Dictionary-driven implicit neural representation for image and video compression

Abstract

In one implementation, a set of INR functions are known to both encoder and decoder. At the encoder side, an input signal is represented as a linear mixing of a subset of the set of INR functions, which may be adjusted by a low-capacity network. Both the linear regression weights for linear mixing and the parameters for the low-capacity network are trained, possibly with sparse constraints in order to reduce the number of parameters to be transmitted. At the decoder side, the non-zero linear weights and parameters for the low-capacity network are decoded for each partition or region of the signal, then each partition or region of the signal is reconstructed with the reconstructed INR network.

Description

[0001] DICTIONARY-DRIVEN IMPLICIT NEURAL REPRESENTATION FOR IMAGE AND VIDEO COMPRESSION TECHNICAL FIELD [1] The present embodiments generally relate to a method and an apparatus for neural compression. BACKGROUND [2] Neural compression or learning-based compression is the application of neural networks and other machine learning methods to data compression. Those techniques are currently being investigated by MPEG, and there is a new ad-hoc group which focuses on the Implicit Neural Representation-based compression (INR-based) within Working Group 4. Typically, INR-based compression techniques have a far lower computational complexity than end-to-end neural compression approaches. SUMMARY [3] According to an embodiment, a method of decoding video data representative of an image or a 3D scene is presented, comprising: obtaining one or more coefficients corresponding to one or more INR (Implicit Neural Representation) basis functions for a region of said image or 3D scene, wherein said one or more INR basis functions are selected from a set of INR basis functions; weighting said one or more INR basis functions by said one or more coefficients, respectively; combining said weighted one or more INR basis functions to form an INR function; and reconstructing said region based on said INR function. [4] According to another embodiment, a method of encoding video data representative of an image or a 3D scene, comprising: obtaining one or more coefficients corresponding to one or more INR (Implicit Neural Representation) basis functions for a region of said image or 3D scene, wherein said one or more INR basis functions are selected from a set of INR basis functions; weighting said one or more INR basis functions by said one or more coefficients, respectively; combining said weighted one or more INR basis functions to form an INR function; and reconstructing said region based on said INR function. [5] According to another embodiment, an apparatus for decoding video data representative of an image or a 3D scene, comprising at least one memory or one or more processors, wherein said one or more processors are configured to: obtain one or more coefficients corresponding to one or more INR (Implicit Neural Representation) basis functions for a region of said image or 3D scene, wherein said one or more INR basis functions are selected from a set of INR basis functions; weight said one or more INR basis functions by said one or more coefficients, respectively; combine said weighted one or more INR basis functions to form an INR function; and reconstruct said region based on said INR function. [6] According to another embodiment, an apparatus for encoding video data representative of an image or a 3D scene, comprising at least one memory and one or more processors, wherein said one or more processors are configured to: obtain one or more coefficients corresponding to one or more INR (Implicit Neural Representation) basis functions for a region of said image or 3D scene, wherein said one or more INR basis functions are selected from a set of INR basis functions; weight said one or more INR basis functions by said one or more coefficients, respectively; combine said weighted one or more INR basis functions to form an INR function; and reconstruct said region based on said INR function. [7] One or more embodiments also provide a computer program comprising instructions which when executed by one or more processors cause the one or more processors to perform the encoding method or decoding method according to any of the embodiments described herein. One or more of the present embodiments also provide a computer readable storage medium having stored thereon instructions for video encoding or decoding according to the methods described herein. [8] One or more embodiments also provide a computer readable storage medium having stored thereon video data generated according to the methods described above. One or more embodiments also provide a method and apparatus for transmitting or receiving the video data generated according to the methods described herein. BRIEF DESCRIPTION OF THE DRAWINGS [9] FIG. 1 illustrates a block diagram of a system within which aspects of the present embodiments may be implemented.

[0010] FIG. 2 illustrates a simple neural network used for Implicit Neural Representation (INR).

[0011] FIG.3 illustrates a typical process to encode a signal using INR.

[0012] FIG. 4 illustrates a process to encode a signal using INR basis functions, according to an embodiment.

[0013] FIG. 5 illustrates a process to decode a signal using INR basis functions, according to an embodiment. DETAILED DESCRIPTION

[0014] FIG. 1 illustrates a block diagram of an example of a system in which various aspects and embodiments can be implemented. System 100 may be embodied as a device including the various components described below and is configured to perform one or more of the aspects described in this application. Examples of such devices, include, but are not limited to, various electronic devices such as personal computers, laptop computers, smartphones, tablet computers, digital multimedia set top boxes, digital television receivers, personal video recording systems, connected home appliances, and servers. Elements of system 100, singly or in combination, may be embodied in a single integrated circuit, multiple ICs, and / or discrete components. For example, in at least one embodiment, the processing and encoder / decoder elements of system 100 are distributed across multiple ICs and / or discrete components. In various embodiments, the system 100 is communicatively coupled to other systems, or to other electronic devices, via, for example, a communications bus or through dedicated input and / or output ports. In various embodiments, the system 100 is configured to implement one or more of the aspects described in this application.

[0015] The system 100 includes at least one processor 110 configured to execute instructions loaded therein for implementing, for example, the various aspects described in this application. Processor 110 may include embedded memory, input output interface, and various other circuitries as known in the art. The system 100 includes at least one memory 120 (e.g., a volatile memory device, and / or a non-volatile memory device). System 100 includes a storage device 140, which may include non-volatile memory and / or volatile memory, including, but not limited to, EEPROM, ROM, PROM, RAM, DRAM, SRAM, flash, magnetic disk drive, and / or optical disk drive. The storage device 140 may include an internal storage device, an attached storage device, and / or a network accessible storage device, as non-limiting examples.

[0016] System 100 includes an encoder / decoder module 130 configured, for example, to process data to provide an encoded video or decoded video, and the encoder / decoder module 130 may include its own processor and memory. The encoder / decoder module 130 represents module(s) that may be included in a device to perform the encoding and / or decoding functions. As is known, a device may include one or both of the encoding and decoding modules. Additionally, encoder / decoder module 130 may be implemented as a separate element of system 100 or may be incorporated within processor 110 as a combination of hardware and software as known to those skilled in the art.

[0017] Program code to be loaded onto processor 110 or encoder / decoder 130 to perform the various aspects described in this application may be stored in storage device 140 and subsequently loaded onto memory 120 for execution by processor 110. In accordance with various embodiments, one or more of processor 110, memory 120, storage device 140, and encoder / decoder module 130 may store one or more of various items during the performance of the processes described in this application. Such stored items may include, but are not limited to, the input video, the decoded video or portions of the decoded video, the bitstream, matrices, variables, and intermediate or final results from the processing of equations, formulas, operations, and operational logic.

[0018] In several embodiments, memory inside of the processor 110 and / or the encoder / decoder module 130 is used to store instructions and to provide working memory for processing that is needed during encoding or decoding. In other embodiments, however, a memory external to the processing device (for example, the processing device may be either the processor 110 or the encoder / decoder module 130) is used for one or more of these functions. The external memory may be the memory 120 and / or the storage device 140, for example, a dynamic volatile memory and / or a non-volatile flash memory. In several embodiments, an external non-volatile flash memory is used to store the operating system of a television. In at least one embodiment, a fast external dynamic volatile memory such as a RAM is used as working memory for video coding and decoding operations, such as for MPEG-2, JPEG Pleno, MPEG-I, HEVC, VVC or MPEG VCM.

[0019] The input to the elements of system 100 may be provided through various input devices as indicated in block 105. Such input devices include, but are not limited to, (i) an RF portion that receives an RF signal transmitted, for example, over the air by a broadcaster, (ii) a Composite input terminal, (iii) a USB input terminal, and / or (iv) an HDMI input terminal.

[0020] In various embodiments, the input devices of block 105 have associated respective input processing elements as known in the art. For example, the RF portion may be associated with elements suitable for (i) selecting a desired frequency (also referred to as selecting a signal, or band-limiting a signal to a band of frequencies), (ii) down converting the selected signal, (iii) band-limiting again to a narrower band of frequencies to select (for example) a signal frequency band which may be referred to as a channel in certain embodiments, (iv) demodulating the down converted and band-limited signal, (v) performing error correction, and (vi) demultiplexing to select the desired stream of data packets. The RF portion of various embodiments includes one or more elements to perform these functions, for example, frequency selectors, signal selectors, band-limiters, channel selectors, filters, downconverters, demodulators, error correctors, and demultiplexers. The RF portion may include a tuner that performs various of these functions, including, for example, down converting the received signal to a lower frequency (for example, an intermediate frequency or a near-baseband frequency) or to baseband. In one set-top box embodiment, the RF portion and its associated input processing element receives an RF signal transmitted over a wired (for example, cable) medium, and performs frequency selection by filtering, down converting, and filtering again to a desired frequency band. Various embodiments rearrange the order of the above-described (and other) elements, remove some of these elements, and / or add other elements performing similar or different functions. Adding elements may include inserting elements in between existing elements, for example, inserting amplifiers and an analog-to-digital converter. In various embodiments, the RF portion includes an antenna.

[0021] Additionally, the USB and / or HDMI terminals may include respective interface processors for connecting system 100 to other electronic devices across USB and / or HDMI connections. It is to be understood that various aspects of input processing, for example, Reed- Solomon error correction, may be implemented, for example, within a separate input processing IC or within processor 110 as necessary. Similarly, aspects of USB or HDMI interface processing may be implemented within separate interface ICs or within processor 110 as necessary. The demodulated, error corrected, and demultiplexed stream is provided to various processing elements, including, for example, processor 110, and encoder / decoder 130 operating in combination with the memory and storage elements to process the datastream as necessary for presentation on an output device.

[0022] Various elements of system 100 may be provided within an integrated housing. Within the integrated housing, the various elements may be interconnected and transmit data therebetween using suitable connection arrangement 115, for example, an internal bus as known in the art, including the I2C bus, wiring, and printed circuit boards.

[0023] The system 100 includes communication interface 150 that enables communication with other devices via communication channel 190. The communication interface 150 may include, but is not limited to, a transceiver configured to transmit and to receive data over communication channel 190. The communication interface 150 may include, but is not limited to, a modem or network card and the communication channel 190 may be implemented, for example, within a wired and / or a wireless medium.

[0024] Data is streamed to the system 100, in various embodiments, using a Wi-Fi network such as IEEE 802. 11. The Wi-Fi signal of these embodiments is received over the communications channel 190 and the communications interface 150 which are adapted for Wi- Fi communications. The communications channel 190 of these embodiments is typically connected to an access point or router that provides access to outside networks including the Internet for allowing streaming applications and other over-the-top communications. Other embodiments provide streamed data to the system 100 using a set-top box that delivers the data over the HDMI connection of the input block 105. Still other embodiments provide streamed data to the system 100 using the RF connection of the input block 105.

[0025] The system 100 may provide an output signal to various output devices, including a display 165, speakers 175, and other peripheral devices 185. The other peripheral devices 185 include, in various examples of embodiments, one or more of a stand-alone DVR, a disk player, a stereo system, a lighting system, and other devices that provide a function based on the output of the system 100. In various embodiments, control signals are communicated between the system 100 and the display 165, speakers 175, or other peripheral devices 185 using signaling such as AV. Link, CEC, or other communications protocols that enable device-to-device control with or without user intervention. The output devices may be communicatively coupled to system 100 via dedicated connections through respective interfaces 160, 170, and 180. Alternatively, the output devices may be connected to system 100 using the communications channel 190 via the communications interface 150. The display 165 and speakers 175 may be integrated in a single unit with the other components of system 100 in an electronic device, for example, a television. In various embodiments, the display interface 160 includes a display driver, for example, a timing controller (T Con) chip.

[0026] The display 165 and speaker 175 may alternatively be separate from one or more of the other components, for example, if the RF portion of input 105 is part of a separate set-top box. In various embodiments in which the display 165 and speakers 175 are external components, the output signal may be provided via dedicated output connections, including, for example, HDMI ports, USB ports, or COMP outputs.

[0027] FIG.2 illustrates a simple neural network used for implicit neural representation (INR). Such a neural network used for INR can be referred to as an INR network. For clarity, we use for illustration a 2D signal such as an image, but INR can be used for signals of any dimension. INR parameterizes a signal as a function (200), which takes coordinates (210) as input and outputs approximated values (220) of a signal at these coordinates. INR has recently been applied to images, 2D videos or 3D objects among other applications. In the image case, the inputs (210) can be pixel coordinates ^ ^^, ^^^ and the INR may output (220) the color values ^ ^^, ^^, ^^^ or ^ ^^, ^^, ^^^ of the input pixels. In the video case, the input can include the frame index ^^ in addition to pixel coordinates.

[0028] The input coordinates may be modified by a transformation before being used as input for the neural network. This transformation can be a Fourier mapping, coordinate transformation, normalization etc. In this document, we will illustrate our methods using the Fourier mapping, where an input point with ^ ^^, ^^^ pixel coordinates is mapped into a higher dimensional feature space before being passed through the network: ^^^ ^^^ ൌ ^ ^^ ^^ ^^^2π ^^ ^^^, ^^ ^^ ^^^2π ^^ ^^^^்(1) where B is a random Gaussian matrix, whose each entry is drawn independently from a normal distribution N(0, σ2).

[0029] The INR can be used to reconstruct a signal by computing the signal values for every necessary coordinate input. It can be used to upsample a signal by generating output for input coordinates corresponding to the upsampled pixels, for example the mean of the coordinates between two consecutive pixels for upsampling by a factor of 2.

[0030] An INR network (200) is typically a neural network composed of multiple neural layers, such as fully connected layers. In FIG. 2, the network has four neural layers. Intermediate outputs are represented by circles. Each neural layer can be described as a function that first multiplies the input by a tensor, adds a vector called the bias and then applies a nonlinear function on the resulting values. In this document, we may also refer to “neural layer” simply as “layer.” The shape (and other characteristics) of the tensor and the type of non-linear functions are called the architecture of the network. We will denote the values of the tensor and the bias by the term “weights”. The weights and, if applicable, the parameters of the non- linear functions, are called the parameters ^^ of the network. The architecture and the parameters define a “model”. We will use ^^ఏto denote an INR function parameterized by ^^.

[0031] FIG. 3 illustrates a typical process to encode a signal using INR. This is done by optimizing (310) the parameters ^^ (or a subset of them) of the INR network to reconstruct the signal and optionally encoding (320) parameters to create the output bitstream. For an image ^^ of size ^ ^^ ൈ ^^^, the parameters θ or (the chosen subset) can for example be optimized by minimizing the following loss function: ^^ ^^ ^^ ^^ ൌ ^^^ ^^, ^^^^^ ^ ^^ ^^^ ^^^ (2) ^ where ^^ is a (reconstructed) by ^^ఏand the original image ^^, ^^ is the bitrate of the encoded parameters and ^^ a trade-off parameter between ^^ and ^^, ^^ could be any differentiable distortion measure, such as mean squared error as shown in Eq. (3), and M and N are the width and height of an image, respectively. Other metrics such as LPIPS (Learned Perceptual Image Patch Similarity) can also be used in this case. The optimization of the parameters ^^ is typically performed by a machine learning approach such as a batch / stochastic gradient descent method.

[0032] To decompress the signal, ^^ఏis evaluated at all relevant coordinates. These coordinates can be selected at decoding. A typical choice would be all pixel coordinates for an image or video. As an example, for a 256x256 pixel image, these coordinates could be all pairs ^ ^^, ^^^ for all ^^ ∈ ^0,1, … ,255^ and ^^ ∈ ^0,1, … ,255^. Other choices are possible, for example to upsample, downsample or extend the original image.

[0033] In this document, we describe a method to compress an image or a video, using a learned dictionary of INR representation that has been known or trained beforehand, instead of a simple function ^^^^. The training of the dictionary can be performed, for example, as described in a commonly owned EP Application No. 23306188.6 (“Approximating Implicit Neural Representation through Learnt Dictionary Atoms”, hereinafter ‘188), where we propose to decompose the INR network into head and tail layers, where the head layers are responsible for the global information and tail for the local information and the weights of the head layers are approximated through the dictionary basis.

[0034] The INR method is trained for each sample to be encoded and transmitted. In one embodiment, we assume that a collection, or dictionary, of INR networks is known by both the encoder and decoder, and propose to leverage the collection of dictionary functions, to train an INR representation with sparsity constraints.

[0035] In the following, a dictionary-aware training method is first described, which leads to an encoding of the image using a linear regression of dictionary functions. We then describe the modified bitstream that will be used to encode the image / video, and the procedure used to decode the image / video.

[0036] Let us assume that a collection of INR functions is known by the encoder and decoder. These functions may be chosen randomly, learned on the first frame of a video sequence, or learned using a large database of images. Let us refer to this basis of INR functions as a collection of ^^ functions parametrized by the vectors ^^^, … , ^^^, leading to the corresponding functions Ϝ ൌ ^ ^^ఏభ, … , ^^ఏೖ^. We may approximate or represent an input signal ^^^ ^^, ^^^ as: ^^^ ^^, ^^^ ^ ∑^^ୀ^^^^^^ఏ^^ ^^, ^^^ , (4) where ^^^are linear weights. where the head layers are dictionary based, the input signal ^^^^^, ^^^can be represented as: ^^^ ^^, ^^^ ^ ^^ ∘ ∑^^ୀ^^^^^^ఏ^^ ^^, ^^^ , (5) where ^^ represents the tail

[0037] One may interpret these functions (Ϝ ൌ ^ ^^ఏభ, … , ^^ఏೖ^) as basis functions that ideally decompose any input signal as orthogonal the functions will be referred to as atoms, dictionary components, or basis functions. All these terminologies refer to the same functions.

[0038] In one embodiment, we propose to leverage this collection of basis functions to represent, compress and transmit an image or video. FIG. 4 illustrates the process at the encoder, and FIG.5 illustrates the process at the decoder, according to this embodiment.

[0039] Overfit the INR with a given collection of basis functions (410)

[0040] The function set Ϝ is first used to represent the image function ^^ , for example, as described in Eq. (4) or (5). This approximation can be performed on the entire image, or a set of image partitions without any loss of generality. Relating an INR function to a CTU has been described in a commonly owned EP Application No.23305282.8 (“Coding Unit Based Implicit Neural Representation (INR)”).

[0041] We propose here to perform the INR training using explicitly the set Ϝ. This can be achieved as the optimization of the following cost: ^^^, ^^̂ ൌ ^^ ^^ ^^m^^i,௧n ∑^௫,௬^∈^ห ^^^ ^^, ^^^ െ ^^ ∘ ∑^^ୀ^^^^^^ఏ^^ ^^, ^^^ หଶ^ ^^| ^^|^^ ^^ | ^^|^(6) where ^^ ൌ ^ ^^^, … , ^^^^, blocks, superpixels, etc), ^^ is parametrized as a low-capacity neural network and serves the purpose of a local adaptation or fine-tuning. The coefficients ^^^play the role of linear mixing of the INR dictionary components. In the ‘188 application, the dictionaries ( ^^^) are learned on the weights to more efficiently represent the weights. In this work, we use the dictionary components ( ^^ఏ^) to overfit the input image / video for more efficient compression of the image / video. In general, because now the optimization is more direct on representing the image / video, it should have a closer representation of the image / video to be encoded. Here, the optimization is based on representation in Eq. (5). The optimization can also be performed when the image / video is represented as in Eq. (4) or in other forms.

[0042] In one variation, the atom functions ^^ఏ^are MLP (Multi-Layer Perceptron) containing only a linear combination of input without the bias term. The biases can be added during this INR overfitting phase, leading to an additional set of coefficients ^^^to be transmitted.

[0043] The second (and optional) term is a L1 norm on the coefficients ^^ and stands as a proxy for L0 norm. Its role is to enforce some sparsity constraint on the coefficients, so that a minimal number of atoms is used, leading to a smaller number of coefficients to transmit. A hyperparameter ^^ is chosen to control the level of sparsity of ^^ . Alternatively, another sparsity-enforcing norm could be used here like L0 norm.

[0044] A third (and optional) term is a L1 norm on the tail network coefficients ^^௧and stands as a proxy for L0 norm. Its role is to enforce some sparsity constraint on the tail coefficients ^^௧, so that a minimal number of tail parameters is used, leading to a smaller number of coefficients to transmit. A hyperparameter ^^ is chosen to control the level of sparsity of ^^௧. Alternatively, another sparsity-enforcing norm could be used here like L0 norm.

[0045] Once the parameters are found by optimization, the image on domain ^^ can be represented by the coefficients ^^ and ^^ (and eventually biases ^^) as: ^^^ ^^, ^^^ ^ ^^ ∘ ∑^^ୀ^^^^^^ఏ^^ ^^, ^^^ . (7)

[0046] Because of the input signal can be represented by a small number of basis functions (selected from Ϝ ൌ ^ ^^ఏభ, … , ^^ఏೖ^). Further, as the basis functions Ϝ ൌ ^ ^^ఏభ, … , ^^ఏೖ^ are known at both the encoder and decoder, we only need to signal which coefficients (^ ^^^, … , ^^^^, ^^௧) are non-zero and the values of these non-zero coefficients. By using the INR basis functions, different partitions can be represented as different combinations of the basis functions. For example, partition 1 may be represented by ^^ఏభand ^^ఏమ, and partition 2 may be represented by ^^ఏభ, ^^ఏమ and ^^ఏయ. In another example, two partitions may be both represented by ^^ఏభand ^^ఏమ, however they are weighted by different ^^^and ^^ଶvalues. Thus, such a design can adapt to different regions better than using a single INR function designed for the entire image.

[0047] In a derivative embodiment, a first minimization is performed. Then, the smallest ^^^coefficients are set to zero, for example, coefficient ^^^is set to 0 if the value of ^^^is a threshold or a threshold on the number of coefficients to retain can be used. Then, the loss function is minimized again with these zero values. In particular, if a coefficient ^^^is set to 0, it is forced to zero in the second minimization, while other coefficients are re-calculated.

[0048] Quantize parameters (420)

[0049] Once the parameters are estimated, they should be quantized to be transmitted over the network. We here describe a simple procedure to do so. It should be noted that other techniques could be used. ^ For each set of parameters ^^, ^^, the maximal value is found: ^^^ൌ m ^ax ^^^(similarly for ^^௧). ^ The values are normalized as: ^^^^ൌ ^^^ / ^^^(similarly for ^^௧^. ^ Fixed bit quantization using 2^bits is performed to obtain the symbols to be transmitted ^^^^ൌ ^^^ ^^^^^ ൌ ^^ ^^ ^^ ^^ ^^^ ^^^^∗ ^2^െ 1^^ (similarly for ^^^ ^^^^^. ^ In a the tail layers of the INR network are re-trained using the quantized values for all parameters, meaning that the linear regression coefficients ( ^^) and the tail network coefficients ( ^^௧) are replaced by the dequantized values: ^^^ൌ ^^ି^^^^^^^ൌ ఈ^^ଶ^ି^∗ ^^^(similarly for tail parameters, and eventually biases).

[0050] Encode parameters (430)

[0051] The bitstream to be transmitted is modified to include all information needed to reconstruct the linear regression weights, as well as the tail coefficients: o The quantization value q is first transmitted, for example, prior to any INR representation. o Then, for each image partition / region, the bitstream includes: ^ The maximum value ^^^, ^^^; ^ The quantized values of symbols ^^^^, ^^^௧^, encoded using any available method.

[0052] Decode the bitstream

[0053] At the decoder side, we apply the following process to decode (510) the bitstream: ^ The quantization value q is decoded. ^ For each partition / region of the image, the following values are decoded: o The maximum value ^^^, ^^^; o The list of quantized values ^^^^, ^^^௧^. ^ All coefficients are dequantizedି^ : ^^ ^ ^^^^^ ൌఈ^^ଶ^ି^∗ ^^^. Same for the tail network coefficients ^^ି^൫ ^^^௧^൯.

[0054] Decode the whole image / video)

[0055] To reconstruct the image, based on the decoded linear regression coefficients and tail coefficients, for each partition / region, ^ the networks are reconstructed (530) using the known functions Ϝ. Then the signal values are computed by performing (540) inference using the appropriate INR and using as inputs coordinates within each partition / region.

[0056] In the above, the proposed methods are mainly described with respects to 2D video compression. However, INR is investigated for many other signals, in particular 3D scenes or objects, and the proposed methods can be used for any signal. With respect to the bitstream, we mention that the bitstream is to be transmitted. It should be noted that the bitstream can also be stored in a storage.

[0057] While in the above the unmodified coordinates of the image are used as input and rgb values are output. More generally, the input / output can be in other representations. For example, the input can be normalized coordinates, or the output can be in the YUV format. In addition, the image itself could also be encoded differently, for example, the output could be Fourier or Cosine transforms coefficients.

[0058] Various numeric values are used in the present application. The specific values are for example purposes and the aspects described are not limited to these specific values.

[0059] Various methods are described herein, and each of the methods comprises one or more steps or actions for achieving the described method. Unless a specific order of steps or actions is required for proper operation of the method, the order and / or use of specific steps and / or actions may be modified or combined. Additionally, terms such as “first”, “second”, etc. may be used in various embodiments to modify an element, component, step, operation, etc., such as, for example, a “first decoding” and a “second decoding”. Use of such terms does not imply an ordering to the modified operations unless specifically required. So, in this example, the first decoding need not be performed before the second decoding, and may occur, for example, before, during, or in an overlapping time period with the second decoding.

[0060] The implementations and aspects described herein may be implemented in, for example, a method or a process, an apparatus, a software program, a data stream, or a signal. Even if only discussed in the context of a single form of implementation (for example, discussed only as a method), the implementation of features discussed may also be implemented in other forms (for example, an apparatus or program). An apparatus may be implemented in, for example, appropriate hardware, software, and firmware. The methods may be implemented in, for example, an apparatus, for example, a processor, which refers to processing devices in general, including, for example, a computer, a microprocessor, an integrated circuit, or a programmable logic device. Processors also include communication devices, for example, computers, cell phones, portable / personal digital assistants (“PDAs”), and other devices that facilitate communication of information between end-users.

[0061] Reference to “one embodiment” or “an embodiment” or “one implementation” or “an implementation”, as well as other variations thereof, means that a particular feature, structure, characteristic, and so forth described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrase “in one embodiment” or “in an embodiment” or “in one implementation” or “in an implementation”, as well any other variations, appearing in various places throughout this application are not necessarily all referring to the same embodiment.

[0062] Additionally, this application may refer to “determining” various pieces of information. Determining the information may include one or more of, for example, estimating the information, calculating the information, predicting the information, or retrieving the information from memory.

[0063] Further, this application may refer to “accessing” various pieces of information. Accessing the information may include one or more of, for example, receiving the information, retrieving the information (for example, from memory), storing the information, moving the information, copying the information, calculating the information, determining the information, predicting the information, or estimating the information.

[0064] Additionally, this application may refer to “receiving” various pieces of information. Receiving is, as with “accessing”, intended to be a broad term. Receiving the information may include one or more of, for example, accessing the information, or retrieving the information (for example, from memory). Further, “receiving” is typically involved, in one way or another, during operations, for example, storing the information, processing the information, transmitting the information, moving the information, copying the information, erasing the information, calculating the information, determining the information, predicting the information, or estimating the information.

[0065] It is to be appreciated that the use of any of the following “ / ”, “and / or”, and “at least one of”, for example, in the cases of “A / B”, “A and / or B” and least one of A and B”, is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of both options (A and B). As a further example, in the cases of “A, B, and / or C” and “at least one of A, B, and C”, such phrasing is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of the third listed option (C) only, or the selection of the first and the second listed options (A and B) only, or the selection of the first and third listed options (A and C) only, or the selection of the second and third listed options (B and C) only, or the selection of all three options (A and B and C). This may be extended, as is clear to one of ordinary skill in this and related arts, for as many items as are listed.

[0066] As will be evident to one of ordinary skill in the art, implementations may produce a variety of signals formatted to carry information that may be, for example, stored or transmitted. The information may include, for example, instructions for performing a method, or data produced by one of the described implementations. For example, a signal may be formatted to carry the bitstream of a described embodiment. Such a signal may be formatted, for example, as an electromagnetic wave (for example, using a radio frequency portion of spectrum) or as a baseband signal. The formatting may include, for example, encoding a data stream and modulating a carrier with the encoded data stream. The information that the signal carries may be, for example, analog or digital information. The signal may be transmitted over a variety of different wired or wireless links, as is known. The signal may be stored on a processor-readable medium.

Claims

CLAIMS 1. A method of decoding video data representative of an image or a 3D scene, comprising: obtaining one or more coefficients corresponding to one or more INR (Implicit Neural Representation) basis functions for a region of said image or 3D scene, wherein said one or more INR basis functions are selected from a set of INR basis functions; weighting said one or more INR basis functions by said one or more coefficients, respectively; combining said weighted one or more INR basis functions to form an INR function; and reconstructing said region based on said INR function.

2. A method of encoding video data representative of an image or a 3D scene, comprising: obtaining one or more coefficients corresponding to one or more INR (Implicit Neural Representation) basis functions for a region of said image or 3D scene, wherein said one or more INR basis functions are selected from a set of INR basis functions; weighting said one or more INR basis functions by said one or more coefficients, respectively; combining said weighted one or more INR basis functions to form an INR function; and reconstructing said region based on said INR function.

3. The method of claim 2, wherein said obtaining one or more coefficients comprises: obtaining a plurality of reconstructed versions of said image or 3D scene based on a plurality of respective combinations of said set of basis functions; forming a plurality of respective differences between said image or 3D scene and said plurality of reconstructed versions; and selecting said one or more coefficients based on said plurality of respective differences between said image or 3D scene and said plurality of reconstructed versions.

4. The method of any one of claims 1-3, wherein said INR function represents head layers of an INR network, further comprising:applying a neural network to said INR function, wherein said neural network corresponds to tail layers of said INR network.

5. The method of claim 4, wherein said neural network is a low-capacity neural network.

6. The method of any one of claims 1-5, further comprising: obtaining another one or more coefficients corresponding to another one or more INR basis functions for another region of said image or 3D scene, wherein said another one or more INR basis functions are selected from said set of INR basis functions; weighting said another one or more INR basis functions by said another one or more coefficients, respectively; combining said weighted another one or more INR basis functions to form another INR function; and reconstructing said another region based on said another INR function.

7. The method of claim 6, wherein said one or more INR basis functions for said region are different than said another one or more INR basis functions for said another region.

8. The method of claim 6, wherein said one or more INR basis functions for said region are same as said another one or more INR basis functions for said another region, and wherein said one or more coefficients for said one or more INR basis functions are different than said another one or more coefficients for said another one or more INR basis functions.

9. The method of any one of claims 1 and 3-8, wherein said obtaining one or more coefficients comprises: decoding signal indicating values of said one or more coefficients corresponding to said selected one or more INR basis functions.

10. An apparatus for decoding video data representative of an image or a 3D scene, comprising at least one memory or one or more processors, wherein said one or more processors are configured to: obtain one or more coefficients corresponding to one or more INR (Implicit Neural Representation) basis functions for a region of said image or 3D scene, wherein said one or more INR basis functions are selected from a set of INR basis functions;weight said one or more INR basis functions by said one or more coefficients, respectively; combine said weighted one or more INR basis functions to form an INR function; and reconstruct said region based on said INR function.

11. An apparatus for encoding video data representative of an image or a 3D scene, comprising at least one memory and one or more processors, wherein said one or more processors are configured to: obtain one or more coefficients corresponding to one or more INR (Implicit Neural Representation) basis functions for a region of said image or 3D scene, wherein said one or more INR basis functions are selected from a set of INR basis functions; weight said one or more INR basis functions by said one or more coefficients, respectively; combine said weighted one or more INR basis functions to form an INR function; and reconstruct said region based on said INR function.

12. The apparatus of claim 11, wherein said one or more processors are configured to obtain one or more coefficients by performing: obtaining a plurality of reconstructed versions of said image or 3D scene based on a plurality of respective combinations of said set of basis functions; forming a plurality of respective differences between said image or 3D scene and said plurality of reconstructed versions; and selecting said one or more coefficients based on said plurality of respective differences between said image or 3D scene and said plurality of reconstructed versions.

13. The apparatus of any one of claims 10-12, wherein said INR function represents head layers of an INR network, said one or more processors are further configured to: apply a neural network to said INR function, wherein said neural network corresponds to tail layers of said INR network.

14. The apparatus of claim 13, wherein said neural network is a low-capacity neural network.

15. The apparatus of any one of claims 10-14, wherein said one or more processors are further configured to:obtain another one or more coefficients corresponding to another one or more INR basis functions for another region of said image or 3D scene, wherein said another one or more INR basis functions are selected from said set of INR basis functions; weight said another one or more INR basis functions by said another one or more coefficients, respectively; combine said weighted another one or more INR basis functions to form another INR function; and reconstruct said another region based on said another INR function.

16. The apparatus of claim 15, wherein said one or more INR basis functions for said region are different than said another one or more INR basis functions for said another region.

17. The apparatus of claim 15, wherein said one or more INR basis functions for said region are same as said another one or more INR basis functions for said another region, and wherein said one or more coefficients for said one or more INR basis functions are different than said another one or more coefficients for said another one or more INR basis functions.

18. The apparatus of any one of claims 10 and 12-17, wherein said one or more processors are configured to obtain one or more coefficients by performing: decoding signal indicating values of said one or more coefficients corresponding to said selected one or more INR basis functions.

19. A signal comprising video data representative of an image or a 3D scene, formed by performing the method of any one of claims 2-9.

20. A computer readable storage medium having stored thereon instructions for encoding or decoding video data according to the method of any one of claims 1-9.

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