the QPs. Better performance can mean smaller network size and/or better inference performance. In an example, the non-linear function can be approximated by piecewise linear segments. 
     As mentioned, QP may be used as an input to the CNN. In the example of  FIG. 9 , QP is used as an input to the concatenation layer  916 . More specifically, a quadratic function (i.e., QP 2 ) is illustrated in  FIG. 9 . As described above, however, the function used depends on the codec; more specifically, the function used depends on the standard implemented by the codec. For example, a quadratic function may be used in the case of a codec that implements H.263, VP9, or AV1; and an exponential function may be used in the case of a codec that implements H.264 or HEVC. 
     A total of 897 inputs can be received by the concatenation layer  916 . The inputs include 256 inputs of the feature maps  904 , 256 inputs of the feature maps  908 , 256 inputs feature maps  914 , 64 inputs at TOP, 64 inputs at LEFT, and the non-linear value of QP (such as QP 2 . In some implementations, a sample (i.e., a pixel) that is adjacent to the top-left corner of the block  902  can also be used as an input to the concatenation layer  916 . In such a case, the concatenation layer  916  receives 898 inputs. 
     The CNN  900  includes three classifiers, namely classifiers  918 ,  920 , and  922 . Each of the classifiers  918 ,  920 ,  922  includes a set of classification layers and uses convolutions as further described below. 
     The classifier  918  infers (i.e., outputs) partition decisions for sub-blocks of size 16×16 of the block  902 . It is noted that the block  902  can be partitioned into 16 blocks (comprising 4×4 outputs), each block of size 16×16. As such, the classifier  918  reduces, to a size of 4×4, the feature maps (which are each of size 8×8) received from the concatenation layer  916 . 
     First, feature maps  919  are obtained from the feature maps received from the concatenation layer  916  by applying non-overlapping convolutions using 2×2 separable convolution filters to combine some of the feature maps into one, thereby resulting in 256 feature maps, each of size 4×4. 
     Secondly, a series of 1×1 convolutions are applied, successively, to gradually reduce the feature dimension size to 1. As such, 1×1×128 convolutions (where the number of filters is 128) are applied to the feature maps  919 , resulting in 4×4×128 feature maps, to which 1×1×64 convolutions (where the number of filters is 64) are applied, resulting in 4×4×64 feature maps, to which 1×1×32 convolutions are applied resulting in 4×4×32 feature maps, to which a 1×1×1 convolution is applied resulting in a 4×4×1 feature map, namely the feature map  925 . 
     For each 16×16 sub-block of the block  902 , the classifier  918  infers whether to split or not split the sub-block. As such, the classifier  918  outputs 16 decisions corresponding, respectively, to each of the 16×16 sub-blocks of the block  902 . The 16 decisions can be binary decisions. That is, the feature map  925  can be thought of as a matrix of binary decisions. For example, a zero (0) can correspond to a decision not to split a sub-block and a one (1) can correspond to a decision to split the sub-block. The order of the output of the classifier  918  can correspond to a raster scan order of the 16×16 sub-blocks of the block  902 . In another example, the decisions can correspond to probabilities (i.e., values that range from 0 to 1), or some other values, such as values that range from 0 to 100. When a decision is greater than a threshold that is appropriate for the range of the decision values (e.g., 0.9, 0.75%, 90, etc.), it can be considered to correspond to a binary decision of 1. 
     The classifier  920  infers (i.e., outputs) partition decisions for sub-blocks of size 32×32 of the block  902 . The classifier  920  receives the feature maps  919  and convolves each of the feature maps with 2×2 separable convolution filters to combine feature maps of the feature maps  919  into one, thereby resulting in feature maps  921 . It is noted that the block  902  can be partitioned into 2×2 blocks, each of size 32×32. As such, the classifier  920  reduces, to the size of 2×2, the feature maps  919  (which are each of size 4×4) through a series of non-overlapping convolutions using 1×1 filters to gradually reduce the feature dimension size to 1, as described above with respect to the feature maps  919 , thereby resulting in a feature map  927 . For each 32×32 sub-block of the block  902 , the classifier  920  infers whether to split or not split the sub-block. As such, the classifier  920  outputs 4 decisions corresponding, respectively, to each of the 32×32 sub-blocks of the block  902 . 
     The classifier  922  infers (i.e., outputs) partition decisions for the block  902  itself. The classifier  922  receives the feature maps  921  and convolves each of the feature maps with a 2×2 separable convolution filter resulting in feature maps  923 , which combines some of the feature maps of the features maps  921  into 1. It is noted that the block  902  can be partitioned into only one 1×1 block of size 64×64. As such, the classifier  922  reduces, to the size of 1×1, the feature maps  923  (which are each of size 1×1) through a series of non-overlapping convolutions using 1×1 filters to gradually reduce the feature dimension size to 1, as described above with respect to the feature maps  919 , thereby resulting in a feature map  929 . For the block  902 , the classifier  922  infers whether to split or not split the block  902 . As such, the classifier  922  outputs one decision corresponding to whether to split or not split the block  902  into four 32×32 sub-blocks. 
     Separable convolution filters of size 2×2 are described to obtain the feature maps  919 ,  921 , and  923  (of the classifiers  918 ,  920 , and  922 , respectively) in order to ultimately determine, for a block of size 64×64, 4×4 16×16 partitions (i.e., the feature map  925 ), 2×2 32×32 partitions (i.e., the feature map  927 ), and 1×1 64×64 partition (i.e., the feature map  929 ), respectively. However, in the general case, any convolutional filters of size 2 k  can be used as long the classifiers  918 ,  920 , and  922  determine, as described, 4×4 16×16 partitions (i.e., the feature map  925 ), 2×2 32×32 partitions (i.e., the feature map  927 ), and 1×1 64×64 partition (i.e., the feature map  929 ). 
     In the classifier  918 , the feature map  925 , which has a dimension of 4×4×1, is shown as being directly derived (i.e., there are no additional intervening convolution operations) from a feature maps  934 , which is of size 4×4×32. However, that need not be the case and any number of additional convolution operations can be used between the feature maps  934  and the feature map  925 . This is illustrated by a dot-dashed line  936 . The same can be applicable to the classifiers  920  and  922  with respect to the feature map  927  and the feature map  929 , respectively. 
     In an example, a parameter can be used as a configuration parameter (i.e., a threshold parameter) of the CNN. If the number of remaining features is less than or equal to the threshold parameter, then the number of features of the next layer can be set to 1. In the example of the CNN  900  of  FIG. 9 , the threshold parameter is set to 32. Because the number of features of the feature maps  934  is equal to the threshold parameter (i.e., 32), then the next layer corresponds to the layer that produces the feature map  925 , which has a feature dimension of 1. In an example, each of the classifiers can be configured with a different respective threshold parameter. In another example, all the classifiers can be configured to use the same threshold parameter. 
     In an example, the feature map dimensionality (i.e., the last dimension of a feature maps) within a classifier can be reduced using a feature reduction parameter F. For example, a classifier can reduce the number of channels according to the progression IncomingFeature, IncomingFeature/F, IncomingFeature/F 2 , . . . , 1, where IncomingFeature is the number of features that are initially received by the layer. In an example, each of the classifiers can be configured with a different respective feature reduction parameter. In another example, all the classifiers can be configured to use the same feature reduction parameter. 
     The classifier  918  is now used to illustrate the threshold parameter and the feature reduction parameter. With respect to the classifier  918 , IncomingFeature is 256 (as illustrated by the features maps  919 , which is of size 4×4×256), the feature reduction parameter F is 2, and the threshold parameter is 32. As such, the classifier  918  reduces the number of channels according to the progression 256, 256/2, 256/2 2 , 256/2 3 , and 1. That is, the classifier  918  reduces the number of channels according to the progression 256, 128, 64, 32, and 1. The classifier  918  does not include a layer where the number of channels is 256/2 4  (i.e., 16) because the threshold parameter 32 for the number of channels is reached at the progression 256/2 3  (i.e., 32). 
     The CNN  900  can be extended to infer partition decisions for other block sizes. For example, an encoder may allow the smallest partition to be of size 4×4. As such, to infer partition decisions for sub-blocks of size 8×8, a branch can be added to the feature extraction layers  903  such that each branch of the feature extraction layers  903  can generate feature maps, each of size 4×4, as inputs to the concatenation layer  916 . Additionally, a classifier can be added between the concatenation layer  916  and the classifier  918 . The added classifier infers (i.e., outputs) partition decisions for sub-blocks of size 8×8 of the block  902 . It is noted that the block  902  can be partitioned into 8×8 sub-blocks, each of size 8×8. The added classifier reduces, to a size of 8×8×1, the feature maps received from the concatenation layer  916  through a series of non-overlapping convolutions using 2×2 filters in this example. 
     The CNN  900  can be configured to infer partition decisions of a 128×128 block. For the 128×128 block, a CNN can be configured to include classifiers that determine, respectively, one (i.e., a 1×1 output matrix) 128×128 decision (i.e., one decision corresponding to whether the block is or is not to be split), four (i.e., a 2×2 output matrix) 64×64 decisions, 16 (i.e., a 4×4 output matrix) 32×32 decisions, and 64 (i.e., a 8×8 output matrix) 16×16 decisions. 
     In some implementations, the CNN  900  can include early termination features. For example, if the classifier  922  infers that the block  902  is not to be split, then processing through the classifiers  920  and  918  need not be continued. Similarly, if the classifier  920  infers that none of the 32×32 sub-blocks of the block  902  are to be split, then processing through the classifier  920  need not be continued. 
     The CNN  900  is one example of an all convolution architecture that is receptive field conformant. Receptive field conformance may be further explained with reference to  FIG. 11 .  FIG. 11  is an example  1100  of receptive fields according to implementations of this disclosure. The example  1100  includes an input  1102 . The example  1100  and the explanation herein are adapted from Dang Ha The Hien, “A guide to receptive field arithmetic for Convolutional Neural Networks,” April 2017, [retrieved on Aug. 6, 2018]. Retrieved from the Internet &lt;URL: https://medium.com/mlreview/a-guide-to-receptive-field-arithmetic-for-convolutional-neural-networks-e0f514068807&gt;. 
     The input  1102  can be a portion of an image for which it is desirable to extract features (e.g., a feature map). The input  1102  can be, for example, the block  700 , one of the blocks  700 - 1 ,  700 - 2 ,  700 - 3 , and  700 - 4 , or one of the block  702 - 1 ,  702 - 2 ,  702 - 3 , and  702 - 4 . The input  1102  is shown as having a size of 5×5 pixels. However, the size of the input  1102  is not pertinent to the description of the concept of a receptive field. 
     The example  1100  illustrates convolution operations that use filters/kernels of size k=3×3 (also referred to as a kernel size of 3), a padding size p=1×1, and a stride s=2×2 (also referred to as a stride value of 2). An example of a filter of size k=3×3 with a stride value of 3 is illustrated with respect to the filter  1004  of  FIG. 10 . Padding defines how the border of a sample is handled during a convolution. Further descriptions of the concepts of padding, stride, and kernel (i.e., filter) size are omitted herein as such concepts are well-known to a person skilled in the art. 
     The example  1100  illustrates a first feature map  1104  that is the result of convolving the input  1102  with a first filter and a second feature map  1106  that is the result of convolving the first feature map with a second filter. The first filter and the second filter can have different values. In machine learning, the values of the filters can be determined (e.g., learned) during the training phase. 
     A pixel  1108  (which may also be referred to as a feature) of the first feature map  1104  results from the convolution of pixels of the input  1102 . Such pixels are the receptive field of the pixel  1108 . Note that because the convolution uses padding, some of the pixels (e.g., the padding pixels) used for generating the pixel  1108  are outside of the input. The receptive field of the pixel  1108  is defined by a square whose corners are marked by black squares, such as a black square  1113 . Dashed lines, such as a dashed line  1112 , emanating from the corners of the pixel  1108  also illustrate the receptive field of the pixel  1108 . The end points of the dashed lines are the black squares. 
     A pixel  1110  (which may also be referred to as a feature) of the second feature map  1106  results from the convolution of pixels of the first feature map  1104 . Such pixels are the receptive field of the pixel  1110  in the first feature map  1104  and can be further projected onto the input  1102  to determine receptive field in the input  1102 . Note that because the convolution uses padding, some of the pixels (e.g., the padding pixels) used for generating the pixel  1110  are outside of the first feature map  1104 . The padding pixels of the first feature map  1104  are not shown so as to not clutter  FIG. 11 . The receptive field of the pixel  1110  in the input  1102  is defined by a square whose corners are marked by black circles, such as a black circle  1115 . Dot-dashed lines, such as a dot-dashed line  1114 , emanating from the corners of the pixel  1110  also illustrate the receptive field in the input  1102  of the pixel  1110 . The end points of the dot-dashed lines are the black circles. 
     The receptive field can play an important role in image analysis during video encoding. The receptive field of a series of convolution layers can be interpreted as the “region” of the image (e.g., a block, a superblock, a frame, or any other portion of an image) that each pixel (e.g., a feature) “sees” (e.g., influenced by, summarizes, etc.) when computing the pixel. Pixels at the initial input layer (e.g., the input  1102 ) become features (via a series of convolutions) for later layers (e.g., the second layer, which includes the second feature map  1106 ) of a CNN that will aid the CNN to analyze the initial input layer. 
     When using a CNN to analyze a model for determining a mode decision (e.g., a partitioning using quad-tree representations), it is desirable that each analysis region becomes confined to the boundaries of its quad-tree representation. That is, for example, it is desirable that features describing a region of an image, and which are used for inferring a mode decision of the region of the image, do not mix pixels from other regions of the image. For example and referring again to  FIG. 7 , features describing the blocks  70 - 2  and/or the blocks  702 - 1 ,  702 - 2 ,  702 - 3 , and  702 - 4  desirably do not include, in their respective fields, pixels from any of the blocks  700 - 1 ,  700 - 3 , or  700 - 4 . 
     The following four equations can be used to calculate the receptive field in each layer of a CNN. 
     
       
         
           
             
               
                 
                   
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     In the above, n out  is the number of output features in a layer. In the example  1100 , a first layer corresponds to (e.g., includes) the first feature map  1104  and a second layer corresponds to (e.g., includes) the second feature map  1106 . Further, n in  is the number of input features to the layer. For example, the number of input features to the second layer is the number of features in the first feature map  1104 , namely 9. The variables k, p, and s (collectively referred to as the convolution properties) are, respectively, the convolution kernel size, the convolution padding size, and the convolution stride size/value. 
     Equation (1) calculates the number of output features of a layer based on the number of input features and the convolution properties. Equation (2) calculates a distance (i.e., a jump j out ) between two adjacent features in the output feature map. Equation (3) calculates the receptive field size (i.e., r out ) of the output feature map, which is define as the area that is covered by k input features and the extra area that is covered by the receptive field of the input feature that is on the border. Equation (4) calculates the center position (i.e., start out ) of the receptive field of the first output feature (e.g., the pixel  1108  and the pixel  1110  correspond, respectively, to the first output feature in the first feature map  1104  and the second feature map  1106 ). 
     Having described the concept of receptive fields in more detail, characteristics shared by receptive field conforming CNN architectures according to the teachings herein are next described, along with variations. 
     As mentioned briefly above, the CNN architectures described herein are all-convolutional networks. That is, the feature extraction and the classification layers use convolution operations. In the feature extraction layers, non-overlapping convolution operations are performed on the input at each layer. At at least some of the feature extraction layers, the non-overlapping convolution operations are performed by setting the stride value the same as the kernel size. At least some of the kernel sizes can be even numbers (i.e., multiples of 2). 
     For example, in  FIG. 9 , each convolution layer in the feature extraction layers uses a 2×2 kernel, with the stride of 2. This non-overlapping convolution operation ensures that, at the last feature extraction layer (i.e., immediately before the concatenation layer  916 ), each one of the N×N channels (i.e., feature maps of size N×N), where N=8 in the example of  FIG. 9 , only sees (e.g., uses, is affected by, etc.) information from its corresponding sub-block of size (64/N)×(64/N), where 64×64, in the example of  FIG. 9 , corresponds to the size of the block  902  (i.e., the input block). In an example, N can be 2 k . 
     In the classification layers, instead of fully connected layers, convolution reduction with 1×1 kernels is performed until the number of desired outputs is reached. Convolutional layers are used in the classification layers. As such, the receptive fields are respected (e.g., preserved). 
     For example, in the CNN  900 , in order to infer partition decisions (i.e., by the classifier  918 ) for sub-blocks of size 16×16 (i.e., as the feature map  925 , which is the output of the classifier  918 ), non-overlapping convolution operations (i.e., between the concatenation layer  916  and the first layer of the classifiers  918 ) with a kernel size 2 are performed to reduce the number of channels from 8×8 (i.e., the size of each of the feature maps of the concatenation layer  916  as described above) to 4×4 (i.e., the size of each of the feature maps  919 ), and from then on apply kernel size 1×1 and gradually reduce the feature dimension size to 1 (i.e., the feature map  925 , which is of size 4×4×1). The output of the last classification layer is 4×4×1, which is the partition determination of the 16 sub-blocks of the input  902 . Each of the 16 sub-blocks is of size 16×16 pixels. 
     Similarly, the partition decision for each of the 32×32 sub-blocks can be inferred by the classifiers  920 ; and the partition of the 64×64 block can be inferred by the classifiers  922 . 
     As a person skilled in the art recognizes, a kernel of size 1×1 can be used to reduce the dimensionality of feature maps. For example, an input of size 4×4×32 (32 features maps, each of size 4×4), when convolved with one filter of size 1×1 would result in a feature map of size of 4×4×1. As such, a kernel of size 1×1 can be used to pool (e.g., combine) information from multiple feature maps. Further, a kernel of size 1×1, as used herein, does not mix values from different locations of the input. That is, continuing with the example above, when determining the value at location (x, y) of the feature map of size 4×4×1, only the 32 values at the location (x, y) of the each of the 32 maps of the feature maps of size 4×4×32 are used. As such, by using 1×1 convolutions, the receptive fields can be preserved (e.g., respected). 
     The inventive CNN architectures described herein include the combination of using non-overlapping kernel sizes with an all-convolutional network (for feature extraction and for classification) that respects receptive fields. This combination allows for a flexible CNN architecture of reduced size over using fully connected layers for classification. Further, the CNN architectures described herein can improve inferences over alternative structures. 
     As mentioned, the CNN architecture described herein is flexible in that the number of layers, the number of feature extraction branches, and the number of features used in each layer are all configurable. This allows for deployment flexibility of the model architecture for different application constraints. For example, a larger model such as the model of  FIG. 9 , can be used for applications with higher accuracy requirements and lower power/hardware footprint constraint. A smaller model, such as the examples described below in regards to  FIGS. 12-15 , can be used when accuracy is less important and/or a higher power/hardware footprint constraint exists. Whether using a relatively small or a relatively large model, a concatenation layer, such as the concatenation layer  916 , is optional. 
       FIG. 12  is a block diagram of a second example of a CNN  1200  for a mode decision according to implementations of this disclosure. Like the CNN  900 , the CNN  1200  includes inputs  1202 , feature extraction layers  1204 , and classifiers  1206 . Among other differences, the CNN  1200  of  FIG. 12  has fewer feature extraction layers, fewer classification layers in the classifiers, and fewer number of features in each layer than the CNN  900 . 
     In general, for a CNN herein, where an input has a size 64×64×1, partition decisions for 16×16 sub-blocks (i.e., a feature map of size 4×4×1 at the output) means that the multiplication of the kernels/strides can be at most 16. Partition decisions for 32×32 sub-blocks (i.e., a feature map of size 2×2×1 at the output) means that the multiplication of the kernels/strides can be at most 32. Finally, partition decisions for the 64×64 block (i.e., a feature map of size 1×1×1 at the output) means that the multiplication of the kernels/strides can be at most 64. This general principle in a receptive field conformant CNN can be seen with reference to  FIG. 9 . Namely, given the input  902 , where the end is the feature map  925 , the feature map  927 , or the feature map  929 , the multiplication where the kernel size equals the stride value has at most 64/4, 64/2, or 64/1, or respectively 16, 32, or 64 for partitions of 16×16, 32×32, or 64×64. Similar determinations may be used for partitioning 128×128, 8×8, or 4×4, for example, using 128×128, 8×8, or 4×4 inputs. 
     This general principle may also be applied where, like in  FIG. 12 , the inputs  1202  include a (e.g., luma) input block having a size 65×65×1, and the output comprises partition decisions for 16×16 sub-blocks (i.e., a feature map of size 4×4×1 at the output), partition decisions for 32×32 sub-blocks (i.e., a feature map of size 2×2×1 at the output), and partition decisions for the 64×64 block (i.e., a feature map of size 1×1×1 at the output). As described above with regard to  FIG. 9 , if a partitioning of a 64×64 block is to be determined, then a block of size 65×65×1 can be used as input to the CNN  1200 . That is, for example, the (e.g., left and top) neighboring pixels of the block for which a partitioning is to determined can be included in the input block to the CNN  1200 . In such a case, and in order to preserve the receptive field property as described above, a first filter (e.g., a first filter in each branch of the feature extraction layers) can be of size 2 k +1 and the stride can be 2 k . Stated more specifically, the multiplication of the kernels/strides as shown in  FIG. 12  (and in the variations described below) is such that the initial feature extraction layer  1210 - 0 ,  1212 - 0 ,  1214 - 0  in each branch  1208 -A,  1208 -B,  1208 -C of the feature classification layers  1204  has a kernel size of 2 k +1 and a stride value of 2 k.  Successive layers have kernel sizes equal to stride values such that 64/(2 k *product of remaining strides)=4, 2, or 1. The same determinations may be used for partitioning 128×128, 8×8, or 4×4 blocks, for example, using 129×129, 9×9, or 5×5 inputs. 
       FIG. 12  shows that an image block to be encoded is presented as inputs  1202  to the CNN  1200 . The image block can be a one color-plane block, such as the luminance block 65×65×1. While a superblock of size 64×64 is used to describe the CNN  1200 , the block can be of any size. 
     The feature extraction layers  1204  form three branches  1208 -A,  1208 -B,  1208 -C. The number of branches in the feature extraction layer can be configurable to include more or fewer branches. Each of the branches can include one or more of the feature extraction layers  1204 . At each layer, respective feature maps is extracted. In this example, the feature extraction layers comprise a number of branches equal to a number or cardinality of possible quad-tree partition decisions for the block, but this is not required. In any event, each of the branches comprises at least one of the feature extraction layers. 
     The branch  1208 -A extracts, in a first or initial layer  1210 - 0  of the branch  1208 -A, features corresponding to 8×8 blocks of the block. The branch  1208 -A convolves k filters with the block, each having a size 8×8. A stride that is equal to 2 k +1 is used. As a result, 16 feature maps, each of size 8×8, are extracted. The same convolution operation is performed at each first layer  1212 - 0 ,  1214 - 0  of the branches  1208 -B,  1208 -C. 
     At a second layer  1210 - 1  of the branch  1208 -A, each of the 16 feature maps of the initial layer  1210 - 0  is convolved using filters having a size equal to a stride value to extract 32 feature maps, each of size 4×4. At a third layer  1210 - 2  of the branch  1208 -A, each of the 32 feature maps of the second layer  1210 - 1  is convolved using filters having a size equal to a stride value to extract 32 feature maps, each of size 2×2. Finally, at a fourth layer  1210 - 3  of the branch  1208 -A, each of the 32 feature maps of the third layer  1210 - 2  is convolved using filters having a size equal to a stride value to extract 64 feature maps, each of size 1×1. 
     At a second layer  1212 - 1  of the branch  1208 -B, each of the 16 feature maps of the initial layer  1212 - 0  is convolved using filters having a size equal to a stride value to extract 32 feature maps, each of size 4×4. At a third layer  1212 - 2  of the branch  1208 -B, each of the 32 feature maps of the second layer  1212 - 1  is convolved using filters having a size equal to a stride value to extract 64 feature maps, each of size 2×2. 
     At a second layer  1214 - 1  of the branch  1208 -C, each of the 16 feature maps of the initial layer  1214 - 0  is convolved using filters having a size equal to a stride value to extract 64 feature maps, each of size 4×4. 
     The CNN  1200  includes three classifiers, namely classifiers  1220 -A,  1220 -B, and  1220 -C. Each of the classifiers  1220 -A,  1220 -B,  1220 -C includes one or more classification layers and uses convolutions as further described below. In this example, the multiple classifiers comprise a respective classifier corresponding to a respective branch of the branches of the feature extraction layers. The feature maps received by the initial classification layer of a respective classifier  1220 -A,  1220 -B, and  1220 -C may be configured to infer the partition decisions for sub-blocks of size (αS)×(αS) of the block comprising a convolution of N feature maps having respective feature dimension (N/2 β )×(N/2 β ), wherein β is an integer and β0, . . . , (the number of branches−1). 
     In the example of  FIG. 12 , each of the final layers of the feature extraction layers  1204  before the classifiers  1206 , namely the fourth layer  1210 - 3  of the first branch  1208 -A, the third layer  1212 - 1  of the second branch  1208 -B, and the second layer  1214 - 1  of the third branch, include N feature maps. The dimension of the N feature maps in each branch is equal to the number of possible mode decisions (e.g., the quad-tree partitions) for the block size associated with the corresponding classifier of the classifiers  1206 . That is, the classifier  1220 -A receives 64 feature maps of size 1×1 from the layer  1210 - 3 , and the classifier  1220 -A infers (i.e., outputs) one partition decision for the 64×64 input block. The classifier  1220 -B receives 64 feature maps of size 2×2 from the layer  1212 - 2 , and the classifier  1220 -B infers four partition decisions, one for each of the 32×32 sub-blocks. The classifier  1220 -C receives 64 feature maps of size 4×4 from the layer  1214 - 1 , and the classifier  1220 -C infers sixteen partition decisions, one for each of the 16×16 sub-blocks. The decisions can be binary decisions. That is, the feature maps output from each of the classifiers  1220 -A,  1220 -B,  1220 -C can be thought of as a matrix of binary decisions. For example, a zero (0) can correspond to a decision not to split a sub-block and a one (1) can correspond to a decision to split the sub-block. The order of the output of a classifier can correspond to a raster scan order of the sub-blocks of the input block. In another example, the decisions can correspond to probabilities (i.e., values that range from 0 to 1), or some other values, such as values that range from 0 to 100. When a decision is greater than a threshold that is appropriate for the range of the decision values (e.g., 0.9, 0.75%, 90, etc.), it can be considered to correspond to a binary decision of 1. 
     At the classifier  1220 -A, a series of convolutions, at least one of which is a 1×1 convolution, is applied, successively, to gradually reduce the feature dimension size to 1. At the first or initial classification layer  1222 - 0  of the classifier  1220 -A, convolutions are applied to the 64 feature maps from the extraction layer  1210 - 3 , resulting in 1×1×24 feature maps, to which convolutions are applied at the second classification layer  1222 - 1  of the classifier  1220 -A, resulting in 1×1×8 feature maps, to which convolutions are applied at the third classification layer  1222 - 2  of the classifier  1220 -A, resulting in a final 1×1×1 feature map. 
     At the classifier  1220 -B, a series of convolutions, at least one of which is a 1×1 convolution, is applied, successively, to gradually reduce the feature dimension size to 1. At the first or initial classification layer  1224 - 0  of the classifier  1220 -B, convolutions are applied to the 64 feature maps from the extraction layer  1212 - 2 , resulting in 2×2×24 feature maps, to which convolutions are applied at the second classification layer  1224 - 1  of the classifier  1220 -B, resulting in 2×2×8 feature maps, to which convolutions are applied at the third classification layer  1224 - 2  of the classifier  1220 -B, resulting in a final 2×2×1 feature map. 
     At the classifier  1220 -C, a series of convolutions, at least one of which is a 1×1 convolution, is applied, successively, to gradually reduce the feature dimension size to 1. At the first or initial classification layer  1226 - 0  of the classifier  1220 -C, convolutions are applied to the 64 feature maps from the extraction layer  1212 - 2 , resulting in 4×4×24 feature maps, to which convolutions are applied at the second classification layer  1226 - 1  of the classifier  1220 -C, resulting in 4×4×8 feature maps, to which convolutions are applied at the third classification layer  1226 - 2  of the classifier  1220 -C, resulting in a final 4×4×1 feature map. 
     In each of the classifiers  1206 , (e.g., non-overlapping) convolutional filters of any size can be used as long the classifiers  1206  determine, as described, 4×4 16×16 partitions, 2×2 32×32 partitions, and 1×1 64×64 partition. 
     Although not expressly shown in  FIG. 12 , a QP may be used as input to one or more of the feature extraction layers  1204  of the CNN  1200 . The QP can be input as a non-linear function f(QP). For example, the input function can be QP 2  or QP n . The variable n may be a real number. The variable n may be a non-zero (e.g., positive) integer with an absolute value greater than 1. 
       FIG. 12  shows a CNN  1200  where inputs  1202  extend from luminance-only (luma) data of the block to luma and chrominance (chroma) data of the block. For example, where the luma input has dimensions of 64×64, two chroma channels with a half resolution in each channel can be included with the inputs. The chroma channels may input in dimensions 32×32×2 in an arrangement such as that in  FIG. 9 . In this case, the first kernel size may equal the stride value. In  FIG. 12 , the chroma data is included in the inputs  1202  with dimensions of 33×33×2 by including the neighboring pixels (one row and one column in this example). In this example, the first kernel is 2 k +1 with a stride value of 2 k  as described with respect to the luma channel. In either implementation, the kernel and stride relationships are those described in regards to the luma channel to obtain 16-4×4 partitions, except that the multiplication of kernels/strides can be at most 8 because 32/4 is equal to 8. 
     More specifically, and referring to  FIG. 12 , the branch  1208 -A extracts, in a second kernel of the initial layer  1210 - 0 , features corresponding to 4×4 blocks of the chroma blocks. The branch  1208 -A convolves k filters with the chroma blocks, each having a size 4×4. A stride that is equal to 2 k +1 is used. As a result, 8 feature maps, each of size 4×4, are extracted. The same convolution operation is performed at each first layer  1212 - 0 ,  1214 - 0  of the branches  1208 -B,  1208 -C. Then, each of the 8 feature maps having the size 4×4 is convolved with the feature maps corresponding to the luma block for the additional feature extraction layers  1204 . 
     The inclusion of chroma data is optional but may improve the inference performance of a CNN over using luma data alone. For example, in some videos, content may not be well captured in the luma channel. By including the additional data in chroma channels, additional features are available for feature extraction, such as in the feature extraction layers  1204 , improving inference accuracy at the classifiers, such as the classifiers  1206 . 
     Although  FIG. 12  and its variations refer to luminance and chrominance data in the YUV color space, the CNN architectures described herein may be used with other color spaces, such as RGB or LUV, for example. 
     In these implementations, one column and one row of pixels is used for the (e.g., left and top) neighboring pixels in each of the luma and chroma inputs. In some implementations, more than one row/column represented by the value ν may be used. Accordingly, the input would be (64+ν)×(64+ν)×1 for a 64×64 luma block and (32+ν)×(32+ν)×2 for the two 32×32 chroma blocks, and the first kernel has a kernel size of 2 k +ν and a stride value of 2 k . It is worth noting that these examples of luma and chroma block sizes refer to 4:2:0 format. If another format is used, the relative block sizes between the luma and chroma samples will differ from these examples. 
     In addition to adjusting the number of features on each convolution layer, the architecture of  FIGS. 9 and 12 , and their variations described herein can be designed so that a global feature adjustment rate r may be applied across all layers for reducing/expanding the number of features. This feature adjustment rate can be a configurable hyper-parameter. After applying the feature adjustment rate, the number of features can be reduced/expended from n to n*r. 
     The flexible architecture described herein allows different classifiers to have distinct feature extraction as in the CNNs  900 ,  1200 , or share one or more feature extraction layers, such as shown in the example of  FIG. 13 .  FIG. 13  is a block diagram of a third example of a CNN  1300  for a mode decision according to implementations of this disclosure. The CNN  1300  of  FIG. 13  includes feature extraction layers  1304  and classifiers  1306 . The feature extraction layers  1304  include one or more common feature extraction layers  1308  and additional feature extraction layers  1310 ,  1312 ,  1314 . Specifically, the common feature extraction layers  1308  provide features maps to teach of additional 64×64 feature extraction layers  1310 , additional 32×32 feature extraction layers  1312 , and additional 16×16 feature extraction layers  1314 . In this way, the common feature extraction layers  1308  are shared by one or more of the classifiers  1306 . In the CNN  1300 , the common feature extraction layers  1308  are shared by each of the 64×64 classifier layers  1316 , the 32×32 classifier layers  1318 , and the 16×16 classifier layers  1320 . An advantage of not sharing common feature extraction layers is that such a CNN can maximize the inference accuracy through the design of specific extraction layers for each classifier. However, sharing common feature extraction layers between different classifiers has an advantage in that the sharing can effectively reduce model size. Sharing common feature extraction layers may be seen in additional detail in the example of  FIG. 14 . 
       FIG. 14  is a block diagram of a fourth example of a CNN  1400  for a mode decision according to implementations of this disclosure. The CNN  1400  of  FIG. 14  modifies the architecture of the CNN  1200  by forcing the three classifiers  1206  to share some feature extraction layers. The classifiers  1206  (i.e., the layers of the classifiers  1206 ) in the CNN  1400  are unchanged from those in the CNN  1200  of  FIG. 12 . The inputs  1402  comprise luma data in the form of input 65×65×1 and chroma data in the form of inputs 33×33×2. Each of the three classifiers  1220 -A,  1220 -B,  1220 -C share first/initial feature extraction layers  1410 ,  1412  of sizes 8×8×16 and 4×4×8, respectively. Subsequent layers branch therefrom. The classifiers  1220 -A,  1220 -B for 64×64 and 32×32 blocks, respectively, share a subsequent feature classification layer  1414  having a size 4×4×32. As indicated more generally in  FIG. 13 , the CNN  1400  also includes additional feature extraction layers that are specific to each of the classifiers  1206 . For example, the classifier  1220 -C for 16×16 blocks receives input through an additional classification layer  1416  having a size 4×4×32. Similarly, the classifier  1220 -B for 32×32 blocks receives input through an additional classification layer  1418  having a size 2×2×64. The classifier  1220 -A for 64×64 blocks receives input through two additional classification layers  1420  and  1422 , respectively having sizes 2×2×32 and 1×1×64. As mentioned, sharing common feature extraction layers can reduce model size. In addition, sharing common feature extraction layers can increase model robustness to noise. 
     The mode decision inferred by the CNNs described above for a block (e.g., a superblock) is the block partitioning. However, existing video codecs also use brute force approaches to decide the optimal prediction modes and transform unit sizes for compression of the block. These mode decisions are similar to the mode decision of block partitioning in the sense that they all use features based on the raw image content and a quantization value of the block. Further, the same receptive-field-conforming principle should be observed for the decisions of prediction mode (PM) and transform unit (TU) size and/or type on the block/sub-block level. Accordingly, the teachings herein may be extended to include these mode decisions. 
       FIG. 15  is a block diagram of a fifth example of a CNN  1500  for a mode decision according to implementations of this disclosure. The CNN  1500  extends the architecture previously described to infer prediction (e.g., intra prediction) modes and transform unit sizes. As can be seen in  FIG. 15 , the classifiers for PM and TU at each sub-block size can share common feature extraction layers  1502  with the classifiers for the partition decisions, such as those described with regard to  FIGS. 9 and 12 . More specifically, the CNN  1500  indicates that the classifiers for each of the partition decisions for 64×64 blocks, 32×32 blocks, and 16×16 blocks comprises separate classifier layers 0 to m, where m is a positive integer. The layers conform to the rules described above with regard to the multiplication of the kernel sizes and stride values, and to the receptive field conformance. In this example, the classifiers for PM and TU at each sub-block size also share the first/initial classification layers  1504 ,  1506 ,  1508 , respectively with its corresponding block partition classifiers. The initial classification layers  1504 ,  1506 ,  1508  provide respective inputs (e.g., feature maps) to an extra classifier for the PM and TU at each sub-block size, respectively classifiers  1510 ,  1512 ,  1514 . The classifiers  1510 ,  1512 ,  1514  may each comprise one or more classifier layers. This arrangement may be desirable because block partitioning and TU/PM determination can use similar image features for inferring decisions. More desirably, mode decisions for TU/PM have their own classification layers to implement classification rules that are unique to those mode decisions. 
     For simplicity, the CNNs  900 ,  1200 ,  1300 ,  1400 ,  1500  are described for determining a partitioning of a 64×64 block from a 64×64 partition down to whether each 16×16 sub-block should be further partitioned into 8×8 blocks. However, the disclosure herein is not so limited. A CNN architecture according to implementations of the disclosure can be generalized as follows. 
     A CNN for determining a mode decision in video coding, where the block is of size N×N (e.g., 64×64, 128×128) and where a smallest partition determined by the CNN is of size S×S (e.g., 4×4, 8×8), can include feature extraction layers, optionally a concatenation layer, and classifiers. The classifiers include all-convolutional layers. Other values of N and S can be possible. In some examples, N can be 32, 64, or 128, and S can be 4, 8, or 16. 
     When a concatenation layer is included as in the CNN  900 , the layer may receive, from the feature extraction layers, feature maps of the block. Each feature map may be of a defined size, such as 8×8. 
     Whether or not a concatenation layer is included, each of the classifiers includes one or more classification layers. Each classification layer receives feature maps having a respective feature dimension. For example, and referring to  FIG. 9 , the classifier  918  includes 5 classification layers (illustrated by the 5 squares representing the feature maps of each layer), the classifier  920  includes 4 classification layers, and the classifier  922  includes 3 classification layers. For example, and referring to  FIGS. 12 and 14 , each of the classifiers  1220 -A,  1220 -B,  1220 -C includes 3 classification layers (illustrated by the 3 squares representing the feature maps of each layer). 
     Each of the classifiers can be configured to infer a partition decision for sub-blocks of a specific size. That is, a classifier can be configured to infer partition decisions for sub-blocks of size (αS)×(αS) of the block, where α is a power of 2 and α=2, . . . , N/S. As such, when N=64 and S=8, α can have any of the values 2, 4, and 8. For example, with respect to the classifiers  918 ,  1220 -C, α=2 and the classifiers  918 ,  1220 -C infer partition decisions for blocks of size (2×8)×(2×8)=16×16; with respect to the classifiers  920 ,  1220 -B, α=4 and the classifiers  920 ,  1220 -B infer partition decisions for blocks of size (4×8)×(4×8)=32×32; and with respect to the classifiers  922 ,  1220 -A, α=8 and the classifiers  1022 ,  1220 -A infer partition decisions for blocks of size (8×8)×(8×8)=64×64. 
     A classifier can infer partition decisions for sub-blocks of size (αS)×(αS) of the block by instructions that include applying, at each successive classification layer of the classification layers, a kernel of size 1×1 to reduce the respective feature dimension at least in half; and outputting by a last layer of the classification layers an output corresponding to a N/(αS)×N/(αS)×1 output map. Using the classifier  922  as an example where α=8, the classifier  922  convolves the feature maps  923  with 32 kernels, each of size 1×1, thereby resulting in feature maps  931 , which have dimensions of 1×1×32. The feature map  929  (which is of size N/(αS)×N/(αS)×1=64/(8×8)×64/(8×8)1=1×1×1) corresponds to the decision whether the block of size N×N should be split or not. As can be seen from  FIGS. 12 and 14 , a classifier may convolve the feature maps of a previous layer with a different number of kernels to reduce the respective feature dimension by more than half (here, by 2 3 ). 
     In the example of  FIG. 9 , a first classifier  918 , can receive the first feature maps as an output of a final feature extraction layer of the feature extraction layers through the concatenation layer (e.g., the concatenation layer  916 ), wherein a first non-overlapping convolution operation using a first 2×2 kernel is applied to reduce the first feature maps to a size of (S/2)×(S/2). For example, as described with respect to the classifier  918 , the first layer of the classifier  918  receives the 8×8 feature maps from the concatenation layer  916  and reduces them to the size of 4×4 (i.e., the feature maps  919 ). In the example of the classifier  918 , the feature maps  919  is shown as having a dimension of 256. However, that need not be the case so long as the dimension of the last layer of each of the classifiers is N/(αS)×N/(αS)×1 in this example. The CNN may also include a second classifier  922  that infers partition decisions for sub-blocks of size (βS)×(βS). In an example, β=8. The second classifier can receive third feature maps, each of size M×M, from a third classifier. The third classifier can be the classifier  920 . As such, M=2 and the third feature maps can be the features maps  921 . The second classifier can apply a second non-overlapping convolution operation using a second 2×2 kernel to reduce the third feature maps to a size of (M/2)×(M/2). For example, the classifier  922  receives the features maps  921  from the classifier  920  and applies a second non-overlapping convolution operation using a second 2×2 kernel to generate the feature maps  923 . 
     In contrast, in the CNN  1200  and its variations that do not include a concatenation layer, an initial classification layer of each classifier receives the feature maps as an output of a final feature extraction layer of the feature extraction layers, directly from the final feature extraction layer. 
     The feature maps received at an initial classification layer include specific feature dimensionalities for illustrative purposes. The number or cardinality of feature maps received at the first layer of each classifier can be configurable. Kernel sizes that obey the rule kernel=stride size=(2 k , 2 k ), for some k, can be used in some examples. 
     In a case where ν neighboring rows and ν neighboring columns are included in input to the first feature extraction layer(s), such that the input block is of size (64+ν)×(64×ν), (128+ν×128+ν), etc., a kernel of size (2 k +ν, 2 k +ν) and a stride size of (2 k , 2 k ) can be used to propagate the ν left/top information and observe (e.g., preserve) the perception field. 
     While outputs of the classification layers are described as matrices of the form B×B×1 (e.g., 4×4×1, 2×2×1, or 1×1×1), it is to be understood that a classification layer outputs B*B=B 2  values, such that each of the outputs B 2  corresponds to a Cartesian location in the matrix. Each of the output values corresponds a block location and can be a value indicating whether a sub-block at that location should be partitioned or not. For example, a value of 0 can indicate that the sub-block is not to be partitioned and a value of 1 can indicate that the sub-block is to be partitioned. Other values are, of course, possible. 
     The first/initial feature extraction layer can apply a non-overlapping convolution filter to the block to generate feature maps of the block for the next feature extraction layer. Each successive feature extraction layer after the initial feature extraction layer can apply a non-overlapping convolution filter to the feature maps from the previous layer. A non-overlapping convolution operation is performed on input at at least one of the feature extraction layers by setting a stride value equal to a kernel size. 
     For example, a first feature extraction layer can apply a (N/S)×(N/S) non-overlapping convolution filter to the block to generate a first subset (e.g., cardinality) of the feature maps of the block. This can be illustrated by example where the feature extraction layer  903 -A applies a (64/8)×(64/8)=8×8 non-overlapping convolutional filter to the block  902  to generate the feature maps  904 . A second feature extraction layer can apply a M×M non-overlapping convolutional filter to the block to generate maps each of size (N/M)×(N/M), where M is less than S, is greater than 1, and is a power of 2; and successively apply non-overlapping 2×2 convolutional filters to the maps to generate a second subset (e.g., cardinality) of the feature maps of the block. The feature extraction layers  903 -B and  903 -C can be examples of the second feature extraction layer. 
     As described above, a non-linear value of a quantization parameter (QP) can be used as an input to the CNN. In  FIG. 9 , the non-linear value of QP is shown as an input to the concatenation layer  916 . However, that need not be the case and the non-linear value of the QP can be used as an input to other layers of the CNN. For example, the non-linear value of the QP can be used as the input to at least one of the classification layers. 
     A CNN that is configured as described above can be used by an encoder, such as the encoder  400  of  FIG. 4 , to infer mode decisions that include block partitioning and optionally other mode decisions. As such, the mode decisions are not derived by brute force methods as are known in the art. In an example, a CNN described herein can be used by the intra/inter-prediction stage  402 . Subsequent to inferring the block partitioning, an encoder can predict the blocks of the partitions using known prediction techniques, such as inter-prediction, intra-prediction, other techniques, or a combination thereof, or can obtain the prediction mode from the CNN. The resulting residual may be encoded as described with regard to  FIG. 4 , optionally where the transform type/size is also provided by the CNN. 
       FIG. 16  is a flowchart of a process  1600  for encoding, by an encoder, an image block according to implementations of this disclosure. The process  1600  trains, using input data, a machine-learning model to infer one or more mode decisions. The process  1600  then uses the trained machine-learning model to infer a mode decision for an image block, which is to be encoded. In an example, the mode decision can be a quad-tree partition decision of the image block. The image block can be a block of an image (e.g., a video frame) that is encoded using intra-prediction. In another example, the mode decision can be a partition that includes partitions described with respect to  FIG. 17  described below. As further described below, some of the partitions of  FIG. 17  include square and non-square sub-partition; and each of the square sub-partitions can be further partitioned according to one of the partitions of  FIG. 17 . 
     At  1602 , the process  1600  trains the machine-learning (ML) model. The ML model can be trained using a training data  1612 . Each training datum of the training data  1612  can include a video block that was encoded by traditional encoding methods (e.g., by an encoder such as described with respect to  FIGS. 4 and 6-8 ); a QP used by the encoder; zero or more additional inputs corresponding to inputs used by the encoder in determining the mode decision (e.g., block partitioning and optionally prediction mode and/or transform unit size) for encoding the video block; and the resulting mode decision determined by the encoder. In the training phase, parameters of the ML model are generated such that, for at least some of the training data, the ML model can infer, for a training datum, the resulting mode decision of the training datum for a set of inputs that includes the video block, the value corresponding to a quantization parameter, and zero or more additional inputs of the training datum. 
     As described above, the value corresponding to the QP has a non-linear relation to the QP. That is, the value is derived from the QP based on a non-linear function of the QP. In an example, the non-linear function can be an exponential function, a quadratic function, or some other non-linear function of the QP. For example, the non-linear function ƒ(Q)=c QP , where c is a constant, can be used. In an example, c=1/3. The non-linear function ƒ(QP)=QP α , where is a integer that is not equal to 0 or 1 (i.e., α≠#0 and α≠#1), can be used. In an example, α=2. In the general case, the non-linear function is of a same type as a function used by the encoder for determining a multiplier used in a rate-distortion calculation, as described above. 
     In the case that the ML model is used to infer a relationship between blocks and respective quad-tree partitioning of the blocks, the resulting mode decision determined by the encoder can be indicative of the quad-tree partition of the training block of the training datum. Many indications (e.g., representations) of the quad-tree partition are possible. In an example, a vector (e.g., sequence) of binary flags, as described with respect to the quadtree  704  can be used. 
     In the case that the ML model is used to infer a relationship between blocks that are intra-predicted and respective partitioning of the blocks, the zero or more additional inputs corresponding to inputs used by the second encoder in determining the mode decision for encoding the video block can include at least some of the samples (i.e., first samples) of the top neighboring block, at least some of the samples (i.e., second samples) of the left neighboring block of the input block, at least some of the samples of the top-left neighboring block, or a combination thereof. For brevity, and without loss of generality, the top-left neighboring block can be considered to be part of either the top neighboring block or the left neighboring block. As such, in an example, the first samples or the second samples can be considered to include samples from the top-left neighboring block. 
     During the training phase (i.e., at  1602 ), the ML model learns (e.g., trains, builds, derives, etc.) a mapping (i.e., a function) that accepts, as input, a block and a non-linear value of a quantization parameter (e.g., QP 2  as shown in  FIG. 9 ) and outputs at least a partitioning of the block. 
     During the training phase, and so that the learned function can be as useful as possible, it is preferable that the ML model be trained using a large range of input blocks and a large range of possible QP values, such as QP values that are used in representative of real-world applications. 
     With respect to input blocks, if the training data set includes only dark (e.g., pixels having low intensity values) training blocks, then the ML model may well learn how to determine a mode decision for dark blocks but provide unreliable output when presented with non-dark blocks during the inference phase. If the encoder uses a discrete set of the QP values, then it is preferable that each of the QP values is well represented in the training data set. For example, if the QP value can vary from 0 to 1, then it is preferable that the training data include varying QP values in the range 0 to 1. If a QP value is not used (e.g., missed QP value) in the training data, then the ML model may misbehave (e.g., provide erroneous output) when the missed QP value is presented to the ML model during the inference phase. In another example, if a missed QP value (i.e., a QP value that is not used during the training phase) is used during the inference phase, the missed QP can be interpolated from QP values that are used during the training phase and the interpolated QP value can then be used during the inference phase. 
     The ML model can then be used by the process  1600  during an inference phase. The inference phase includes the operations  1604  and  1606 . A separation  1610  indicates that the training phase and the inference phase can be separated in time. As such, the inferencing phase can be performed by a first encoder and the training data  1612  can be generated by a second encoder. In an example, the first encoder and the second encoder are the same encoder. That is, the training data  1612  can be generated by the same encoder that performs the inference phase. In either case, the inference phase uses a machine-learning model that is trained as described with respect to  1602 . 
     At  1604 , inputs are presented to ML module. That is, the inputs are presented to a module that incorporates, includes, executes, implements, and the like the ML model. The inputs include the image block and optionally a non-linear function of a value corresponding to a QP. As described above, the first value is derived (i.e., results) from the non-linear function using the QP as input to the non-linear function. The inputs can also include additional inputs, as described above with respect to the zero or more additional inputs. 
     At  1606 , the process  1600  obtains one or more mode decisions from the machine-learning model. In an example, the process  1600  obtains the mode decisions as described with respect to  FIGS. 9 and 12-15 . That is, for example, the CNN can provide an output that is indicative of a quad-tree partition of an image block. 
     At  1608 , the process  1600  encodes the image block using the one or more mode decisions. That is, and continuing with the example of inferring a block partitioning, for each of the sub-blocks (i.e., according to the output that is indicative of a quad-tree partition), the process  1700  can intra-predict (or inter-predict) the block as described with respect to the intra/inter-prediction stage  402  of  FIG. 4 , and consistent with the description of  FIG. 4 , ultimately entropy encode, as described with respect to the entropy encoding stage  408 , the image block in a compressed bitstream, such as the bitstream  420  of  FIG. 4 . 
     An encoder that uses a machine-learning model, such as one of the ML models described herein, to infer mode decision parameters for image block, can encode the mode decisions in a compressed bitstream, such as the bitstream  420  of  FIG. 4 . As mentioned above, the image block can be a superblock and the mode decision can be indicative of a quad-tree partition of the superblock. 
     As such, a decoder, such as the decoder  500  of  FIG. 5 , can decode the image block using the mode decisions received in the compressed bitstream. The process of decoding an image block can include receiving, in a compressed bitstream, such as the compressed bitstream  420  of  FIG. 5 , an indication of a partitioning of the image block into sub-blocks; and decoding the image block using the indication of the partitioning and optionally the prediction mode and transform unit size (or type) of the image block. 
     As is known in the art, a quad-tree, such as described with respect to  FIG. 7 , can be output in a compressed bitstream, such as the bitstream  420  of  FIG. 4 . A decoder, such as the decoder  500  of  FIG. 5 , can decode from the compressed bitstream the quad-tree in the process of decoding a block (i.e., a superblock). The quad-tree can be determined (e.g., inferred) in the encoder using a CNN that is configured as described above and output in the compressed bitstream. As such, a decoder decodes, from the compressed bitstream, the quad-tree, which was inferred by the CNN that is configured as described with respect to any of  FIG. 9, 12, 13, 14 , or  15 . 
     While inferring a quad-tree partition of a block is described, a CNN according to implementations of this disclosure can be used to infer non-square partitions that may or may not be represented by a quad-tree. That is, for example, a non-square partition can correspond to an internal node of the quad-tree having a number of children that is greater than or equal to two children.  FIG. 17  is an example  1700  of non-square partitions of a block. Some encoders may partition a superblock, such as a super-block of size 64×64, 128×128, or any other size, of a square sub-block of the superblock, into one of the partitions of the example  1700 . 
     A partition type  1702  (which may be referred to as the PARTITION_VERT_A) splits an N×N coding block into two horizontally adjacent square blocks, each of size N/2×N/2, and a rectangular prediction unit of size N×N/2. A partition type  1708  (which may be referred to as the PARTITION_VERT_B) splits an N×N coding block into a rectangular prediction unit of size N×N/2 and two horizontally adjacent square blocks, each of size N/2×N/2. 
     A partition type  1704  (which may be referred to as the PARTITION_HORZ_A) splits an N×N coding block into two vertically adjacent square blocks, each of size N/2×N/2, and a rectangular prediction unit of size N/2×N. A partition type  1710  (which may be referred to as the PARTITION_HORZ_B) splits an N×N coding block into a rectangular prediction unit of size N/2×N and two vertically adjacent square blocks, each of size N/2×N/2. 
     A partition type  1706  (which may be referred to as the PARTITION_VERT_4) splits an N×N coding block into four vertically adjacent rectangular blocks, each of size N×N/4. A partition type  1712  (which may be referred to as the PARTITION_HORZ_4) splits an N×N coding block into four horizontally adjacent rectangular blocks, each of size N/4×N. 
     As is known, other partition types can be used by a codec. The example  1700  illustrates four partition types that may be available at an encoder. A partition type  1714  (also referred to herein as the PARTITION_SPLIT partition type and partition-split partition type) splits an N×N coding block into four equally sized square sub-blocks. For example, if the coding block  1714  is of size N×N, then each of the four sub-blocks of the PARTITION_SPLIT partition type, such as a sub-block  1716 A, is of size N/4×N/4. 
     A partition type  1716  (also referred to herein as the PARTITION_VERT partition type) splits the coding block into two adjacent rectangular prediction units, each of size N×N/2. A partition type  1718  (also referred to herein as the PARTITION_HORZ partition type) splits the coding block into two adjacent rectangular prediction units, each of size N/2×N. A partition type  1720  (also referred to herein as the PARTITION_NONE partition type and partition-none partition type) uses one prediction unit for the coding block such that the prediction unit has the same size (i.e., N×N) as the coding block. 
     The partition types  1714 - 1720  are referred to herein as basic partition types and the partitions  1702 - 1712  are referred to herein as extended partition types. 
     A partition can be represented by a tree. A tree can be represented by a vector. Let P denote the set of all valid partitions (or, equivalently, the respective representations of the partitions). Accordingly, a CNN can be trained to infer a mapping into the set P. Configuring a CNN to infer the partitions described with respect to  FIG. 17  includes defining an appropriate set P and using appropriate training data. 
     Assuming that there are N possible outcomes, then there are N*M possible decisions (in an example, M=21 and N=4) for simplicity, and each p(n, j) can be combined by a softmax function, so that sum(n in range(N)) p(n, j)=1 for some any j. 
     For example, in the case of VP9, which uses a coding unit size of 64×64 and the four basic partition types, for quad-tree partitions only, there are 21 decisions corresponding to one 64×64, four 32×32, and 16 16×16 decisions (i.e., 1+4+16=21 decisions). In a case where a CNN is used to also determine non-quad-tree partitions, then there are 21*4=84 possible decisions, where 21 corresponds to the quad-tree partitions and four corresponds to the basic partition types; namely, PARTITION_SPLIT, PARTITION_VERT, PARTITION_HORZ, and PARTITION_NONE. 
     For example, in the case of AV1, which uses a coding unit size of 128×128 and the basic and extended partitions types (for a total of 10 partition types), for quad-tree partitions only, there are 85 decisions (corresponding to one 128×128, four 64×64, 16 32×32, and 64 16×16 decisions) per partition type. In a case where a CNN is used to also determine non-quad-tree partitions, then there are 850 decisions (corresponding to 85 decisions multiplied by 10 partition types=850 decisions). 
     More generally, non-square partitions can be composed by smaller square groups. Accordingly, the techniques described herein may be generalized to non-square partitions such as shown in  FIG. 17 . 
     For simplicity of explanation, the processes depicted and described herein are shown as a series of blocks, steps, or operations. However, the blocks, steps, or operations in accordance with this disclosure can occur in various orders and/or concurrently. Additionally, other steps or operations not presented and described herein may be used. Furthermore, not all illustrated steps or operations may be required to implement a technique in accordance with the disclosed subject matter. 
     The aspects of encoding and decoding described above illustrate some encoding and decoding techniques. However, it is to be understood that “encoding” and “decoding,” as those terms are used in the claims, could mean compression, decompression, transformation, or any other processing or change of data. 
     The words “example” or “implementation” are used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “example” or “implementation” is not necessarily to be construed as being preferred or advantageous over other aspects or designs. Rather, use of the words “example” or “implementation” 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 clearly indicated otherwise by the context, “X includes A or B” is intended to mean any of the natural inclusive permutations thereof. 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 the context to be directed to a singular form. Moreover, use of the term “an implementation” or “one implementation” throughout is not intended to mean the same embodiment or implementation unless described as such. 
     Implementations of the transmitting station  102  and/or the receiving station  106  (and the algorithms, methods, instructions, etc., stored thereon and/or executed thereby, including by the encoder  400  and the decoder  500 ) 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  102  and the receiving station  106  do not necessarily have to be implemented in the same manner. 
     Further, in one aspect, for example, the transmitting station  102  or the receiving station  106  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, which can contain other hardware for carrying out any of the methods, algorithms, or instructions described herein, can be utilized. 
     The transmitting station  102  and the receiving station  106  can, for example, be implemented on computers in a video conferencing system. Alternatively, the transmitting station  102  can be implemented on a server, and the receiving station  106  can be implemented on a device separate from the server, such as a handheld communications device. In this instance, the transmitting station  102 , using an encoder  400 , can encode content 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  102 . Other transmitting station  102  and receiving station  106  implementation schemes are available. For example, the receiving station  106  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 of the present disclosure 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 semiconductor device. Other suitable mediums are also available. 
     The above-described embodiments, implementations, and aspects have been described in order to allow easy understanding of the present disclosure and do not limit the present disclosure. On the contrary, the disclosure is intended to cover various modifications and equivalent arrangements included within the scope of the appended claims, which scope is to be accorded the broadest interpretation as is permitted under the law so as to encompass all such modifications and equivalent arrangements.