WO2017131900A1 - Motion vector prediction using prior frame residual - Google Patents
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- WO2017131900A1 WO2017131900A1 PCT/US2016/067792 US2016067792W WO2017131900A1 WO 2017131900 A1 WO2017131900 A1 WO 2017131900A1 US 2016067792 W US2016067792 W US 2016067792W WO 2017131900 A1 WO2017131900 A1 WO 2017131900A1
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Definitions
- Digital video streams typically represent video using a sequence of frames or still images. Each frame can include a number of blocks, which in turn may contain information describing the value of color, brightness or other attributes for pixels.
- the amount of data in a video stream is large, and transmission and storage of video can use significant computing or communications resources. Due to the large amount of data involved in video data, high performance compression is needed for transmission and storage. This often involves inter prediction using motion vectors.
- This disclosure relates in general to encoding and decoding visual data, such as video stream data, using motion vector prediction using a prior frame residual.
- One aspect of an apparatus described herein is an apparatus for encoding or decoding a video signal, the video signal including frames defining a video sequence, the frames having blocks formed of pixels.
- the apparatus comprises a processor and a non- transitory memory that stores includes instruction causing the processor to perform a method including generating a mask for a current block within a current frame in the video sequence from a residual that is a difference between pixel values of at least two frames other than the current frame, and encoding or decoding the current block by inter-prediction using the mask.
- FIG. 1 Another aspect of an apparatus described herein is an apparatus for generating a mask for encoding or decoding a current block of a video signal, the video signal including frames defining a video sequence, the frames having blocks, and the blocks formed of pixels.
- the apparatus comprises a processor and a non-transitory memory that stores includes instruction causing the processor to perform a method including calculating a residual by subtracting pixel values within a first frame from pixel values within a second frame, each of the first frame and the second frame located before the current frame within the video sequence, applying a threshold value to pixel values for respective pixel locations within the residual to generate a threshold residual comprising pixels, each pixel within the threshold residual having one of a first value or a second value different from the first value, and expanding at least one of a first area of the threshold residual comprising pixels having the first value or a second area of the threshold residual comprising pixels having the second value to form the mask having a first contiguous portion of pixel locations with the first value and a second contiguous portion
- FIG. 1 is a schematic of a video encoding and decoding system.
- FIG. 2 is a block diagram of an example of a computing device that can implement a transmitting station or a receiving station.
- FIG. 5 is a block diagram of a video decompression system according to another aspect of the teachings herein.
- FIG. 6 is a flowchart diagram of a process for encoding or decoding a block by motion vector prediction using a prior frame residual according to one implementation of this disclosure.
- a video stream may be compressed by a variety of techniques to reduce bandwidth required transmit or store the video stream.
- a video stream can be encoded into a bitstream, which can involve compression, and then transmitted to a decoder that can decode or decompress the video stream to prepare it for viewing or further processing.
- Encoding a video stream can involve parameters that make trade-offs between video quality and bitstream size, where increasing the perceived quality of a decoded video stream can increase the number of bits required to transmit or store the bitstream.
- the teachings herein describe the generation and use of an inter- predictor that does not require (e.g., square) blocks so as to better match objects within a frame. This can be implemented by using the residual of a prior frame to create a cliff mask for a block that allows two different motion vectors to be applied to the block. Further details are described after an initial discussion of the environment in which the teachings herein may be used.
- a network 104 can connect the transmitting station 102 and a receiving station 106 for encoding and decoding of the video stream.
- the video stream can be encoded in the transmitting station 102 and the encoded video stream can be decoded in the receiving station 106.
- the network 104 can be, for example, the Internet.
- the network 104 can also be a local area network (LAN), wide area network (WAN), virtual private network (VPN), cellular telephone network or any other means of transferring the video stream from the transmitting station 102 to, in this example, the receiving station 106.
- the receiving station 106 in one example, can be a computer having an internal configuration of hardware such as that described in FIG. 2. However, other suitable implementations of the receiving station 106 are possible. For example, the processing of the receiving station 106 can be distributed among multiple devices.
- a video stream can be encoded and then stored for transmission at a later time to the receiving station 106 or any other device having memory.
- the receiving station 106 receives (e.g., via the network 104, a computer bus, and/or some communication pathway) the encoded video stream and stores the video stream for later decoding.
- a real-time transport protocol RTP
- a transport protocol other than RTP may be used, e.g., a Hypertext Transfer Protocol (HTTP)- based video streaming protocol.
- HTTP Hypertext Transfer Protocol
- the transmitting station 102 and/or the receiving station 106 may include the ability to both encode and decode a video stream as described below.
- the receiving station 106 could be a video conference participant who receives an encoded video bitstream from a video conference server (e.g., the transmitting station 102) to decode and view and further encodes and transmits its own video bitstream to the video conference server for decoding and viewing by other participants.
- FIG. 2 is a block diagram of an example of a computing device 200 that can implement a transmitting station or a receiving station.
- the computing device 200 can implement one or both of the transmitting station 102 and the receiving station 106 of FIG. 1.
- the computing device 200 can be in the form of a computing system including multiple computing devices, or in the form of a single computing device, for example, a mobile phone, a tablet computer, a laptop computer, a notebook computer, a desktop computer, and the like.
- the computing device 200 can also include one or more output devices, such as a display 218.
- the display 218 may be, in one example, a touch sensitive display that combines a display with a touch sensitive element that is operable to sense touch inputs.
- the display 218 can be coupled to the CPU 202 via the bus 212.
- Other output devices that permit a user to program or otherwise use the computing device 200 can be provided in addition to or as an alternative to the display 218.
- the output device is or includes a display
- the display can be implemented in various ways, including by a liquid crystal display (LCD), a cathode-ray tube (CRT) display or light emitting diode (LED) display, such as an organic LED (OLED) display.
- LCD liquid crystal display
- CRT cathode-ray tube
- LED light emitting diode
- OLED organic LED
- FIG. 2 depicts the CPU 202 and the memory 204 of the computing device 200 as being integrated into a single unit, other configurations can be utilized.
- the operations of the CPU 202 can be distributed across multiple machines (each machine having one or more of processors) that can be coupled directly or across a local area or other network.
- the memory 204 can be distributed across multiple machines such as a network- based memory or memory in multiple machines performing the operations of the computing device 200.
- the bus 212 of the computing device 200 can be composed of multiple buses.
- the secondary storage 214 can be directly coupled to the other components of the computing device 200 or can be accessed via a network and can comprise a single integrated unit such as a memory card or multiple units such as multiple memory cards.
- the computing device 200 can thus be implemented in a wide variety of configurations.
- the frame 306 may be further subdivided into blocks 310, which can contain data corresponding to, for example, 16x16 pixels in frame 306.
- the blocks 310 can also be arranged to include data from one or more planes of pixel data.
- the blocks 310 can also be of any other suitable size such as 4x4 pixels, 8x8 pixels, 16x8 pixels, 8x16 pixels, 16x16 pixels or larger. Unless otherwise noted, the terms block and macroblock are used interchangeably herein.
- the frame 306 may be partitioned according to the teachings herein as discussed in more detail below.
- the frame 306 can be processed in units of blocks.
- a block can be encoded using intra-frame prediction (also called intra prediction) or inter-frame prediction (also called inter prediction or inter-prediction herein).
- intra-frame prediction also called intra prediction
- inter-frame prediction also called inter prediction or inter-prediction herein
- a prediction block can be formed.
- intra-prediction a prediction block may be formed from samples in the current frame that have been previously encoded and reconstructed.
- inter- prediction a prediction block may be formed from samples in one or more previously constructed reference frames as discussed in more detail below.
- the prediction block can be subtracted from the current block at the intra/inter prediction stage 402 to produce a residual block (also called a residual).
- the transform stage 404 transforms the residual into transform coefficients in, for example, the frequency domain using block-based transforms.
- block-based transforms include, for example, the Discrete Cosine Transform (DCT) and the Asymmetric Discrete Sine Transform (ADST).
- DCT Discrete Cosine Transform
- ADST Asymmetric Discrete Sine Transform
- combinations of different transforms may be applied to a single residual.
- the DCT transforms the residual block into the frequency domain where the transform coefficient values are based on spatial frequency.
- the lowest frequency (DC) coefficient at the top-left of the matrix and the highest frequency coefficient at the bottom- right of the matrix may be different from the size of the transform block.
- the prediction block may be split into smaller blocks to which separate transforms are applied.
- the reconstruction path in FIG. 4 can be used to ensure that both the encoder 400 and a decoder 500 (described below) use the same reference frames to decode the compressed bitstream 420.
- the reconstruction path performs functions that are similar to functions that take place during the decoding process that are discussed in more detail below, including dequantizing the quantized transform coefficients at the dequantization stage 410 and inverse transforming the dequantized transform coefficients at the inverse transform stage 412 to produce a derivative residual block (also called a derivative residual).
- the prediction block that was predicted at the intra/inter prediction stage 402 can be added to the derivative residual to create a reconstructed block.
- the loop filtering stage 416 can be applied to the reconstructed block to reduce distortion such as blocking artifacts.
- encoder 400 can be used to encode the compressed bitstream 420.
- a non-transform based encoder 400 can quantize the residual signal directly without the transform stage 404 for certain blocks or frames.
- an encoder 400 can have the quantization stage 406 and the dequantization stage 410 combined into a single stage.
- FIG. 5 is a block diagram of a decoder 500 in accordance with another implementation.
- the decoder 500 can be implemented in the receiving station 106, for example, by providing a computer software program stored in the memory 204.
- the computer software program can include machine instructions that, when executed by a processor such as the CPU 202, cause the receiving station 106 to decode video data in the manner described in FIG. 5.
- the decoder 500 can also be implemented in hardware included in, for example, the transmitting station 102 or the receiving station 106.
- the decoder 500 similar to the reconstruction path of the encoder 400 discussed above, includes in one example the following stages to perform various functions to produce an output video stream 516 from the compressed bitstream 420: an entropy decoding stage 502, a dequantization stage 504, an inverse transform stage 506, an intra/inter prediction stage 508, a reconstruction stage 510, a loop filtering stage 512 and a deblocking filtering stage 514.
- stages to perform various functions to produce an output video stream 516 from the compressed bitstream 420 includes in one example the following stages to perform various functions to produce an output video stream 516 from the compressed bitstream 420: an entropy decoding stage 502, a dequantization stage 504, an inverse transform stage 506, an intra/inter prediction stage 508, a reconstruction stage 510, a loop filtering stage 512 and a deblocking filtering stage 514.
- Other structural variations of the decoder 500 can be used to decode the compressed bitstream 420.
- the decoder 500 can use the intra/inter prediction stage 508 to create the same prediction block as was created in the encoder 400, e.g., at the intra/inter prediction stage 402.
- the prediction block can be added to the derivative residual to create a reconstructed block.
- the loop filtering stage 512 can be applied to the reconstructed block to reduce blocking artifacts. Other filtering can be applied to the reconstructed block.
- the deblocking filtering stage 514 is applied to the reconstructed block to reduce blocking distortion, and the result is output as an output video stream 516.
- the output video stream 516 can also be referred to as a decoded video stream, and the terms will be used
- decoder 500 can be used to decode the compressed bitstream 420.
- the decoder 500 can produce the output video stream 516 without the deblocking filtering stage 514.
- a block may be encoded or decoded by motion vector prediction using a prior frame residual.
- a mask for the block is generated from a residual calculated between pixels of two frames (e.g., the last two frames before the current frame), and then the block is encoded or decoded by inter-prediction using the mask.
- a mask that allows two different motion vectors to be applied to a block can be used to better match objects within an image, improving video compression.
- FIG. 6 is a flowchart diagram of a process 600 for encoding or decoding a block by motion vector prediction using a prior frame residual according to one implementation of this disclosure.
- the method or process 600 can be implemented in a system such as the computing device 200 to aid the encoding or decoding of a video stream.
- the process 600 can be implemented, for example, as a software program that is executed by a computing device such as the transmitting station 102 or the receiving station 106.
- the software program can include machine-readable instructions that are stored in a memory such as the memory 204 that, when executed by a processor such as the CPU 202, cause the computing device to perform the process 600.
- the process 600 can also be implemented using hardware in whole or in part.
- computing devices may have multiple memories and multiple processors, and the steps or operations of the process 600 may in such cases be distributed using different processors and memories.
- processors and “memory” in the singular herein encompasses computing devices that have only one processor or one memory as well as devices having multiple processors or memories that may each be used in the performance of some but not necessarily all recited steps.
- process 600 is depicted and described as a series of steps or operations. However, steps and operations in accordance with this disclosure can occur in various orders and/or concurrently. Additionally, steps or operations in accordance with this disclosure may occur with other steps or operations not presented and described herein. Furthermore, not all illustrated steps or operations may be required to implement a method in accordance with the disclosed subject matter.
- the process 600 may be repeated for each frame of the input signal.
- the input signal can be, for example, the video stream 300.
- the input signal can be received by the computing performing the process 600 in any number of ways.
- the input signal can be captured by the image-sensing device 220 or received from another device through an input connected to the bus 212.
- the input signal could be retrieved from the secondary storage 214 in another implementation.
- Other ways of receiving and other sources of the input signal are possible.
- the input signal can be an encoded bitstream such as the compressed bitstream 420.
- FIG. 7 is a flowchart diagram of a process 700 for generating a mask using a prior frame residual according to one implementation of this disclosure.
- FIGS. 8A-8C are diagrams used to explain the process 700 of FIG. 7.
- the method or process 700 can be implemented in a system such as the computing device 200 to aid the encoding or decoding of a video stream.
- the process 700 can be implemented, for example, as a software program that is executed by a computing device such as the transmitting station 102 or the receiving station 106.
- the software program can include machine-readable instructions that are stored in a memory such as the memory 204 that, when executed by a processor such as the CPU 202, cause the computing device to perform the process 700.
- the process 700 can also be implemented using hardware in whole or in part. As explained above, some computing devices may have multiple memories and multiple processors, and the steps or operations of the process 700 may in such cases be distributed using different processors and memories.
- the process 700 is depicted and described as a series of steps or operations. However, steps and operations in accordance with this disclosure can occur in various orders and/or concurrently. Additionally, steps or operations in accordance with this disclosure may occur with other steps or operations not presented and described herein. Furthermore, not all illustrated steps or operations may be required to implement a method in accordance with the disclosed subject matter.
- the process 700 may be repeated for each block or each frame of the input signal.
- generating the mask includes calculating a residual between two frames at 702. More specifically, the residual may be calculated by subtracting pixel values within a first frame from pixel values within a second frame or vice versa.
- the first and second frames may be located before the current frame within a video sequence defined by the input signal.
- the first and second frames may be adjacent frames, but more desirably they are separated by one or more frames within the video sequence and a defined amount of time.
- the defined amount of time is 200 ms in an example, but other values are possible.
- the pixel values may represent, for example, the luma components or chroma components of some or all of the pixel locations within the first and second frames.
- the pixel values of pixels within the second frame are subtracted from the pixel values of collocated pixels within the first frame or vice versa. Collocated pixels have the same pixel coordinates within different frames.
- the pixels within the second frame and the collocated pixels within the first frame are collocated with pixels of the current block.
- the pixels within the second frame and the collocated pixels within the first frame are shifted by a motion vector relative to pixels of the current block.
- the pixels in one of the first frame or the second frame may be collocated with the current frame, while the pixels in the other are shifted by a motion vector relative to the current block.
- the pixel values are reconstructed pixel values obtained from the encoding and subsequent decoding process of an encoder, such as that described with respect to FIG. 4.
- the last two adjacent frames before the current frame are used.
- the last frame before the current frame may be selected, along with the frame most identified as a reference frame for the last frame.
- other frames may be selected so as to provide a residual for the mask generation process.
- the two frames may be discerned from header information within the encoded bitstream as discussed in more detail below.
- the residual can represent the entirety of a frame or only a portion of the frame. That is, the residual can be calculated for the entire dimensions of the frame or for only portions of the frame, such as a block of the frame. An example is shown in FIG. 8A.
- the residual frame (or residual) 806 As can be seen from FIG. 8A, a round object 808, such as a ball, the moon, etc. is moving from a first position in the first frame 802 to a second position in the second frame 804.
- the residual 806 shows a crescent shape 810 that is the difference between pixel values of the first frame 802 and the second frame 804.
- the residual is calculated using the entire area of a frame. However, this calculation or subsequent steps of the process 700 may be performed on a portion of the frames, e.g., a block basis.
- Generating the mask in the process 700 also includes, at 704, applying a threshold to the residual generated at 702. More specifically, the process 700 can include applying a threshold value to pixel values for respective pixel locations within the residual to generate a threshold residual.
- the threshold residual comprises pixels having the same dimensions as the residual or portion of the residual to which the threshold value is applied.
- each pixel within the threshold residual has one of a first value or a second value different from the first value.
- the threshold value could be a positive value or a negative value, or could define a range of values.
- applying the threshold value includes comparing a pixel value of respective pixel locations within the residual with the threshold value.
- a block 812 that is a portion of the residual 806 from FIG. 8 A is shown.
- the edge and hatched areas represent the movement of the round object 808 (e.g., its edge) between the first frame 802 and the second frame 804.
- Applying the threshold value to the block 812 results in the edge and hatched areas being assigned a value of 1, while other areas are assigned a value of 1.
- pixel locations within a new block (i.e., the threshold residual) that correspond to pixels within the block 812 having a value within the range of + 75 are assigned the value of 1, while other pixel locations within the threshold residual that correspond to pixels outside the range are assigned the value of 0.
- a non-island-like residual is seen across two borders, so the block 812 may generate a useful mask.
- the process 700 for generating a mask may also include modifying the threshold residual.
- the threshold residual resulting from applying the threshold to the residual at 704 is modified using, for example, a growth and/or a shrink function on the threshold residual. That is, the threshold residual is cleaned up.
- the modification involves recursively applying a grow step only right and down within the threshold residual. In such an implementation, if any neighbor above or to the left is set (i.e., has a value of 1), then the current pixel is set (i.e., is converted to the value of 1). Speed of the recursive grow may be improved by working in larger "chunks" or portions of the threshold residual.
- modifying the threshold residual includes applying a growth function to expand an area defined by a minimum number of contiguous pixels having a first value of the two values based on values of pixels adjacent to the area.
- Modifying the threshold residual at 706 may include additional steps to reduce these discontinuities.
- modifying the threshold residual includes applying a shrink function to remove an area defined by a maximum number of contiguous pixels having the first value that are surrounded by pixels having the second value of the two values or to remove an area defined by the maximum number of contiguous pixels having the second value that are surrounded by pixels having the first value. By removing the area, it means to change the values so that the first and second values form non-overlapping contiguous regions within a block or frame.
- FIG. 8C One example of a mask resulting from modifying a threshold residual is seen in FIG. 8C.
- the mask 814 is generated by thresholding the block 812 of FIG. 8B and modifying the resulting threshold residual using growth and shrink functions so that from a cliff mask with pixels on one side of a line all have a first value while pixels on the other side of the line all have a second value.
- a cliff mask can be used (e.g., just black and white)
- an optional final step in generating a mask according to the process 700 of FIG. 7 includes applying a blur to a border within the mask.
- the value of a blur will be discussed in more detail below. At this point, it is noted that the blur results in values about the border that form a smoother transition between the areas.
- the blur may be one small tap blur formed according to a variety of interpolation techniques.
- the process 700 ends once the mask is generated.
- one implementation of encoding or decoding the current block using the mask includes inter-predicting a first prediction block portion at 604, inter- predicting a second prediction block portion at 606, generating a prediction block using the portions at 608, and encoding or decoding the current block using the prediction block at 610.
- inter-predicting a first prediction block portion at 604 includes performing a first motion search within a reference frame for pixel values within a first contiguous portion of pixel locations of the current block using the mask. That is, a first motion vector that results in the best match for pixel values within the current block that are collocated with the first contiguous portion of the mask is found. The best match defines the first prediction block portion.
- inter-predicting a second prediction block portion at 606 includes performing a second motion search within a reference frame for pixel values within a second contiguous portion of pixel locations of the current block using the mask.
- Generating a prediction block using the portions at 608 when the process 600 is an encoding process may include generating the prediction block by combining a result of the first motion search with a result of the second motion search using the mask. This combining may be achieved by combining the pixels values of the best matches into a single prediction block.
- the prediction block may have pixels at positions within a first portion substantially coincident with first contiguous portion of the mask that have values corresponding to the first prediction block portion and pixels at positions within a second portion substantially coincident with the second continuous portion of the mask that have values corresponding to the second prediction block portion.
- the pixel values are a combination of pixel values in accordance with the blur.
- the mask can be modified for use in the inter-predictions of 604 and 606. That is, for example, the mask can be rotated. This changes the pixels selected for each search from the current block. Performing the motion searches thus comprise performing the first and second motion searches within the reference frame using the mask as rotated—that is, finding the best match for pixels from the current frame that are collocated with each of the separate contiguous portions of the rotated mask. Then, generating the prediction block at 608 similarly uses the mask as rotation to combine the best matches for the portions.
- the mask can also be modified for use in the inter-predictions of 604 and 606 by shifting the mask by a motion vector.
- benefits of encoding a portion of the current frame corresponding to the size of the mask may benefit from adjusting the border between the separate contiguous portions of the mask.
- the border may be adjusted by, for example, adjusting the pixel values so that the contiguous portion to one side of the mask increases in size and the contiguous portion on the opposite side of the mask decreases in size within the bounds of the mask by one of the motion vectors in a previous (e.g., the last) frame before the current frame.
- the motion vector used to move the boundary, and hence shift the mask could be a motion vector of a block of the last frame that is collocated with the current block being predicted.
- Encoding the current block using the prediction block at 610 includes generating a residual for the current block, and encoding the residual into an encoded bitstream with information necessary for decoding the current block.
- the encoding process could include processing the residual using the transform stage 404, the quantization stage 406, and the entropy encoding stage 408 as described with respect to FIG. 4.
- the information necessary for decoding the current block may include a mode indicator (sometimes called a flag) that indicates that the current block was encoded using a mask, indicators of which frames were used to generate the mask in the encoder (such as frame IDs), the motion vectors found as a result of the motion searches, the identification of the reference frame, and an indicator of any modification to the mask.
- the bitstream would include such an indication.
- the information may be included in frame, slice, segment, or block headers, and not all of the information need be transmitted in the same header. Moreover, not all information need be transmitted. For example, if there are no changes to the mask after it is generated (e.g., it is not rotated), there is no need to send an indicator of a modification. Further, if the past two frames are always used with encoding in this mask mode, there is no need to identify the two frames used within the bitstream. Other modifications are possible.
- the processing of FIG. 6 may be incorporated into one or more rate- distortion loops that perform inter-prediction using different masks (or the same masks rotated) so as to find the mask and motion vectors for encoding the current block with the lowest encoding cost (e.g., number of bits to encode).
- the process 600 is a decoding process
- generating a mask from a frame residual at 602 is performed according to FIG. 7.
- the frames used to calculate the residual are obtained from the encoded bitstream (e.g., by entropy decoding the header containing the information) when the mask mode is used.
- the frames may be known by the use of the mask mode. For example, if the prior two adjacent frames to the current frame are always used, there is no need to separately signal the identification of the frames to the decoder.
- a first motion vector for inter-predicting the first prediction block portion at 604 and a second motion vector for inter-predicting the second prediction block portion at 606 may be obtained from a header within the bitstream.
- Inter-predicting the first prediction block portion at 604 may include generating a first reference block using the first motion vector and applying the mask to the first reference block to generate a first masked reference block (i.e., the first prediction block portion).
- inter-predicting the second prediction block portion at 606 may include generating a second reference block using the second motion vector and applying the mask to the second reference block to generate a second masked reference block (i.e., the second prediction block portion).
- the prediction block is generated at 608 using the portions in a like manner as in described above with respect to the encoding process.
- Pixel prediction is used to reduce the amount of data encoded within a bitstream.
- One technique is to copy blocks of pixels from prior encoded frames using a motion vector.
- objects do not often fall on regular block boundaries.
- a predictor e.g., a prediction block
- a prediction block that better follows the edge shapes of objects and thus may improve video compression.
- example is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “example” is not necessarily to be construed as preferred or advantageous over other aspects or designs. Rather, use of the word “example” is intended to present concepts in a concrete fashion.
- the term “or” is intended to mean an inclusive “or” rather than an exclusive “or”. That is, unless specified otherwise, or clear from context, "X includes A or B” is intended to mean any of the natural inclusive permutations. That is, if X includes A; X includes B; or X includes both A and B, then "X includes A or B" is satisfied under any of the foregoing instances.
- the transmitting station 102 or the receiving station 106 can be implemented using a general purpose computer or general purpose processor with a computer program that, when executed, carries out any of the respective methods, algorithms and/or instructions described herein.
- a special purpose computer/processor can be utilized which can contain other hardware for carrying out any of the methods, algorithms, or instructions described herein.
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