Patent Publication Number: US-2021176486-A1

Title: Methods and apparatuses for motion compensation

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present disclosure claims priority to U.S. Provisional Application No. 62/945,393, filed on Dec. 9, 2019, which is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The present disclosure generally relates to video processing, and more particularly, to methods and apparatuses for performing motion compensation. 
     BACKGROUND 
     A video is a set of static pictures (or “frames”) capturing the visual information. To reduce the storage memory and the transmission bandwidth, a video can be compressed before storage or transmission and decompressed before display. The compression process is usually referred to as encoding and the decompression process is usually referred to as decoding. There are various video coding formats which use standardized video coding technologies, most commonly based on prediction, transform, quantization, entropy coding and in-loop filtering. The video coding standards, such as the High Efficiency Video Coding (HEVC/H.265) standard, the Versatile Video Coding (VVC/H.266) standard AVS standards, specifying the specific video coding formats, are developed by standardization organizations. With more and more advanced video coding technologies being adopted in the video standards, the coding efficiency of the new video coding standards get higher and higher. 
     SUMMARY OF THE DISCLOSURE 
     In some embodiments, an exemplary video processing method includes: determining intermediate interpolation coefficients of an interpolation filter based on a position of an integer sample and a fractional position of a fractional sample; determining integer interpolation coefficients of the interpolation filter, comprising rounding each of the intermediate interpolation coefficients to an integer; and applying the interpolation filter on a picture to perform motion compensation prediction. 
     In some embodiments, an exemplary video processing apparatus includes at least one memory for storing instructions and at least one processor. The at least one processor is configured to execute the instructions to cause the apparatus to perform: determining intermediate interpolation coefficients of an interpolation filter based on a position of an integer sample and a fractional position of a fractional sample; determining integer interpolation coefficients of the interpolation filter, comprising rounding each of the intermediate interpolation coefficients to an integer; and applying the interpolation filter on a picture to perform motion compensation prediction. 
     In some embodiments, an exemplary non-transitory computer readable storage medium stores a set of instructions. The set of instructions are executable by one or more processing devices to cause a video processing apparatus to perform: determining intermediate interpolation coefficients of an interpolation filter based on a position of an integer sample and a fractional position of a fractional sample; determining integer interpolation coefficients of the interpolation filter, comprising rounding each of the intermediate interpolation coefficients to an integer; and applying the interpolation filter on a picture to perform motion compensation prediction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments and various aspects of the present disclosure are illustrated in the following detailed description and the accompanying figures. Various features shown in the figures are not drawn to scale. 
         FIG. 1  is a schematic diagram illustrating structures of an example video sequence, according to some embodiments of the present disclosure. 
         FIG. 2A  illustrates a schematic diagram of an exemplary encoding process of a hybrid video coding system, consistent with embodiments of the disclosure. 
         FIG. 2B  illustrates a schematic diagram of another exemplary encoding process of a hybrid video coding system, consistent with embodiments of the disclosure. 
         FIG. 3A  illustrates a schematic diagram of an exemplary decoding process of a hybrid video coding system, consistent with embodiments of the disclosure. 
         FIG. 3B  illustrates a schematic diagram of another exemplary decoding process of a hybrid video coding system, consistent with embodiments of the disclosure. 
         FIG. 4  illustrates a block diagram of an exemplary apparatus for encoding or decoding a video, according to some embodiments of the present disclosure. 
         FIG. 5  illustrates a schematic diagram of an exemplary frequency response of a low-pass filter, according to some embodiments of the present disclosure. 
         FIG. 6  illustrates an exemplary Table 1 showing exemplary luma interpolation filter in High Efficiency Video Coding (HEVC), according to some embodiments of the present disclosure. 
         FIG. 7  illustrates an exemplary Table 2 showing exemplary chroma interpolation filter in HEVC, according to some embodiments of the present disclosure. 
         FIG. 8  illustrates an exemplary Table 3 showing exemplary luma interpolation filter in Versatile Video Coding (VVC), according to some embodiments of the present disclosure. 
         FIG. 9  illustrates an exemplary Table 4 showing exemplary chroma interpolation filter in VVC, according to some embodiments of the present disclosure. 
         FIG. 10  illustrates an exemplary Table 5 showing exemplary luma interpolation filter for 4×4 motion compensation, according to some embodiments of the present disclosure. 
         FIG. 11  illustrates an exemplary Table 6 showing exemplary values of smoothing parameter, according to some embodiments of the present disclosure. 
         FIG. 12  illustrates an exemplary Table 7 showing exemplary 6-tap real-number luma interpolation filter, according to some embodiments of the present disclosure. 
         FIG. 13  illustrates an exemplary Table 8 showing exemplary 6-tap integer-number luma interpolation filter, according to some embodiments of the present disclosure. 
         FIG. 14  illustrates an exemplary Table 9 showing exemplary 6-tap integer-number luma interpolation filter, according to some embodiments of the present disclosure. 
         FIG. 15  illustrates an exemplary Table 10 showing exemplary 6-tap real-number luma interpolation filter without a smoothing window function, according to some embodiments of the present disclosure. 
         FIG. 16  illustrates an exemplary Table 11 showing exemplary 6-tap integer-number luma interpolation filter without a smoothing window function, according to some embodiments of the present disclosure. 
         FIG. 17  illustrates an exemplary Table 12 showing exemplary 6-tap real-number luma interpolation filter, according to some embodiments of the present disclosure. 
         FIG. 18  illustrates an exemplary Table 13 showing exemplary 6-tap real-number luma interpolation filter, according to some embodiments of the present disclosure. 
         FIG. 19  illustrates an exemplary Table 14 showing exemplary 6-tap integer-number luma interpolation filter, according to some embodiments of the present disclosure. 
         FIG. 20  illustrates an exemplary Table 15 showing exemplary values of a smoothing parameter, according to some embodiments of the present disclosure. 
         FIG. 21  illustrates an exemplary Table 16 showing exemplary 6-tap real-number luma interpolation filter, according to some embodiments of the present disclosure. 
         FIG. 22  illustrates an exemplary Table 17 showing exemplary 6-tap integer-number luma interpolation filter, according to some embodiments of the present disclosure. 
         FIG. 23  illustrates exemplary frequency responses of a tested filter and a reference filter 6-tap integer-number luma interpolation filter, according to some embodiments of the present disclosure. 
         FIG. 24  illustrates an exemplary Table 18 showing exemplary response values corresponding to cutoff points for each fractional position, according to some embodiments of the present disclosure. 
         FIG. 25  illustrates an exemplary Table 19 showing exemplary 6-tap integer-number luma interpolation filter, according to some embodiments of the present disclosure. 
         FIG. 26  illustrates a flowchart of an exemplary video processing method, according to some embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. The following description refers to the accompanying drawings in which the same numbers in different drawings represent the same or similar elements unless otherwise represented. The implementations set forth in the following description of exemplary embodiments do not represent all implementations consistent with the present disclosure. Instead, they are merely examples of apparatuses and methods consistent with aspects related to the present disclosure as recited in the appended claims. Particular aspects of the present disclosure are described in greater detail below. The terms and definitions provided herein control, if in conflict with terms and/or definitions incorporated by reference. 
     The Joint Video Experts Team (JVET) of the ITU-T Video Coding Expert Group (ITU-T VCEG) and the ISO/IEC Moving Picture Expert Group (ISO/IEC MPEG) is currently developing the Versatile Video Coding (VVC/H.266) standard. The VVC standard is aimed at doubling the compression efficiency of its predecessor, the High Efficiency Video Coding (HEVC/H.265) standard. In other words, VVC&#39;s goal is to achieve the same subjective quality as HEVC/H.265 using half the bandwidth. 
     In order to achieve the same subjective quality as HEVC/H.265 using half the bandwidth, the JVET has been developing technologies beyond HEVC using the joint exploration model (JEM) reference software. As coding technologies were incorporated into the JEM, the JEM achieved substantially higher coding performance than HEVC. 
     The VVC standard has been developed recent, and continues to include more coding technologies that provide better compression performance. VVC is based on the same hybrid video coding system that has been used in modern video compression standards such as HEVC, H.264/AVC, MPEG2, H.263, etc. 
     A video is a set of static pictures (or “frames”) arranged in a temporal sequence to store visual information. A video capture device (e.g., a camera) can be used to capture and store those pictures in a temporal sequence, and a video playback device (e.g., a television, a computer, a smartphone, a tablet computer, a video player, or any end-user terminal with a function of display) can be used to display such pictures in the temporal sequence. Also, in some applications, a video capturing device can transmit the captured video to the video playback device (e.g., a computer with a monitor) in real-time, such as for surveillance, conferencing, or live broadcasting. 
     For reducing the storage space and the transmission bandwidth needed by such applications, the video can be compressed before storage and transmission and decompressed before the display. The compression and decompression can be implemented by software executed by a processor (e.g., a processor of a generic computer) or specialized hardware. The module for compression is generally referred to as an “encoder,” and the module for decompression is generally referred to as a “decoder.” The encoder and decoder can be collectively referred to as a “codec.” The encoder and decoder can be implemented as any of a variety of suitable hardware, software, or a combination thereof. For example, the hardware implementation of the encoder and decoder can include circuitry, such as one or more microprocessors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), discrete logic, or any combinations thereof. The software implementation of the encoder and decoder can include program codes, computer-executable instructions, firmware, or any suitable computer-implemented algorithm or process fixed in a computer-readable medium. Video compression and decompression can be implemented by various algorithms or standards, such as MPEG-1, MPEG-2, MPEG-4, H.26x series, or the like. In some applications, the codec can decompress the video from a first coding standard and re-compress the decompressed video using a second coding standard, in which case the codec can be referred to as a “transcoder.” 
     The video encoding process can identify and keep useful information that can be used to reconstruct a picture and disregard unimportant information for the reconstruction. If the disregarded, unimportant information cannot be fully reconstructed, such an encoding process can be referred to as “lossy.” Otherwise, it can be referred to as “lossless.” Most encoding processes are lossy, which is a tradeoff to reduce the needed storage space and the transmission bandwidth. 
     The useful information of a picture being encoded (referred to as a “current picture”) include changes with respect to a reference picture (e.g., a picture previously encoded and reconstructed). Such changes can include position changes, luminosity changes, or color changes of the pixels, among which the position changes are mostly concerned. Position changes of a group of pixels that represent an object can reflect the motion of the object between the reference picture and the current picture. 
     A picture coded without referencing another picture (i.e., it is its own reference picture) is referred to as an “I-picture.” A picture coded using a previous picture as a reference picture is referred to as a “P-picture.” A picture coded using both a previous picture and a future picture as reference pictures (i.e., the reference is “bi-directional”) is referred to as a “B-picture.” 
       FIG. 1  illustrates structures of an example video sequence  100 , according to some embodiments of the present disclosure. Video sequence  100  can be a live video or a video having been captured and archived. Video  100  can be a real-life video, a computer-generated video (e.g., computer game video), or a combination thereof (e.g., a real-life video with augmented-reality effects). Video sequence  100  can be inputted from a video capture device (e.g., a camera), a video archive (e.g., a video file stored in a storage device) containing previously captured video, or a video feed interface (e.g., a video broadcast transceiver) to receive video from a video content provider. 
     As shown in  FIG. 1 , video sequence  100  can include a series of pictures arranged temporally along a timeline, including pictures  102 ,  104 ,  106 , and  108 . Pictures  102 - 106  are continuous, and there are more pictures between pictures  106  and  108 . In  FIG. 1 , picture  102  is an I-picture, the reference picture of which is picture  102  itself. Picture  104  is a P-picture, the reference picture of which is picture  102 , as indicated by the arrow. Picture  106  is a B-picture, the reference pictures of which are pictures  104  and  108 , as indicated by the arrows. In some embodiments, the reference picture of a picture (e.g., picture  104 ) can be not immediately preceding or following the picture. For example, the reference picture of picture  104  can be a picture preceding picture  102 . It should be noted that the reference pictures of pictures  102 - 106  are only examples, and the present disclosure does not limit embodiments of the reference pictures as the examples shown in  FIG. 1 . 
     Typically, video codecs do not encode or decode an entire picture at one time due to the computing complexity of such tasks. Rather, they can split the picture into basic segments, and encode or decode the picture segment by segment. Such basic segments are referred to as basic processing units (“BPUs”) in the present disclosure. For example, structure  110  in  FIG. 1  shows an example structure of a picture of video sequence  100  (e.g., any of pictures  102 - 108 ). In structure  110 , a picture is divided into 4×4 basic processing units, the boundaries of which are shown as dash lines. In some embodiments, the basic processing units can be referred to as “macroblocks” in some video coding standards (e.g., MPEG family, H.261, H.263, or H.264/AVC), or as “coding tree units” (“CTUs”) in some other video coding standards (e.g., H.265/HEVC or H.266/VVC). The basic processing units can have variable sizes in a picture, such as  128   x  128, 64-64, 32×32, 16×16, 4×8, 16×32, or any arbitrary shape and size of pixels. The sizes and shapes of the basic processing units can be selected for a picture based on the balance of coding efficiency and levels of details to be kept in the basic processing unit. 
     The basic processing units can be logical units, which can include a group of different types of video data stored in a computer memory (e.g., in a video frame buffer). For example, a basic processing unit of a color picture can include a luma component (Y) representing achromatic brightness information, one or more chroma components (e.g., Cb and Cr) representing color information, and associated syntax elements, in which the luma and chroma components can have the same size of the basic processing unit. The luma and chroma components can be referred to as “coding tree blocks” (“CTBs”) in some video coding standards (e.g., H.265/HEVC or H.266/VVC). Any operation performed to a basic processing unit can be repeatedly performed to each of its luma and chroma components. 
     Video coding has multiple stages of operations, examples of which are shown in  FIGS. 2A-2B  and  FIGS. 3A-3B . For each stage, the size of the basic processing units can still be too large for processing, and thus can be further divided into segments referred to as “basic processing sub-units” in the present disclosure. In some embodiments, the basic processing sub-units can be referred to as “blocks” in some video coding standards (e.g., MPEG family, H.261, H.263, or H.264/AVC), or as “coding units” (“CUs”) in some other video coding standards (e.g., H.265/HEVC or H.266/VVC). A basic processing sub-unit can have the same or smaller size than the basic processing unit. Similar to the basic processing units, basic processing sub-units are also logical units, which can include a group of different types of video data (e.g., Y, Cb, Cr, and associated syntax elements) stored in a computer memory (e.g., in a video frame buffer). Any operation performed to a basic processing sub-unit can be repeatedly performed to each of its luma and chroma components. It should be noted that such division can be performed to further levels depending on processing needs. It should also be noted that different stages can divide the basic processing units using different schemes. 
     For example, at a mode decision stage (an example of which is shown in  FIG. 2B ), the encoder can decide what prediction mode (e.g., intra-picture prediction or inter-picture prediction) to use for a basic processing unit, which can be too large to make such a decision. The encoder can split the basic processing unit into multiple basic processing sub-units (e.g., CUs as in H.265/HEVC or H.266/VVC), and decide a prediction type for each individual basic processing sub-unit. 
     For another example, at a prediction stage (an example of which is shown in  FIGS. 2A-2B ), the encoder can perform prediction operation at the level of basic processing sub-units (e.g., CUs). However, in some cases, a basic processing sub-unit can still be too large to process. The encoder can further split the basic processing sub-unit into smaller segments (e.g., referred to as “prediction blocks” or “PBs” in H.265/HEVC or H.266/VVC), at the level of which the prediction operation can be performed. 
     For another example, at a transform stage (an example of which is shown in  FIGS. 2A-2B ), the encoder can perform a transform operation for residual basic processing sub-units (e.g., CUs). However, in some cases, a basic processing sub-unit can still be too large to process. The encoder can further split the basic processing sub-unit into smaller segments (e.g., referred to as “transform blocks” or “TBs” in H.265/HEVC or H.266/VVC), at the level of which the transform operation can be performed. It should be noted that the division schemes of the same basic processing sub-unit can be different at the prediction stage and the transform stage. For example, in H.265/HEVC or H.266/VVC, the prediction blocks and transform blocks of the same CU can have different sizes and numbers. 
     In structure  110  of  FIG. 1 , basic processing unit  112  is further divided into 3×3 basic processing sub-units, the boundaries of which are shown as dotted lines. Different basic processing units of the same picture can be divided into basic processing sub-units in different schemes. 
     In some implementations, to provide the capability of parallel processing and error resilience to video encoding and decoding, a picture can be divided into regions for processing, such that, for a region of the picture, the encoding or decoding process can depend on no information from any other region of the picture. In other words, each region of the picture can be processed independently. By doing so, the codec can process different regions of a picture in parallel, thus increasing the coding efficiency. Also, when data of a region is corrupted in the processing or lost in network transmission, the codec can correctly encode or decode other regions of the same picture without reliance on the corrupted or lost data, thus providing the capability of error resilience. In some video coding standards, a picture can be divided into different types of regions. For example, H.265/HEVC and H.266/VVC provide two types of regions: “slices” and “tiles.” It should also be noted that different pictures of video sequence  100  can have different partition schemes for dividing a picture into regions. 
     For example, in  FIG. 1 , structure  110  is divided into three regions  114 ,  116 , and  118 , the boundaries of which are shown as solid lines inside structure  110 . Region  114  includes four basic processing units. Each of regions  116  and  118  includes six basic processing units. It should be noted that the basic processing units, basic processing sub-units, and regions of structure  110  in  FIG. 1  are only examples, and the present disclosure does not limit embodiments thereof. 
       FIG. 2A  illustrates a schematic diagram of an example encoding process  200 A, consistent with embodiments of the disclosure. For example, the encoding process  200 A can be performed by an encoder. As shown in  FIG. 2A , the encoder can encode video sequence  202  into video bitstream  228  according to process  200 A. Similar to video sequence  100  in  FIG. 1 , video sequence  202  can include a set of pictures (referred to as “original pictures”) arranged in a temporal order. Similar to structure  110  in  FIG. 1 , each original picture of video sequence  202  can be divided by the encoder into basic processing units, basic processing sub-units, or regions for processing. In some embodiments, the encoder can perform process  200 A at the level of basic processing units for each original picture of video sequence  202 . For example, the encoder can perform process  200 A in an iterative manner, in which the encoder can encode a basic processing unit in one iteration of process  200 A. In some embodiments, the encoder can perform process  200 A in parallel for regions (e.g., regions  114 - 118 ) of each original picture of video sequence  202 . 
     In  FIG. 2A , the encoder can feed a basic processing unit (referred to as an “original BPU”) of an original picture of video sequence  202  to prediction stage  204  to generate prediction data  206  and predicted BPU  208 . The encoder can subtract predicted BPU  208  from the original BPU to generate residual BPU  210 . The encoder can feed residual BPU  210  to transform stage  212  and quantization stage  214  to generate quantized transform coefficients  216 . The encoder can feed prediction data  206  and quantized transform coefficients  216  to binary coding stage  226  to generate video bitstream  228 . Components  202 ,  204 ,  206 ,  208 ,  210 ,  212 ,  214 ,  216 ,  226 , and  228  can be referred to as a “forward path.” During process  200 A, after quantization stage  214 , the encoder can feed quantized transform coefficients  216  to inverse quantization stage  218  and inverse transform stage  220  to generate reconstructed residual BPU  222 . The encoder can add reconstructed residual BPU  222  to predicted BPU  208  to generate prediction reference  224 , which is used in prediction stage  204  for the next iteration of process  200 A. Components  218 ,  220 ,  222 , and  224  of process  200 A can be referred to as a “reconstruction path.” The reconstruction path can be used to ensure that both the encoder and the decoder use the same reference data for prediction. 
     The encoder can perform process  200 A iteratively to encode each original BPU of the original picture (in the forward path) and generate predicted reference  224  for encoding the next original BPU of the original picture (in the reconstruction path). After encoding all original BPUs of the original picture, the encoder can proceed to encode the next picture in video sequence  202 . 
     Referring to process  200 A, the encoder can receive video sequence  202  generated by a video capturing device (e.g., a camera). The term “receive” used herein can refer to receiving, inputting, acquiring, retrieving, obtaining, reading, accessing, or any action in any manner for inputting data. 
     At prediction stage  204 , at a current iteration, the encoder can receive an original BPU and prediction reference  224 , and perform a prediction operation to generate prediction data  206  and predicted BPU  208 . Prediction reference  224  can be generated from the reconstruction path of the previous iteration of process  200 A. The purpose of prediction stage  204  is to reduce information redundancy by extracting prediction data  206  that can be used to reconstruct the original BPU as predicted BPU  208  from prediction data  206  and prediction reference  224 . 
     Ideally, predicted BPU  208  can be identical to the original BPU. However, due to non-ideal prediction and reconstruction operations, predicted BPU  208  is generally slightly different from the original BPU. For recording such differences, after generating predicted BPU  208 , the encoder can subtract it from the original BPU to generate residual BPU  210 . For example, the encoder can subtract values (e.g., greyscale values or RGB values) of pixels of predicted BPU  208  from values of corresponding pixels of the original BPU. Each pixel of residual BPU  210  can have a residual value as a result of such subtraction between the corresponding pixels of the original BPU and predicted BPU  208 . Compared with the original BPU, prediction data  206  and residual BPU  210  can have fewer bits, but they can be used to reconstruct the original BPU without significant quality deterioration. Thus, the original BPU is compressed. 
     To further compress residual BPU  210 , at transform stage  212 , the encoder can reduce spatial redundancy of residual BPU  210  by decomposing it into a set of two-dimensional “base patterns,” each base pattern being associated with a “transform coefficient.” The base patterns can have the same size (e.g., the size of residual BPU  210 ). Each base pattern can represent a variation frequency (e.g., frequency of brightness variation) component of residual BPU  210 . None of the base patterns can be reproduced from any combinations (e.g., linear combinations) of any other base patterns. In other words, the decomposition can decompose variations of residual BPU  210  into a frequency domain. Such a decomposition is analogous to a discrete Fourier transform of a function, in which the base patterns are analogous to the base functions (e.g., trigonometry functions) of the discrete Fourier transform, and the transform coefficients are analogous to the coefficients associated with the base functions. 
     Different transform algorithms can use different base patterns. Various transform algorithms can be used at transform stage  212 , such as, for example, a discrete cosine transform, a discrete sine transform, or the like. The transform at transform stage  212  is invertible. That is, the encoder can restore residual BPU  210  by an inverse operation of the transform (referred to as an “inverse transform”). For example, to restore a pixel of residual BPU  210 , the inverse transform can be multiplying values of corresponding pixels of the base patterns by respective associated coefficients and adding the products to produce a weighted sum. For a video coding standard, both the encoder and decoder can use the same transform algorithm (thus the same base patterns). Thus, the encoder can record only the transform coefficients, from which the decoder can reconstruct residual BPU  210  without receiving the base patterns from the encoder. Compared with residual BPU  210 , the transform coefficients can have fewer bits, but they can be used to reconstruct residual BPU  210  without significant quality deterioration. Thus, residual BPU  210  is further compressed. 
     The encoder can further compress the transform coefficients at quantization stage  214 . In the transform process, different base patterns can represent different variation frequencies (e.g., brightness variation frequencies). Because human eyes are generally better at recognizing low-frequency variation, the encoder can disregard information of high-frequency variation without causing significant quality deterioration in decoding. For example, at quantization stage  214 , the encoder can generate quantized transform coefficients  216  by dividing each transform coefficient by an integer value (referred to as a “quantization parameter”) and rounding the quotient to its nearest integer. After such an operation, some transform coefficients of the high-frequency base patterns can be converted to zero, and the transform coefficients of the low-frequency base patterns can be converted to smaller integers. The encoder can disregard the zero-value quantized transform coefficients  216 , by which the transform coefficients are further compressed. The quantization process is also invertible, in which quantized transform coefficients  216  can be reconstructed to the transform coefficients in an inverse operation of the quantization (referred to as “inverse quantization”). 
     Because the encoder disregards the remainders of such divisions in the rounding operation, quantization stage  214  can be lossy. Typically, quantization stage  214  can contribute the most information loss in process  200 A. The larger the information loss is, the fewer bits the quantized transform coefficients  216  can need. For obtaining different levels of information loss, the encoder can use different values of the quantization parameter or any other parameter of the quantization process. 
     At binary coding stage  226 , the encoder can encode prediction data  206  and quantized transform coefficients  216  using a binary coding technique, such as, for example, entropy coding, variable length coding, arithmetic coding, Huffman coding, context-adaptive binary arithmetic coding, or any other lossless or lossy compression algorithm. In some embodiments, besides prediction data  206  and quantized transform coefficients  216 , the encoder can encode other information at binary coding stage  226 , such as, for example, a prediction mode used at prediction stage  204 , parameters of the prediction operation, a transform type at transform stage  212 , parameters of the quantization process (e.g., quantization parameters), an encoder control parameter (e.g., a bitrate control parameter), or the like. The encoder can use the output data of binary coding stage  226  to generate video bitstream  228 . In some embodiments, video bitstream  228  can be further packetized for network transmission. 
     Referring to the reconstruction path of process  200 A, at inverse quantization stage  218 , the encoder can perform inverse quantization on quantized transform coefficients  216  to generate reconstructed transform coefficients. At inverse transform stage  220 , the encoder can generate reconstructed residual BPU  222  based on the reconstructed transform coefficients. The encoder can add reconstructed residual BPU  222  to predicted BPU  208  to generate prediction reference  224  that is to be used in the next iteration of process  200 A. 
     It should be noted that other variations of the process  200 A can be used to encode video sequence  202 . In some embodiments, stages of process  200 A can be performed by the encoder in different orders. In some embodiments, one or more stages of process  200 A can be combined into a single stage. In some embodiments, a single stage of process  200 A can be divided into multiple stages. For example, transform stage  212  and quantization stage  214  can be combined into a single stage. In some embodiments, process  200 A can include additional stages. In some embodiments, process  200 A can omit one or more stages in  FIG. 2A . 
       FIG. 2B  illustrates a schematic diagram of another example encoding process  200 B, consistent with embodiments of the disclosure. Process  200 B can be modified from process  200 A. For example, process  200 B can be used by an encoder conforming to a hybrid video coding standard (e.g., H.26x series). Compared with process  200 A, the forward path of process  200 B additionally includes mode decision stage  230  and divides prediction stage  204  into spatial prediction stage  2042  and temporal prediction stage  2044 . The reconstruction path of process  200 B additionally includes loop filter stage  232  and buffer  234 . 
     Generally, prediction techniques can be categorized into two types: spatial prediction and temporal prediction. Spatial prediction (e.g., an intra-picture prediction or “intra prediction”) can use pixels from one or more already coded neighboring BPUs in the same picture to predict the current BPU. That is, prediction reference  224  in the spatial prediction can include the neighboring BPUs. The spatial prediction can reduce the inherent spatial redundancy of the picture. Temporal prediction (e.g., an inter-picture prediction or “inter prediction”) can use regions from one or more already coded pictures to predict the current BPU. That is, prediction reference  224  in the temporal prediction can include the coded pictures. The temporal prediction can reduce the inherent temporal redundancy of the pictures. 
     Referring to process  200 B, in the forward path, the encoder performs the prediction operation at spatial prediction stage  2042  and temporal prediction stage  2044 . For example, at spatial prediction stage  2042 , the encoder can perform the intra prediction. For an original BPU of a picture being encoded, prediction reference  224  can include one or more neighboring BPUs that have been encoded (in the forward path) and reconstructed (in the reconstructed path) in the same picture. The encoder can generate predicted BPU  208  by extrapolating the neighboring BPUs. The extrapolation technique can include, for example, a linear extrapolation or interpolation, a polynomial extrapolation or interpolation, or the like. In some embodiments, the encoder can perform the extrapolation at the pixel level, such as by extrapolating values of corresponding pixels for each pixel of predicted BPU  208 . The neighboring BPUs used for extrapolation can be located with respect to the original BPU from various directions, such as in a vertical direction (e.g., on top of the original BPU), a horizontal direction (e.g., to the left of the original BPU), a diagonal direction (e.g., to the down-left, down-right, up-left, or up-right of the original BPU), or any direction defined in the used video coding standard. For the intra prediction, prediction data  206  can include, for example, locations (e.g., coordinates) of the used neighboring BPUs, sizes of the used neighboring BPUs, parameters of the extrapolation, a direction of the used neighboring BPUs with respect to the original BPU, or the like. 
     For another example, at temporal prediction stage  2044 , the encoder can perform the inter prediction. For an original BPU of a current picture, prediction reference  224  can include one or more pictures (referred to as “reference pictures”) that have been encoded (in the forward path) and reconstructed (in the reconstructed path). In some embodiments, a reference picture can be encoded and reconstructed BPU by BPU. For example, the encoder can add reconstructed residual BPU  222  to predicted BPU  208  to generate a reconstructed BPU. When all reconstructed BPUs of the same picture are generated, the encoder can generate a reconstructed picture as a reference picture. The encoder can perform an operation of “motion estimation” to search for a matching region in a scope (referred to as a “search window”) of the reference picture. The location of the search window in the reference picture can be determined based on the location of the original BPU in the current picture. For example, the search window can be centered at a location having the same coordinates in the reference picture as the original BPU in the current picture and can be extended out for a predetermined distance. When the encoder identifies (e.g., by using a pel-recursive algorithm, a block-matching algorithm, or the like) a region similar to the original BPU in the search window, the encoder can determine such a region as the matching region. The matching region can have different dimensions (e.g., being smaller than, equal to, larger than, or in a different shape) from the original BPU. Because the reference picture and the current picture are temporally separated in the timeline (e.g., as shown in  FIG. 1 ), it can be deemed that the matching region “moves” to the location of the original BPU as time goes by. The encoder can record the direction and distance of such a motion as a “motion vector.” When multiple reference pictures are used (e.g., as picture  106  in  FIG. 1 ), the encoder can search for a matching region and determine its associated motion vector for each reference picture. In some embodiments, the encoder can assign weights to pixel values of the matching regions of respective matching reference pictures. 
     The motion estimation can be used to identify various types of motions, such as, for example, translations, rotations, zooming, or the like. For inter prediction, prediction data  206  can include, for example, locations (e.g., coordinates) of the matching region, the motion vectors associated with the matching region, the number of reference pictures, weights associated with the reference pictures, or the like. 
     For generating predicted BPU  208 , the encoder can perform an operation of “motion compensation.” The motion compensation can be used to reconstruct predicted BPU  208  based on prediction data  206  (e.g., the motion vector) and prediction reference  224 . For example, the encoder can move the matching region of the reference picture according to the motion vector, in which the encoder can predict the original BPU of the current picture. When multiple reference pictures are used (e.g., as picture  106  in  FIG. 1 ), the encoder can move the matching regions of the reference pictures according to the respective motion vectors and average pixel values of the matching regions. In some embodiments, if the encoder has assigned weights to pixel values of the matching regions of respective matching reference pictures, the encoder can add a weighted sum of the pixel values of the moved matching regions. 
     In some embodiments, the inter prediction can be unidirectional or bidirectional. Unidirectional inter predictions can use one or more reference pictures in the same temporal direction with respect to the current picture. For example, picture  104  in  FIG. 1  is a unidirectional inter-predicted picture, in which the reference picture (i.e., picture  102 ) precedes picture  104 . Bidirectional inter predictions can use one or more reference pictures at both temporal directions with respect to the current picture. For example, picture  106  in  FIG. 1  is a bidirectional inter-predicted picture, in which the reference pictures (i.e., pictures  104  and  108 ) are at both temporal directions with respect to picture  104 . 
     Still referring to the forward path of process  200 B, after spatial prediction  2042  and temporal prediction stage  2044 , at mode decision stage  230 , the encoder can select a prediction mode (e.g., one of the intra prediction or the inter prediction) for the current iteration of process  200 B. For example, the encoder can perform a rate-distortion optimization technique, in which the encoder can select a prediction mode to minimize a value of a cost function depending on a bit rate of a candidate prediction mode and distortion of the reconstructed reference picture under the candidate prediction mode. Depending on the selected prediction mode, the encoder can generate the corresponding predicted BPU  208  and predicted data  206 . 
     In the reconstruction path of process  200 B, if intra prediction mode has been selected in the forward path, after generating prediction reference  224  (e.g., the current BPU that has been encoded and reconstructed in the current picture), the encoder can directly feed prediction reference  224  to spatial prediction stage  2042  for later usage (e.g., for extrapolation of a next BPU of the current picture). If the inter prediction mode has been selected in the forward path, after generating prediction reference  224  (e.g., the current picture in which all BPUs have been encoded and reconstructed), the encoder can feed prediction reference  224  to loop filter stage  232 , at which the encoder can apply a loop filter to prediction reference  224  to reduce or eliminate distortion (e.g., blocking artifacts) introduced by the inter prediction. The encoder can apply various loop filter techniques at loop filter stage  232 , such as, for example, deblocking, sample adaptive offsets, adaptive loop filters, or the like. The loop-filtered reference picture can be stored in buffer  234  (or “decoded picture buffer”) for later use (e.g., to be used as an inter-prediction reference picture for a future picture of video sequence  202 ). The encoder can store one or more reference pictures in buffer  234  to be used at temporal prediction stage  2044 . In some embodiments, the encoder can encode parameters of the loop filter (e.g., a loop filter strength) at binary coding stage  226 , along with quantized transform coefficients  216 , prediction data  206 , and other information. 
       FIG. 3A  illustrates a schematic diagram of an example decoding process  300 A, consistent with embodiments of the disclosure. Process  300 A can be a decompression process corresponding to the compression process  200 A in  FIG. 2A . In some embodiments, process  300 A can be similar to the reconstruction path of process  200 A. A decoder can decode video bitstream  228  into video stream  304  according to process  300 A. Video stream  304  can be very similar to video sequence  202 . However, due to the information loss in the compression and decompression process (e.g., quantization stage  214  in  FIGS. 2A-2B ), generally, video stream  304  is not identical to video sequence  202 . Similar to processes  200 A and  200 B in  FIGS. 2A-2B , the decoder can perform process  300 A at the level of basic processing units (BPUs) for each picture encoded in video bitstream  228 . For example, the decoder can perform process  300 A in an iterative manner, in which the decoder can decode a basic processing unit in one iteration of process  300 A. In some embodiments, the decoder can perform process  300 A in parallel for regions (e.g., regions  114 - 118 ) of each picture encoded in video bitstream  228 . 
     In  FIG. 3A , the decoder can feed a portion of video bitstream  228  associated with a basic processing unit (referred to as an “encoded BPU”) of an encoded picture to binary decoding stage  302 . At binary decoding stage  302 , the decoder can decode the portion into prediction data  206  and quantized transform coefficients  216 . The decoder can feed quantized transform coefficients  216  to inverse quantization stage  218  and inverse transform stage  220  to generate reconstructed residual BPU  222 . The decoder can feed prediction data  206  to prediction stage  204  to generate predicted BPU  208 . The decoder can add reconstructed residual BPU  222  to predicted BPU  208  to generate predicted reference  224 . In some embodiments, predicted reference  224  can be stored in a buffer (e.g., a decoded picture buffer in a computer memory). The decoder can feed predicted reference  224  to prediction stage  204  for performing a prediction operation in the next iteration of process  300 A. 
     The decoder can perform process  300 A iteratively to decode each encoded BPU of the encoded picture and generate predicted reference  224  for encoding the next encoded BPU of the encoded picture. After decoding all encoded BPUs of the encoded picture, the decoder can output the picture to video stream  304  for display and proceed to decode the next encoded picture in video bitstream  228 . 
     At binary decoding stage  302 , the decoder can perform an inverse operation of the binary coding technique used by the encoder (e.g., entropy coding, variable length coding, arithmetic coding, Huffman coding, context-adaptive binary arithmetic coding, or any other lossless compression algorithm). In some embodiments, besides prediction data  206  and quantized transform coefficients  216 , the decoder can decode other information at binary decoding stage  302 , such as, for example, a prediction mode, parameters of the prediction operation, a transform type, parameters of the quantization process (e.g., quantization parameters), an encoder control parameter (e.g., a bitrate control parameter), or the like. In some embodiments, if video bitstream  228  is transmitted over a network in packets, the decoder can depacketize video bitstream  228  before feeding it to binary decoding stage  302 . 
       FIG. 3B  illustrates a schematic diagram of another example decoding process  300 B, consistent with embodiments of the disclosure. Process  300 B can be modified from process  300 A. For example, process  300 B can be used by a decoder conforming to a hybrid video coding standard (e.g., H.26x series). Compared with process  300 A, process  300 B additionally divides prediction stage  204  into spatial prediction stage  2042  and temporal prediction stage  2044 , and additionally includes loop filter stage  232  and buffer  234 . 
     In process  300 B, for an encoded basic processing unit (referred to as a “current BPU”) of an encoded picture (referred to as a “current picture”) that is being decoded, prediction data  206  decoded from binary decoding stage  302  by the decoder can include various types of data, depending on what prediction mode was used to encode the current BPU by the encoder. For example, if intra prediction was used by the encoder to encode the current BPU, prediction data  206  can include a prediction mode indicator (e.g., a flag value) indicative of the intra prediction, parameters of the intra prediction operation, or the like. The parameters of the intra prediction operation can include, for example, locations (e.g., coordinates) of one or more neighboring BPUs used as a reference, sizes of the neighboring BPUs, parameters of extrapolation, a direction of the neighboring BPUs with respect to the original BPU, or the like. For another example, if inter prediction was used by the encoder to encode the current BPU, prediction data  206  can include a prediction mode indicator (e.g., a flag value) indicative of the inter prediction, parameters of the inter prediction operation, or the like. The parameters of the inter prediction operation can include, for example, the number of reference pictures associated with the current BPU, weights respectively associated with the reference pictures, locations (e.g., coordinates) of one or more matching regions in the respective reference pictures, one or more motion vectors respectively associated with the matching regions, or the like. 
     Based on the prediction mode indicator, the decoder can decide whether to perform a spatial prediction (e.g., the intra prediction) at spatial prediction stage  2042  or a temporal prediction (e.g., the inter prediction) at temporal prediction stage  2044 . The details of performing such spatial prediction or temporal prediction are described in  FIG. 2B  and will not be repeated hereinafter. After performing such spatial prediction or temporal prediction, the decoder can generate predicted BPU  208 . The decoder can add predicted BPU  208  and reconstructed residual BPU  222  to generate prediction reference  224 , as described in  FIG. 3A . 
     In process  300 B, the decoder can feed predicted reference  224  to spatial prediction stage  2042  or temporal prediction stage  2044  for performing a prediction operation in the next iteration of process  300 B. For example, if the current BPU is decoded using the intra prediction at spatial prediction stage  2042 , after generating prediction reference  224  (e.g., the decoded current BPU), the decoder can directly feed prediction reference  224  to spatial prediction stage  2042  for later usage (e.g., for extrapolation of a next BPU of the current picture). If the current BPU is decoded using the inter prediction at temporal prediction stage  2044 , after generating prediction reference  224  (e.g., a reference picture in which all BPUs have been decoded), the encoder can feed prediction reference  224  to loop filter stage  232  to reduce or eliminate distortion (e.g., blocking artifacts). The decoder can apply a loop filter to prediction reference  224 , in a way as described in  FIG. 2B . The loop-filtered reference picture can be stored in buffer  234  (e.g., a decoded picture buffer in a computer memory) for later use (e.g., to be used as an inter-prediction reference picture for a future encoded picture of video bitstream  228 ). The decoder can store one or more reference pictures in buffer  234  to be used at temporal prediction stage  2044 . In some embodiments, when the prediction mode indicator of prediction data  206  indicates that inter prediction was used to encode the current BPU, prediction data can further include parameters of the loop filter (e.g., a loop filter strength). 
       FIG. 4  is a block diagram of an example apparatus  400  for encoding or decoding a video, consistent with embodiments of the disclosure. As shown in  FIG. 4 , apparatus  400  can include processor  402 . When processor  402  executes instructions described herein, apparatus  400  can become a specialized machine for video encoding or decoding. Processor  402  can be any type of circuitry capable of manipulating or processing information. For example, processor  402  can include any combination of any number of a central processing unit (or “CPU”), a graphics processing unit (or “GPU”), a neural processing unit (“NPU”), a microcontroller unit (“MCU”), an optical processor, a programmable logic controller, a microcontroller, a microprocessor, a digital signal processor, an intellectual property (IP) core, a Programmable Logic Array (PLA), a Programmable Array Logic (PAL), a Generic Array Logic (GAL), a Complex Programmable Logic Device (CPLD), a Field-Programmable Gate Array (FPGA), a System On Chip (SoC), an Application-Specific Integrated Circuit (ASIC), or the like. In some embodiments, processor  402  can also be a set of processors grouped as a single logical component. For example, as shown in  FIG. 4 , processor  402  can include multiple processors, including processor  402   a , processor  402   b , and processor  402   n.    
     Apparatus  400  can also include memory  404  configured to store data (e.g., a set of instructions, computer codes, intermediate data, or the like). For example, as shown in  FIG. 4 , the stored data can include program instructions (e.g., program instructions for implementing the stages in processes  200 A,  200 B,  300 A, or  300 B) and data for processing (e.g., video sequence  202 , video bitstream  228 , or video stream  304 ). Processor  402  can access the program instructions and data for processing (e.g., via bus  410 ), and execute the program instructions to perform an operation or manipulation on the data for processing. Memory  404  can include a high-speed random-access storage device or a non-volatile storage device. In some embodiments, memory  404  can include any combination of any number of a random-access memory (RAM), a read-only memory (ROM), an optical disc, a magnetic disk, a hard drive, a solid-state drive, a flash drive, a security digital (SD) card, a memory stick, a compact flash (CF) card, or the like. Memory  404  can also be a group of memories (not shown in  FIG. 4 ) grouped as a single logical component. 
     Bus  410  can be a communication device that transfers data between components inside apparatus  400 , such as an internal bus (e.g., a CPU-memory bus), an external bus (e.g., a universal serial bus port, a peripheral component interconnect express port), or the like. 
     For ease of explanation without causing ambiguity, processor  402  and other data processing circuits are collectively referred to as a “data processing circuit” in this disclosure. The data processing circuit can be implemented entirely as hardware, or as a combination of software, hardware, or firmware. In addition, the data processing circuit can be a single independent module or can be combined entirely or partially into any other component of apparatus  400 . 
     Apparatus  400  can further include network interface  406  to provide wired or wireless communication with a network (e.g., the Internet, an intranet, a local area network, a mobile communications network, or the like). In some embodiments, network interface  406  can include any combination of any number of a network interface controller (NIC), a radio frequency (RF) module, a transponder, a transceiver, a modem, a router, a gateway, a wired network adapter, a wireless network adapter, a Bluetooth adapter, an infrared adapter, an near-field communication (“NFC”) adapter, a cellular network chip, or the like. 
     In some embodiments, optionally, apparatus  400  can further include peripheral interface  408  to provide a connection to one or more peripheral devices. As shown in  FIG. 4 , the peripheral device can include, but is not limited to, a cursor control device (e.g., a mouse, a touchpad, or a touchscreen), a keyboard, a display (e.g., a cathode-ray tube display, a liquid crystal display, or a light-emitting diode display), a video input device (e.g., a camera or an input interface coupled to a video archive), or the like. 
     It should be noted that video codecs (e.g., a codec performing process  200 A,  200 B,  300 A, or  300 B) can be implemented as any combination of any software or hardware modules in apparatus  400 . For example, some or all stages of process  200 A,  200 B,  300 A, or  300 B can be implemented as one or more software modules of apparatus  400 , such as program instructions that can be loaded into memory  404 . For another example, some or all stages of process  200 A,  200 B,  300 A, or  300 B can be implemented as one or more hardware modules of apparatus  400 , such as a specialized data processing circuit (e.g., an FPGA, an ASIC, an NPU, or the like). 
     In the quantization and inverse quantization functional blocks (e.g., quantization  214  and inverse quantization  218  of  FIG. 2A  or  FIG. 2B , inverse quantization  218  of  FIG. 3A  or  FIG. 3B ), a quantization parameter (QP) is used to determine the amount of quantization (and inverse quantization) applied to the prediction residuals. Initial QP values used for coding of a picture or slice may be signaled at the high level, for example, using init_qp_minus26 syntax element in the Picture Parameter Set (PPS) and using slice_qp_delta syntax element in the slice header. Further, the QP values may be adapted at the local level for each CU using delta QP values sent at the granularity of quantization groups. 
     Interpolation tasks arise naturally in the context of video coding because the true displacements of objects from one picture to another are independent of the sampling grid of cameras. Therefore, in motion compensation (MC) prediction, fractional-sample accuracy is used to more accurately capture continuous motion. Samples available at integer positions are filtered to estimate values at fractional positions. HEVC supports motion vectors with quarter-pixel accuracy for the luma component and one-eighth pixel accuracy for chroma components. If the motion vector has a half or quarter-pixel accuracy, samples at fractional positions can be interpolated using the samples at integer-sample positions. This spatial domain operation can be seen in the frequency domain as introducing phase delays to individual frequency components. An ideal interpolation filter for band-limited signals induces a constant phase delay to all frequencies and does not alter their magnitudes, which allows all frequencies below a cutoff frequency pass through with amplitude 1 and stops all frequencies above the cutoff frequency with zero amplitude, as shown in  FIG. 5 . 
     An important parameter for interpolation filters is the number of filter taps as it has a direct influence on both coding efficiency and implementation complexity. In general, filters with more taps can achieve better interpolation performance. In terms of implementation, it not only has an impact on the arithmetic operations but also on the memory bandwidth required to access the reference samples. In some embodiments, the luma interpolation process uses a symmetric 8-tap filter for half-pel positions and an asymmetric 7-tap filter for quarter-pel positions to minimize the additional complexity of the motion compensation process. For chroma samples, a 4-tap filter can be introduced. 
     HEVC interpolation filter can forward transform the known integer samples to the discrete cosine transform (DCT) domain and inverse transform the DCT coefficients to the spatial domain using DCT basis sampled at desired fractional positions, instead of integer positions. These operations can be combined into a single finite impulse response (FIR) filter. The coefficients of the FIR filter are designed using a Fourier decomposition of the discrete cosine transform. The resulting interpolation filter is thus named DCT-based interpolation filter (DCTIF). The DCTIF can be implemented as below. 
     Let l (l=−(N/2)+1, . . . , N/2) denote the position of integer samples, a denote the desired fractional position (e.g. ¼, ½ . . . ). When the filter tap is set to N, the coefficient Filter l (α) can be derived based on the following equations: 
     
       
         
           
             
               
                 
                   
                     
                       
                         Filter 
                         l 
                       
                        
                       
                         ( 
                         α 
                         ) 
                       
                     
                     = 
                     
                       
                         S 
                          
                         
                           ( 
                           m 
                           ) 
                         
                       
                        
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             0 
                           
                           
                             N 
                             - 
                             1 
                           
                         
                          
                         
                           ( 
                           
                             
                               
                                 W 
                                 k 
                               
                                
                               
                                 ( 
                                 α 
                                 ) 
                               
                             
                             · 
                             
                               D 
                               
                                 l 
                                 , 
                                 k 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       W 
                       k 
                     
                      
                     
                       ( 
                       α 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               1 
                               2 
                             
                              
                             
                               ( 
                               
                                 k 
                                 = 
                                 0 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             cos 
                              
                             
                                 
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     
                                       2 
                                       · 
                                       α 
                                     
                                     - 
                                     1 
                                     + 
                                     N 
                                   
                                   
                                     2 
                                     · 
                                     N 
                                   
                                 
                                 · 
                                 k 
                                 · 
                                 π 
                               
                               ) 
                             
                              
                             
                               ( 
                               
                                 k 
                                 = 
                                 
                                   
                                     1 
                                      
                                     … 
                                      
                                     
                                         
                                     
                                      
                                     N 
                                   
                                   - 
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     2 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       D 
                       
                         l 
                         , 
                         k 
                       
                     
                     = 
                     
                       
                         
                           2 
                           N 
                         
                         · 
                         cos 
                       
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 2 
                                 · 
                                 l 
                               
                               - 
                               1 
                               + 
                               N 
                             
                             
                               2 
                               · 
                               N 
                             
                           
                           · 
                           k 
                           · 
                           π 
                         
                         ) 
                       
                     
                   
                   , 
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     3 
                     ) 
                   
                 
               
             
           
         
       
     
     where S(m) is the smoothing window function to make the filter kernel in finite length, which can be based on: 
     
       
         
           
             
               
                 
                   
                     
                       S 
                        
                       
                         ( 
                         m 
                         ) 
                       
                     
                     = 
                     
                       cos 
                        
                       
                         ( 
                         
                           π 
                           · 
                           
                             
                               l 
                               - 
                               α 
                             
                             m 
                           
                         
                         ) 
                       
                     
                   
                   , 
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     4 
                     ) 
                   
                 
               
             
           
         
       
     
     where m is the smoothing parameter. 
     Filter coefficients Filter l (α) are real numbers with magnitude no higher than 1. To enable fixed-point implementations, all filter coefficients are multiplied by a scaling factor 2 s  (where s is 6 in HEVC) and rounded to the nearest integer: 
       filter l (α)=round(Filter l (α)−2 s )  Eq. (5)
 
     The resulting coefficients of the interpolation filter of HEVC are shown in Table 1 of  FIG. 6  and Table 2 of  FIG. 7  for luma and chroma interpolation filters, respectively. 
     In some embodiments, the motion vector resolution can be extended to one-sixteenth accuracy. DCTIF can be used for the motion compensation interpolation. Table 3 of  FIG. 8  and Table 4 of  FIG. 9  illustrate the filter coefficients for luma and chroma interpolation filters, respectively. 
     For the luma components, if half-pel adaptive motion vector resolution (AMVR) mode is selected and interpolated position is half-pel, a 6-tap filter (e.g., [3, 9, 20, 20, 9, 3]) can be used. Otherwise, if the motion compensated block size is 4×4, a 6-tap filters can be used. For example,  FIG. 10  illustrates an exemplary Table 5 showing exemplary luma interpolation filter for 4×4 motion compensation, according to some embodiments of the present disclosure. 
     The 6-tap filter in Table 5 of  FIG. 10  is used for the 4×4 motion compensation block. However, this filter is not derived based on the DCTIF. From the coefficients, the coefficients p[−2], p[3] of 6-tap filter are obtained by adding the coefficients p[−3] and p[4] of 8-tap filters into p[−2] and p[3], respectively. The filter derived by this way may not approximate the ideal impulse response filter, and also not align with the 8-tap DCTIF for the other motion compensation blocks. 
     In some embodiments, a number of filter taps can beset to 6. Let l (l=−2, . . . , 3) denote the position of integer samples, a denote the desired fractional position (e.g. ¼, ½ . . . ). The coefficient Filter l (α) can be derived based on: 
       Filter l (α)= S ( m )Σ k=0   5 ( W   k (α)· D   l,k )  Eq. (6)
 
     and the DCT-based interpolation filter can be derived based on: 
     
       
         
           
             
               
                 
                   
                     
                       
                         Filter 
                         l 
                       
                        
                       
                         ( 
                         α 
                         ) 
                       
                     
                     = 
                     
                       
                         S 
                          
                         
                           ( 
                           m 
                           ) 
                         
                       
                        
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             0 
                           
                           5 
                         
                          
                         
                           ( 
                           
                             
                               
                                 W 
                                 k 
                               
                                
                               
                                 ( 
                                 α 
                                 ) 
                               
                             
                             · 
                             
                               D 
                               
                                 l 
                                 . 
                                 k 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                    
                   
                       
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     7 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       W 
                       k 
                     
                      
                     
                       ( 
                       α 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               1 
                               2 
                             
                              
                             
                               ( 
                               
                                 k 
                                 = 
                                 0 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             cos 
                              
                             
                                 
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     
                                       2 
                                       · 
                                       α 
                                     
                                     + 
                                     5 
                                   
                                   12 
                                 
                                 · 
                                 k 
                                 · 
                                 π 
                               
                               ) 
                             
                              
                             
                               ( 
                               
                                 k 
                                 = 
                                 
                                   
                                     1 
                                      
                                     … 
                                      
                                     
                                         
                                     
                                      
                                     N 
                                   
                                   - 
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     8 
                     ) 
                   
                 
               
             
           
         
       
     
     S(m) is the smoothing window function to make the filter kernel infinite length, which can be defined as: 
     
       
         
           
             
               
                 
                   
                     S 
                      
                     
                       ( 
                       m 
                       ) 
                     
                   
                   = 
                   
                     cos 
                      
                     
                       ( 
                       
                         π 
                         · 
                         
                           
                             l 
                             - 
                             α 
                           
                           m 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     9 
                     ) 
                   
                 
               
             
           
         
       
     
     where m is the smoothing parameter.  FIG. 11  illustrates an exemplary Table 6 showing exemplary values of smoothing parameter, according to some embodiments of the present disclosure. 
     Then, the real-number filter coefficients can be calculated.  FIG. 12  illustrates an exemplary Table 7 showing exemplary 6-tap real-number luma interpolation filter, according to some embodiments of the present disclosure. 
     When rounding the real-number filters to the integer coefficients, a scaling factor of 64 can be used here.  FIG. 13  illustrates an exemplary Table 8 showing exemplary 6-tap integer-number luma interpolation filter, according to some embodiments of the present disclosure. 
     Compared to the current 6-tap filter (e.g., the interpolation filter as shown in Table 5 of  FIG. 10 ), the exemplary 6-tap DCT-based filter in some embodiments can be smoother in some phases. For example, the coefficient variants among different positions decrease to a little extent. 
     To enable fixed-point implementations, the filter coefficients are multiplied by a scaling factor 2 s  and rounded to the nearest integer. Therefore, the scaling and rounding process also impact on the resulting filter. In some embodiments, another rounding method according to embodiments of the disclosure can be provided as below, and the rounding method can include steps as below. 
     At step 1, for the N-tap real-number coefficients F l (α) (l=−(N/2)+1, . . . , N/2) of fractional position α, let f l (α) denote the integer-number coefficient after rounding. The coefficients satisfying the following condition are first rounded to the nearest integer number. 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       l 
                     
                      
                     
                       ( 
                       α 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 
                                   ⌊ 
                                   
                                     
                                       F 
                                       l 
                                     
                                      
                                     
                                       ( 
                                       α 
                                       ) 
                                     
                                   
                                   ⌋ 
                                 
                                  
                                 
                                     
                                 
                                  
                                 if 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     F 
                                     l 
                                   
                                    
                                   
                                     ( 
                                     α 
                                     ) 
                                   
                                 
                               
                               - 
                               
                                 ⌊ 
                                 
                                   
                                     F 
                                     l 
                                   
                                    
                                   
                                     ( 
                                     α 
                                     ) 
                                   
                                 
                                 ⌋ 
                               
                             
                             &lt; 
                             β 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                     ⌈ 
                                     
                                       
                                         F 
                                         l 
                                       
                                        
                                       
                                         ( 
                                         α 
                                         ) 
                                       
                                     
                                     ⌉ 
                                   
                                    
                                   
                                       
                                   
                                    
                                   if 
                                    
                                   
                                       
                                   
                                    
                                   
                                     ⌈ 
                                     
                                         
                                     
                                      
                                     
                                       
                                         F 
                                         l 
                                       
                                        
                                       
                                         ( 
                                         α 
                                         ) 
                                       
                                     
                                     ⌉ 
                                   
                                 
                                 - 
                                 
                                   
                                     F 
                                     l 
                                   
                                    
                                   
                                     ( 
                                     α 
                                     ) 
                                   
                                 
                               
                               &lt; 
                               β 
                             
                              
                             
                                 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     10 
                     ) 
                   
                 
               
             
           
         
       
     
     where β (0&lt;β&lt;1) is a threshold and set to 0.3 here. 
     At step 2, without loss of generality, let F i (α) denote the filter coefficients rounded in step 1 and F j (α) denote other filter coefficients. Thus, 
       Σ f   j (α)=2 s   −Σf   i (α)  Eq. (11)
 
     where s denote the scaling factor and set to 6 here. Based on this constraint, the rounding of F j (α) can be determined by minimizing the rounding displacement based on the following equation: 
       min{Σ| f   j (α)− F   j (α)|}, f   j (α)ϵ{└ F   l (α)┘,┌ F   l (α)┐}  Eq. (12)
 
     Taking α=¼ as the example, the F l (¼) can be: 
     
       
         
           
               
               
            
               
                   
                   
               
               
                   
                 Interpolation filter coefficients for ¼ fractional position 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Stage 
                 l = −3 
                 l = −2 
                 l = −1 
                 l = 0 
                 l = 1 
                 l = 2 
                 l = 3 
                 l = 4 
               
               
                   
               
               
                 F l (¼) 
                 0 
                 1.521 
                 −8.209 
                 56.53 
                 17.94 
                 −4.989 
                 0.88 
                 0 
               
               
                   
               
            
           
         
       
     
     During step 1, it is found that the rounding condition is satisfied for l={−1, 1, 2, 3} and hence 
     
       
         
           
               
               
            
               
                   
                   
               
               
                   
                 Interpolation filter coefficients for ¼ fractional position 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Stage 
                 l = −3 
                 l = −2 
                 l = −1 
                 l = 0 
                 l = 1 
                 l = 2 
                 l = 3 
                 l = 4 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 F l (¼) 
                 0 
                 1.521 
                 −8.209 
                 56.53 
                 17.94 
                 −4.989 
                 0.88 
                 0 
               
               
                 Step 
                 0 
                 1.521 
                 −8 
                 56.53 
                 18 
                 −5 
                 1 
                 0 
               
               
                 1 
               
               
                   
               
            
           
         
       
     
     During step 2, it is first inferred that 
         f   −2 (¼)+ f   0 (¼)=2 6 −(−8+18−5+1)=58  Eq. (13)
 
     Then, it can be determined that f −2 (¼) can be {1, 2} and f 0 (¼) can be (56, 57). After checking all the combinations, it is found that f −2 (¼)=1, f 0 (¼)=57 can minimize the rounding error. Finally, the integer-number filter coefficients for ¼ fractional position are: 
     
       
         
           
               
               
            
               
                   
                   
               
               
                   
                 Interpolation filter coefficients for ¼ fractional position 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Stage 
                 l = −3 
                 l = −2 
                 l = −1 
                 l = 0 
                 l = 1 
                 l = 2 
                 l = 3 
                 l = 4 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 F l (¼) 
                 0 
                 1.521 
                 −8.209 
                 56.53 
                 17.94 
                 −4.989 
                 0.88 
                 0 
               
               
                 Step 
                 0 
                 1.521 
                 −8 
                 56.53 
                 18 
                 −5 
                 1 
                 0 
               
               
                 1 
               
               
                 f l (¼) 
                 0 
                 1 
                 −8 
                 57 
                 18 
                 −5 
                 1 
                 0 
               
               
                   
               
            
           
         
       
     
     In this manner, the exemplary integer 6-tap DCT-based interposition filter is shown in Table 9 of  FIG. 14 . 
     It is appreciated that other rounding methods may be used. For example, the threshold β in step 1 can be set to 0.4. Otherwise, the number of coefficients rounded in step 1 can also be set as a parameter related to the number of filter tap, for example, N−2. 
     Some embodiments of the present disclosure also provide a DCT-based interpolation filter without smoothing window function. 
     If the smooth window function can be removed, the DCTIF can be rewritten as: 
       Filter l (α)=Σ k=0   N−1 ( W   k (α)− D   l,k )  Eq. (14)
 
     where the definitions of W k (α) and D l,k  are the same as above. In this case, the real-number coefficients and the integer-number coefficients of the exemplary filter can be derived based on the above equations.  FIG. 15  illustrates an exemplary Table 10 showing exemplary 6-tap real-number luma interpolation filter without a smoothing window function, according to some embodiments of the present disclosure.  FIG. 16  illustrates an exemplary Table 11 showing exemplary 6-tap integer-number luma interpolation filter without a smoothing window function, according to some embodiments of the present disclosure. 
     Some embodiments of the disclosure also provide a DCT-based interpolation filter with different smoothing window function. 
     In the DCTIF (e.g., the DCTIF of HEVC and VVC), the smoothing window function uses the cosine function cos (π·(l−α)/m). However, the smoothing function may be different for various circumstances. For example, the smoothing function may use different number of interpolation taps. 
     In some embodiments, an exemplary smoothing window of sine function is provided. For example, the sine window function can be based on the following equation: 
     
       
         
           
             
               
                 
                   
                     
                       S 
                        
                       
                         ( 
                         m 
                         ) 
                       
                     
                     = 
                     
                       sin 
                        
                       
                         ( 
                         
                           π 
                           . 
                           
                             
                               m 
                               + 
                               l 
                               - 
                               α 
                             
                             
                               2 
                                
                               m 
                             
                           
                         
                         ) 
                       
                     
                   
                   , 
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     15 
                     ) 
                   
                 
               
             
           
         
       
     
     where m is the smoothing parameter, l represents the position of integer samples and a represents the desired fractional position. The value of smoothing parameter m is not fixed. If given the values of m as shown in Table 12 of  FIG. 17 , the exemplary real-number and integer-number filter coefficients are shown in Table 13 of  FIG. 18  and Table 14 of  FIG. 19 , respectively. 
     When a non-trigonometric smoothing window function is used, the DCTIF function can be expressed based on the following equation: 
     
       
         
           
             
               
                 
                   
                     
                       
                         Filter 
                         l 
                       
                        
                       
                         ( 
                         α 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 W 
                                 k 
                               
                                
                               
                                 ( 
                                 α 
                                 ) 
                               
                             
                             
                               1 
                               + 
                               
                                 m 
                                 · 
                                 
                                   k 
                                   2 
                                 
                               
                             
                           
                           · 
                           
                             D 
                             
                               l 
                               , 
                               k 
                             
                           
                         
                         ) 
                       
                     
                   
                   , 
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     16 
                     ) 
                   
                 
               
             
           
         
       
     
     where m is the smoothing parameter, l represents the position of integer samples and a represents the desired fractional position. The definitions of W k (α) and D l,k  are the same as above. 
     The value of smoothing parameter m may or may not be the same for different fractional positions.  FIG. 20  illustrates an exemplary Table 15 showing exemplary values of a smoothing parameter for different fractional positions, according to some embodiments of the present disclosure.  FIG. 21  illustrates an exemplary Table 16 showing exemplary 6-tap real-number luma interpolation filter, according to some embodiments of the present disclosure. FIG.  22  illustrates an exemplary Table 17 showing exemplary 6-tap integer-number luma interpolation filter, according to some embodiments of the present disclosure. 
     Some embodiments of the present disclosure also provide a method for deriving the smoothing parameter in DCT-based interpolation filter. For the interpolation filter, the smoothing parameter can be used to determine the performance of filter. In some embodiments, a cost function in terms of frequency response is provided to derive the value of smoothing parameter. 
       FIG. 23  illustrates exemplary frequency responses of a tested filter and a reference filter 6-tap integer-number luma interpolation filter, according to some embodiments of the present disclosure. As shown in  FIG. 23 , the dotted curve and the dash curve represent the frequency responses of a tested filter and a reference filter, respectively. The tested filter is determined among the DCT-based interpolation filters with different smoothing window functions, having a search space [−1, +1] of smoothing parameter. The reference filter serves as the reference for cost calculation during the search process. In the shown example, the reference filter is the 8-tap DCTIF. 
     The cost of tested filter considers two aspects: the area of hill  2301  and valley  2303  and the shift  2305  of cutoff points. Hills  2301  in amplitude frequency response can indicate that the corresponding frequency components in the input signal are amplified. Similarly, valleys  2303  in amplitude frequency response can indicate that the corresponding frequency components in the input signal are damped. Both effects are undesirable during interpolation. After the area of hill  2301  and valley  2303 , the frequency response curve tends downward sharply, which is called attenuation. In the frequency response of a filter, at a given amplitude in y-axis (for example 0.76 in  FIG. 23 ), the corresponding frequency is termed as cutoff point c. In general, the cutoff point is related to the fractional position α. The difference between the two cutoff points of tested filter and reference filter is namely the shift  2305  of cutoff. 
     The cost of the tested filter can be expressed as 
         f   cost ( m )=Δ(Filter( m ))+ w ·( c (Filter(ref))− c (Filter( m )))  Eq. (17)
 
     where Δ(·) denotes the area of hills and valleys in one filter, c(·) denotes the cutoff point of one filter. Filter(m) and Filter(ref) are the tested filter with smoothing parameter m and the reference filter, respectively. w is the weight factor, which is set to 1.5 here. 
     In some embodiments, the selection of cutoff point is not fixed, but depends on the fractional position.  FIG. 24  illustrates an exemplary Table 18 showing exemplary response values corresponding to cutoff points for each fractional position, according to some embodiments of the present disclosure.  FIG. 25  illustrates an exemplary Table 19 showing exemplary 6-tap integer-number luma interpolation filter, according to some embodiments of the present disclosure. 
       FIG. 26  illustrates a flowchart of an exemplary video processing method  2600 , according to some embodiments of the present disclosure. Method  2600  can be performed by an encoder (e.g., by process  200 A of  FIG. 2A or 200B  of  FIG. 2B ), a decoder (e.g., by process  300 A of  FIG. 3A or 300B  of  FIG. 3B ) or performed by one or more software or hardware components of an apparatus (e.g., apparatus  400  of  FIG. 4 ). For example, a processor (e.g., processor  402  of  FIG. 4 ) can perform method  2600 . In some embodiments, method  2600  can be implemented by a computer program product, embodied in a computer-readable medium, including computer-executable instructions, such as program code, executed by computers (e.g., apparatus  400  of  FIG. 4 ). 
     At step  2601 , intermediate interpolation coefficients of an interpolation filter can be determined based on a position of an integer sample and a fractional position of a fractional sample. For example, the interpolation filter has 6 filter taps and used for 4×4 motion compensation block. Real-number filter coefficients Filter l (α) can be derived based on Eq. (6)-Eq. (9). In some embodiments, method  2600  can also include: determining real-number interpolation coefficients of the interpolation filter based on the position of the integer sample and the fractional position of the fractional sample, and multiplying the real-number interpolation coefficients of the interpolation filter by a scaling factor. For example, Table 7 of  FIG. 12  illustrates real-number interpolation coefficients of an exemplary 6-tap interpolation filter. A scaling factor of 64 can be used to these real-number interpolation coefficients of Table 7. 
     At step  2603 , integer interpolation coefficients of the interpolation filter can be determined by rounding each of the intermediate interpolation coefficients to an integer. In some embodiments, method  2600  can include determining whether an intermediate interpolation coefficient satisfies a condition in association with a difference between the intermediate interpolation coefficient and an integer that is nearest to the intermediate interpolation coefficient (e.g., the condition based on Eq. (10)), and in response to a first intermediate interpolation coefficient being determined to satisfy the condition, rounding the first intermediate interpolation coefficient to a first integer that is nearest to the first intermediate interpolation coefficient. In some embodiments, the condition can include the difference between the intermediate interpolation coefficient and the integer that is nearest to the intermediate interpolation coefficient is less than a threshold. For example, coefficients satisfying the condition based on Eq. (10) are be rounded to the nearest integer number. The threshold β in Eq. (10) can be set to 0.3, 0.4, or the like. 
     In some embodiments, method  2600  can also include: in response to one or more intermediate interpolation coefficients being determined to not satisfy the condition, generating one or more combinations of candidate integer interpolation coefficients for the one or more intermediate interpolation coefficients, and selecting a first combination that minimizes a sum of rounding displacements of the one or more intermediate interpolation coefficients. For example, for interpolation coefficients not satisfying the condition based on Eq. (10), one or more combinations of candidate integer interpolation coefficients can be determined based on Eq. (11). A combination that minimizing the rounding displacement based on Eq. (12) can be selected. 
     In some embodiments, method  2600  can include determining intermediate interpolation coefficients of the interpolation filter based on a smoothing window function. The smoothing window function can include at least one of: a cosine function (e.g., Eq. (9)) in association with the position of the integer sample, the fractional position of the fractional sample, and a smoothing parameter, a sine function in association with the position of the integer sample, the fractional position of the fractional sample, and a smoothing parameter (e.g., Eq. (15)), a fractional function in association with a smoothing parameter (e.g., Eq. (16)), or a constant function. An output of the constant function can be 1 (e.g., without applying a smoothing window function). In some embodiments, the smoothing parameter has a same value or different values for different fractional positions. 
     In some embodiments, method  2600  can include determining the smoothing parameter based on a cost function (e.g., f cost (m) based on Eq. (17)) in association with a reference filter. Specifically, method  2600  can include: determining a plurality of candidate frequency responses for a plurality of candidate smoothing parameters within a given range, respectively, determining deviations between each of the plurality of candidate frequency responses and a reference frequency response of the reference filter, and determining a candidate smoothing parameter having a smallest deviation as the smoothing parameter in association with the smoothing window function. Method  2600  can also include: determining at least one of a hill or a valley of a candidate frequency response, determining a cutoff shift between the candidate frequency response and the reference frequency response, and determining a deviation between the candidate frequency response and the reference frequency response based on an area of the at least one of the hill or valley and the cutoff shift (e.g., based on Eq. (17)). 
     At step  2605 , the interpolation filter can be applied on a picture to perform motion compensation prediction. 
     It is appreciated that an embodiment of the present disclosure can be combined with another embodiments or some other embodiments. 
     The embodiments may further be described using the following clauses: 
     1. A video processing method, comprising: 
     determining intermediate interpolation coefficients of an interpolation filter based on a position of an integer sample and a fractional position of a fractional sample; 
     determining integer interpolation coefficients of the interpolation filter, comprising rounding each of the intermediate interpolation coefficients to an integer; and 
     applying the interpolation filter on a picture to perform motion compensation prediction. 
     2. The method of clause 1, wherein determining integer interpolation coefficients of the interpolation filter comprises: 
     determining whether an intermediate interpolation coefficient satisfies a condition in association with a difference between the intermediate interpolation coefficient and an integer that is nearest to the intermediate interpolation coefficient; and 
     in response to a first intermediate interpolation coefficient being determined to satisfy the condition, rounding the first intermediate interpolation coefficient to a first integer that is nearest to the first intermediate interpolation coefficient. 
     3. The method of clause 2, wherein the condition comprises: 
     the difference between the intermediate interpolation coefficient and the integer that is nearest to the intermediate interpolation coefficient is less than a threshold. 
     4. The method of any one of clauses 2 and 3, wherein determining integer interpolation coefficients of the interpolation filter further comprises: 
     in response to one or more intermediate interpolation coefficients being determined to not satisfy the condition,
         generating one or more combinations of candidate integer interpolation coefficients for the one or more intermediate interpolation coefficients; and   selecting a first combination that minimizes a sum of rounding displacements of the one or more intermediate interpolation coefficients.
 
5. The method of any one of clauses 1-4, wherein determining intermediate interpolation coefficients of the interpolation filter comprises:
       

     determining intermediate interpolation coefficients of the interpolation filter based on a smoothing window function. 
     6. The method of clause 5, wherein the smoothing window function comprises at least one of: 
     a cosine function in association with the position of the integer sample, the fractional position of the fractional sample, and a smoothing parameter; 
     a sine function in association with the position of the integer sample, the fractional position of the fractional sample, and a smoothing parameter; 
     a fractional function in association with a smoothing parameter; or 
     a constant function. 
     7. The method of clause 6, wherein the smoothing parameter has different values for different fractional positions.
 
8. The method of any one of clauses 6 and 7, further comprising:
 
     determining the smoothing parameter based on a cost function in association with a reference filter. 
     9. The method of clause 8, wherein determining the smoothing parameter based on the cost function in association with the reference filter comprises: 
     determining a plurality of candidate frequency responses for a plurality of candidate smoothing parameters within a given range, respectively; 
     determining deviations between each of the plurality of candidate frequency responses and a reference frequency response of the reference filter; and 
     determining a candidate smoothing parameter having a smallest deviation as the smoothing parameter in association with the smoothing window function. 
     10. The method of clause 9, wherein determining deviations between each of the plurality of candidate frequency responses and the reference frequency response of the reference filter comprises: 
     determining at least one of a hill or a valley of a candidate frequency response; 
     determining a cutoff shift between the candidate frequency response and the reference frequency response; and 
     determining a deviation between the candidate frequency response and the reference frequency response based on an area of the at least one of the hill or valley and the cutoff shift. 
     11. The method of clause 6, wherein an output of the constant function is 1.
 
12. The method of any one of clauses 1-11, wherein determining intermediate interpolation coefficients of the interpolation filter comprises:
 
     determining real-number interpolation coefficients of the interpolation filter based on the position of the integer sample and the fractional position of the fractional sample; and 
     multiplying the real-number interpolation coefficients of the interpolation filter by a scaling factor. 
     13. The method of any one of clauses 1-12, wherein the interpolation filter has 6 filter taps and used for 4×4 motion compensation block.
 
14. A video processing apparatus, comprising:
 
     at least one memory for storing instructions; and 
     at least one processor configured to execute the instructions to cause the apparatus to perform:
         determining intermediate interpolation coefficients of an interpolation filter based on a position of an integer sample and a fractional position of a fractional sample;   determining integer interpolation coefficients of the interpolation filter, comprising rounding each of the intermediate interpolation coefficients to an integer; and   applying the interpolation filter on a picture to perform motion compensation prediction.
 
15. The apparatus of clause 14, wherein the at least one processor is configured to execute the instructions to cause the apparatus to perform:
       

     determining whether an intermediate interpolation coefficient satisfies a condition in association with a difference between the intermediate interpolation coefficient and an integer that is nearest to the intermediate interpolation coefficient; and 
     in response to a first intermediate interpolation coefficient being determined to satisfy the condition, rounding the first intermediate interpolation coefficient to a first integer that is nearest to the first intermediate interpolation coefficient. 
     16. The apparatus of clause 15, wherein the condition comprises: 
     the difference between the intermediate interpolation coefficient and the integer that is nearest to the intermediate interpolation coefficient is less than a threshold. 
     17. The apparatus of any one of clauses 15 and 16, wherein the at least one processor is configured to execute the instructions to cause the apparatus to perform: 
     in response to one or more intermediate interpolation coefficients being determined to not satisfy the condition,
         generating one or more combinations of candidate integer interpolation coefficients for the one or more intermediate interpolation coefficients; and   selecting a first combination that minimizes a sum of rounding displacements of the one or more intermediate interpolation coefficients.
 
18. The apparatus of any one of clauses 14-17, wherein the at least one processor is configured to execute the instructions to cause the apparatus to perform:
       

     determining intermediate interpolation coefficients of the interpolation filter based on a smoothing window function. 
     19. The apparatus of clause 18, wherein the smoothing window function comprises at least one of: 
     a cosine function in association with the position of the integer sample, the fractional position of the fractional sample, and a smoothing parameter; 
     a sine function in association with the position of the integer sample, the fractional position of the fractional sample, and a smoothing parameter; 
     a fractional function in association with a smoothing parameter; or 
     a constant function. 
     20. The apparatus of clause 19, wherein the smoothing parameter has different values for different fractional positions.
 
21. The apparatus of any one of clauses 19 and 20, wherein the at least one processor is configured to execute the instructions to cause the apparatus to perform:
 
     determining the smoothing parameter based on a cost function in association with a reference filter. 
     22. The apparatus of clause 21, wherein the at least one processor is configured to execute the instructions to cause the apparatus to perform: 
     determining a plurality of candidate frequency responses for a plurality of candidate smoothing parameters within a given range, respectively; 
     determining deviations between each of the plurality of candidate frequency responses and a reference frequency response of the reference filter; and 
     determining a candidate smoothing parameter having a smallest deviation as the smoothing parameter in association with the smoothing window function. 
     23. The apparatus of clause 22, wherein the at least one processor is configured to execute the instructions to cause the apparatus to perform: 
     determining at least one of a hill or a valley of a candidate frequency response; 
     determining a cutoff shift between the candidate frequency response and the reference frequency response; and 
     determining a deviation between the candidate frequency response and the reference frequency response based on an area of the at least one of the hill or valley and the cutoff shift. 
     24. The apparatus of clause 19, wherein an output of the constant function is 1.
 
25. The apparatus of any one of clauses 14-24, wherein the at least one processor is configured to execute the instructions to cause the apparatus to perform:
 
     determining real-number interpolation coefficients of the interpolation filter based on the position of the integer sample and the fractional position of the fractional sample; and 
     multiplying the real-number interpolation coefficients of the interpolation filter by a scaling factor. 
     26. The apparatus of any one of clauses 14-25, wherein the interpolation filter has 6 filter taps and used for 4×4 motion compensation block.
 
27. A non-transitory computer readable storage medium storing a set of instructions that are executable by one or more processing devices to cause a video processing apparatus to perform a method comprising:
 
     determining intermediate interpolation coefficients of an interpolation filter based on a position of an integer sample and a fractional position of a fractional sample; 
     determining integer interpolation coefficients of the interpolation filter, comprising rounding each of the intermediate interpolation coefficients to an integer; and 
     applying the interpolation filter on a picture to perform motion compensation prediction. 
     28. The non-transitory computer readable storage medium of clause 27, wherein the set of instructions are executable by the one or more processing devices to cause the video processing apparatus to perform: 
     determining whether an intermediate interpolation coefficient satisfies a condition in association with a difference between the intermediate interpolation coefficient and an integer that is nearest to the intermediate interpolation coefficient; and 
     in response to a first intermediate interpolation coefficient being determined to satisfy the condition, rounding the first intermediate interpolation coefficient to a first integer that is nearest to the first intermediate interpolation coefficient. 
     29. The non-transitory computer readable storage medium of clause 28, wherein the condition comprises: 
     the difference between the intermediate interpolation coefficient and the integer that is nearest to the intermediate interpolation coefficient is less than a threshold. 
     30. The non-transitory computer readable storage medium of any one of clauses 28 and 29, wherein the set of instructions are executable by the one or more processing devices to cause the video processing apparatus to perform: 
     in response to one or more intermediate interpolation coefficients being determined to not satisfy the condition,
         generating one or more combinations of candidate integer interpolation coefficients for the one or more intermediate interpolation coefficients; and   selecting a first combination that minimizes a sum of rounding displacements of the one or more intermediate interpolation coefficients.
 
31. The non-transitory computer readable storage medium of any one of clauses 27-30, wherein the set of instructions are executable by the one or more processing devices to cause the video processing apparatus to perform:
       

     determining intermediate interpolation coefficients of the interpolation filter based on a smoothing window function. 
     32. The non-transitory computer readable storage medium of clause 31, wherein the smoothing window function comprises at least one of: 
     a cosine function in association with the position of the integer sample, the fractional position of the fractional sample, and a smoothing parameter; 
     a sine function in association with the position of the integer sample, the fractional position of the fractional sample, and a smoothing parameter; 
     a fractional function in association with a smoothing parameter; or 
     a constant function. 
     33. The non-transitory computer readable storage medium of clause 32, wherein the smoothing parameter has different values for different fractional positions.
 
34. The non-transitory computer readable storage medium of any one of clauses 32 and 33, wherein the set of instructions are executable by the one or more processing devices to cause the video processing apparatus to perform:
 
     determining the smoothing parameter based on a cost function in association with a reference filter. 
     35. The non-transitory computer readable storage medium of clause 34, wherein the set of instructions are executable by the one or more processing devices to cause the video processing apparatus to perform: 
     determining a plurality of candidate frequency responses for a plurality of candidate smoothing parameters within a given range, respectively; 
     determining deviations between each of the plurality of candidate frequency responses and a reference frequency response of the reference filter; and 
     determining a candidate smoothing parameter having a smallest deviation as the smoothing parameter in association with the smoothing window function. 
     36. The non-transitory computer readable storage medium of clause 35, wherein the set of instructions are executable by the one or more processing devices to cause the video processing apparatus to perform: 
     determining at least one of a hill or a valley of a candidate frequency response; 
     determining a cutoff shift between the candidate frequency response and the reference frequency response; and 
     determining a deviation between the candidate frequency response and the reference frequency response based on an area of the at least one of the hill or valley and the cutoff shift. 
     37. The non-transitory computer readable storage medium of clause 32, wherein an output of the constant function is 1.
 
38. The non-transitory computer readable storage medium of any one of clauses 27-37, wherein the set of instructions are executable by the one or more processing devices to cause the video processing apparatus to perform:
 
     determining real-number interpolation coefficients of the interpolation filter based on the position of the integer sample and the fractional position of the fractional sample; and 
     multiplying the real-number interpolation coefficients of the interpolation filter by a scaling factor. 
     39. The non-transitory computer readable storage medium of any one of clauses 27-38, wherein the interpolation filter has 6 filter taps and used for 4×4 motion compensation block. 
     In some embodiments, a non-transitory computer-readable storage medium including instructions is also provided, and the instructions may be executed by a device (such as the disclosed encoder and decoder), for performing the above-described methods. Common forms of non-transitory media include, for example, a floppy disk, a flexible disk, hard disk, solid state drive, magnetic tape, or any other magnetic data storage medium, a CD-ROM, any other optical data storage medium, any physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM or any other flash memory, NVRAM, a cache, a register, any other memory chip or cartridge, and networked versions of the same. The device may include one or more processors (CPUs), an input/output interface, a network interface, and/or a memory. 
     It should be noted that, the relational terms herein such as “first” and “second” are used only to differentiate an entity or operation from another entity or operation, and do not require or imply any actual relationship or sequence between these entities or operations. Moreover, the words “comprising,” “having,” “containing,” and “including,” and other similar forms are intended to be equivalent in meaning and be open ended in that an item or items following any one of these words is not meant to be an exhaustive listing of such item or items, or meant to be limited to only the listed item or items. 
     As used herein, unless specifically stated otherwise, the term “or” encompasses all possible combinations, except where infeasible. For example, if it is stated that a database may include A or B, then, unless specifically stated otherwise or infeasible, the database may include A, or B, or A and B. As a second example, if it is stated that a database may include A, B, or C, then, unless specifically stated otherwise or infeasible, the database may include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C. 
     It is appreciated that the above described embodiments can be implemented by hardware, or software (program codes), or a combination of hardware and software. If implemented by software, it may be stored in the above-described computer-readable media. The software, when executed by the processor can perform the disclosed methods. The computing units and other functional units described in this disclosure can be implemented by hardware, or software, or a combination of hardware and software. One of ordinary skill in the art will also understand that multiple ones of the above described modules/units may be combined as one module/unit, and each of the above described modules/units may be further divided into a plurality of sub-modules/sub-units. 
     In the foregoing specification, embodiments have been described with reference to numerous specific details that can vary from implementation to implementation. Certain adaptations and modifications of the described embodiments can be made. Other embodiments can be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims. It is also intended that the sequence of steps shown in figures are only for illustrative purposes and are not intended to be limited to any particular sequence of steps. As such, those skilled in the art can appreciate that these steps can be performed in a different order while implementing the same method. 
     In the drawings and specification, there have been disclosed exemplary embodiments. However, many variations and modifications can be made to these embodiments. Accordingly, although specific terms are employed, they are used in a generic and descriptive sense only and not for purposes of limitation.