Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T9/00—Image coding
  • G06T9/001—Model-based coding, e.g. wire frame
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T15/00—3D [Three Dimensional] image rendering
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
  • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
  • H04N19/124—Quantisation
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
  • H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
  • H04N19/18—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being a set of transform coefficients
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
  • H04N19/134—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or criterion affecting or controlling the adaptive coding
  • H04N19/136—Incoming video signal characteristics or properties

Definitions

• This invention relates to a method and apparatus for generating a bitstream representative of a 3D model, and a method and apparatus for decoding the same.
• Efficient compression algorithms for multi-component 3D models that take advantage of repetitive structures in input models are known. Repetitive structures of a 3D model are discovered in various positions, orientations, and scaling factors. The 3D model is then organized into "pattern-instance" representation.
• a pattern is used to denote a representative geometry of a corresponding repetitive structure.
• Components belonging to a repetitive structure are denoted as instances of the corresponding pattern and may be represented by a pattern ID and transformation information, for example, reflection, translation, rotation and possible scaling with respect to the pattern.
• the instance transformation information may be organized into, for example, reflection part, translation part, rotation part, and possible scaling part.
• the present principles provide a method for generating or decoding a bitstream representing a 3D model, comprising the steps of accessing a first quantization parameter used for encoding a pattern associated with the 3D model; determining a scale of an instance of the pattern and a scale of the pattern, the instance being represented as a transformation of the pattern; determining a second quantization parameter for a rotation part of the transformation for the instance in response to the first quantization parameter, the scale of the instance, and the scale of the pattern; and performing encoding or decoding of the rotation part of the transformation for the instance in response to the second quantization parameter as described below.
• the present principles also provide an apparatus for performing these steps.
• the present principles also provide a computer readable storage medium having stored thereon instructions for generating or decoding a bitstream according to the methods described above.
• the present principles also provide a computer readable storage medium having stored thereon a bitstream generated according to the methods described above.
• FIG. 1 shows exemplary 3D models with a large number of connected components and repetitive structures
• FIG. 2A shows pictorial examples depicting patterns
• FIG. 2B shows pictorial examples depicting corresponding instances and reconstructed instances
• FIG. 2C shows pictorial examples depicting corresponding instances and instances with reconstruction errors of rotation parameters
• FIG.3 is a flow diagram depicting an example for encoding patterns and instances of a 3D model, in accordance with an embodiment of the present principles
• FIG.4 is a flow diagram depicting an example for decoding patterns and instances of a 3D model, in accordance with an embodiment of the present principles
• FIG. 5 shows an exemplary encoder of 3D models according to the present principles
• FIG. 6 shows an exemplary decoder of 3D models according to the present principles
• FIG. 7 shows an example depicting bitstream structure, in accordance with an embodiment of the present principles.
• the repetitive structures may be organized into patterns and instances, wherein an instance can be represented as a transformation of a corresponding pattern, for example, using a pattern ID and a transformation matrix which contains information such as translation, rotation, and scaling.
• the pattern ID and the transformation matrix are to be compressed when an instance is represented by a pattern ID and a transformation matrix.
• an instance may be reconstructed through the pattern ID and the decoded transformation matrix, that is, an instance may be reconstructed as transformation (from the decoded transformation matrix) of a decoded pattern indexed by the pattern ID.
• FIGs. 2A and 2B illustrate exemplary components in a 2D representation, wherein components 210 and 220 are patterns, components 230 and 250 (in solid lines) are original instances to be compressed, and components 240 and 260 (in dashed lines) are reconstructed instances.
• instances 230 and 250 can be represented as transformed (i.e., rotated and translated) versions of patterns 210 and 220, respectively.
• FIG. 2B between the original instance and the
• quantization of rotation introduces an error of about 5°, causing differences between original instances and reconstructed instances.
• the rotation errors in angular measure
• the vertex coordinate errors i.e., vertex shifts, for example, from A to A" and from B to B" in FIG. 2C, between original instances and reconstructed instances
• the quality of reconstructed components may be inconsistent, for example, a larger instance may have lower reconstruction quality than a smaller instance.
• the present principles provide a method and apparatus for efficiently quantizing the transformation information for a 3D instance component by
• the quantization considering rate-distortion performance of a 3D encoder.
• the quantization considering the maximum allowed distortion, the quantization
• parameters for the rotation part and translation part of the instance are determined such that rate-distortion performance is improved.
• the number of quantization bits is used as an exemplary quantization parameter.
• the present principles can be applied when other quantization parameters, such as a
• quantization step size are used.
• scaling part of the transformation may be compressed by a lossless floating point codec
• scaling part of the transformation is not involved in the following discussion.
• a vertex v of an original instance can be represented by:
• v R * p + T , (1 )
• p is i s corresponding vertex in the corresponding pattern
• R and T are the rotation matrix and translation vector between pattern and instance, respectively.
• the decoded position of v, v d can be calculated as: where p d s the decoded position of p, and R d and T d are the decoded rotation matrix and decoded translation vector, respectively.
• Eq. (5) can be adapted when other representations or different quantization parameters are used for angles ( ⁇ , ⁇ , ⁇ ) .
• Eq. (4) becomes:
• ⁇ p ⁇ is the maximum distance between any vertex of the corresponding pattern and the center of the corresponding pattern.
• QB_translation may be calculated as:
• Pattem_Scaland Translation_Scal are the scales of the bounding box of the pattern vertices and translations, respectively.
• Translation_Scalcan be measured as the difference between the maximum and minimum possible values of all translations of all instances, and Pattem_Scalcan be measured as the diagonal distance of a bounding box containing all patterns.
• Pattem_Scalcan be measured as the maximum values of x, y, and z dimensions.
• instance translation may use the same number of quantization bits as patterns.
• the scale difference between the bounding box of patterns and the bounding box of instances are considered.
• Parameter Translation_Scal may be sent in the bitstream and it becomes available at both the encoder and decoder, so that Eq. (10) can be used at both the encoder and decoder. According to Eq. (10), all instance translations use the same quantization parameter, which are related to the ratio between the scale of patterns and instance translations.
• the same rotation quantization error in angular measure
• the same rotation quantization error may cause a larger vertex shift in a larger component.
• quantization parameter for the rotation information may be quantized adaptively according to the size of an instance. For example, a finer quantization parameter, such as a larger number of bits or a smaller quantization step size, may be used for quantizing the rotation part of a larger instance.
• the vertex coordinate error caused by rotation quantization error may satisfy
• the upper bound of rotation quantization error for the i L " instance component may be estimated as: a - MaxErr/ _ - MaxErr/ _ _ IMI f / ]
• HalfScalj is the half scale (i.e., half of the diagonal distance of the bounding box of the instance) of the i th instance component.
• HalfScalj may be estimated from the corresponding reconstructed pattern. By estimating HalfScalj using the reconstructed pattern, which can be accessed by both the encoder and decoder, the quantization parameter for the rotation part can be calculated at the decoder, and thus, the encoder need not to explicitly indicate the quantization parameter for the rotation part in the bitstream.
• Ae maxj may be
• Eq. (12) may be updated
• angle_Scal is the scale of the rotation angle.
• angle_Scal can be measured as the difference between the maximum and minimum possible angles of all instance rotations. In another example, we set angle_Scal to 2 ⁇ .
• quantization bits (QP Rotl) for the instance is determined to be larger.
• QP Rotl quantization bits
• Eq. (14) should be adjusted accordingly when the scale of the rotation angle changes, the scaling part of the transformation is considered, or the sizes of patterns and instances are measured differently.
• quantization parameters for the translation part and rotation part of the transformation matrix of an instance may be determined based on the quantization parameter used for encoding patterns, so as to improve
• the number of quantization bits used for encoding patterns (QB_Pattem)may be indicated in the bitstream, the translation part of the transformation matrix of the instance maybe calculated using Eq. (10), and the number of quantization bits for the rotation part may be calculated using Eq. (14).
• the number of quantization bits for encoding patterns may be calculated from the number of quantization bits of the entire 3D input model as follows:
• EntireModel Seal whereQB_EntireModel is the number of quantization bits for the entire 3D input model, and EntireModel_Scal reflects the size of the entire 3D input model.
• Pattern_Scal can be measured using all patterns in the 3D model.
• the patterns are compressed separately and the instances of the same pattern are compressed together. All the patterns may use the same quantization parameter. Further, Pattern_Scal in Eqs. (10)
• FIG. 3 illustrates an exemplary method 300 for encoding patterns and instances of a 3D model.
• Method 300 starts at step 305.
• 3D model data is input and initialization is performed. Additional data, such as quality parameter, quantization parameters for encoding patterns, may also be input or inferred from the input.
• the initialization step may organize the repetitive structures into patterns and instances and generate
• transformation matrices for instances.
• patterns are encoded to form reconstructed patterns.
• the scales of patterns, translation, and rotation are determined.
• the scale of patterns (Pattem_scal) may be measured as a diagonal distance of a bounding box containing all patterns
• the scale of translation (Translation_scal) may be obtained from metadata and sent in the bitstream
• the rotation scale (angle_scal) may be determined based on the angular representation, for example, angle_scal is set to 2 ⁇ when Eular
• the quantization parameter for the translation part of the transformation matrix for an instance component may be determined, for example, using Eq. (10).
• transformation matrix may be determined, for example, using Eq. (14).
• the transformation matrix for the instance is then encoded at step 370. It checks whether more instances need to be processed at step 380. If more instances are to be processed, the control is returned to step 350. Otherwise, the control is passed to the end step 399.
• FIG. 4 illustrates an exemplary method 400 for decoding patterns and instance of a 3D model.
• the input of method 400 may include a bitstream, for example, a bitstream generated using method 300.
• Method 400 starts at step 405.
• initialization is performed, for example, the quantization parameter used for encoding patterns is derived from the input bitstream.
• Patterns are decoded at step 420.
• the scales of patterns, translation, and rotation are determined.
• the quantization parameter for the translation part and/or rotation part of the transformation matrix for an instance component may be determined.
• the transformation matrix is decoded at step 450.
• the instance is then reconstructed at step 460, for example, using a corresponding reconstructed pattern and decoded transformation matrix. It checks at step 470 whether more instances need to be processed. If yes, the control is returned to step 435. Otherwise, the control is passed to the end step 499.
• steps 435 and 440 should correspond to steps 350 and 360, respectively.
• all patterns in the 3D model are encoded or decoded before instances.
• encoding/decoding of each pattern may be followed by encoding/decoding of corresponding instances.
• how to allocate the number of quantization bits are discussed given the maximum allowed error.
• Eq. (7) can also be used for rate control, that is, for determining the quantization parameters given the number of bits in order to optimize the quality of the decoded 3D model.
• the size, measured in the number of bits, of a compressed pattern may be calculated as:
• Compr _ Insta (QB _ translation * 3 + ⁇ QB _ Rot t * 3) * C msta , (17) where C ms ta is a pre-determined value.
• the size for compressed unique component can be calculated as:
• Compr_UniComp QB_UniComp*UniComp_ Ver_Num*C pv +UniComp_ Tri_Num*C pt , ( 18) where QB_UniComp is the number of quantization bits for encoding the unique components, UniComp_ Ver_Num and UniComp_Tri_Num are the number of vertices and the number of triangles of unique components, respectively.
• QB— UniCom 'p may J be calculated as follows:
• Compr_EntireModel Compr_Pattern + Compr nsta + Compr_UniComp.(20)
• FIG. 5 depicts a block diagram of an exemplary 3D model encoder 500.
• the input of apparatus 500 may include a 3D model, quality parameter for encoding the 3D model and other metadata.
• the 3D model first goes through the repetitive structure discovery module 510, which outputs the 3D model in terms of patterns, instances and unique components.
• a pattern encoder520 is employed to compress the patterns and a unique component encoder550 is employed to encode the unique components.
• the instance component information is encoded based on a user-selected mode. If instance information group mode is selected, the instance information is encoded using grouped instance information encoder540; otherwise, it is encoded using an elementary instance information encoder530.
• the encoded components are further verified in the repetitive structure verifier 560. If an encoded component does not meet its quality requirement, it will be encoded using unique component encoder 550.
• Bitstreams for patterns, instances, and unique components are assembled at bitstream assembler 570.
• all components of the original 3D model may be translated such that the centers of components are aligned.
• the translations of the centers need to be compressed and indicated in the bitstream.
• the rate- distortion performance may be improved as the bounding box of the components could be much smaller (in most cases) and less quantization bits are required for the same coding error.
• a pattern may be generated by translating the center of a component to the origin, and the original component may be regarded as an instance.
• the original component may be regarded as an instance.
• the compressed bitstream For pattern components (components corresponding to patterns), only translations are indicated the compressed bitstream. If there are no or not enough repetitive structures to guarantee the bitrate saving from the pattern-instance representation, all components of the input 3D model may be regarded as unique components.
• FIG.6 depicts a block diagram of an exemplary 3D model decoder 600.
• the input of apparatus 600 may include a bitstream of a 3D model, for example, a bitstream generated by encoder 500.
• the information related to patterns in the compressed bitstream is decoded by pattern decoder 620.
• Information related to unique components is decoded by unique component decoder650.
• the decoding of the instance information also depends on the user-selected mode. If instance information group mode is selected, the instance information is decoded using a grouped instance information decoder640; otherwise, it is decoded using an elementary instance information decoder 630.
• the decoded patterns, instance information and unique components are reconstructed to generate an output 3D model at model reconstruction module 660.
• FIG. 7 illustrates an exemplary method 700 for generating a compressed bitstream.
• the bitstream starts with the header buffer (PB3DMC_stream_header, 710), which contains all the necessary information for decoding the compressed stream.
• the information may include:
• the remaining part of the bitstream is the compressed input 3D model (730) using the 3D model compression method indicated in PB3DMC_stream_header. Otherwise, the next part in the bitstream is the compressed result of all unique components (745) if there are some (740). If there is at least one repetitive structure (750), the next data field is the compressed result of all patterns (760). Depending on which instance transformation packing mode is chosen in the bitstream (770), either compr_insta_grouped_data (780) or compr_insta_elementary_data (785) is the next part in the bitstream.
• ⁇ ver_num This 32-bit unsigned integer contains the number of vertices of the entire 3D model. This value can be used to verify the decoded 3D model.
• tri_num This 32-bit unsigned integer contains the number of triangles of the entire 3D model. This value can be used to verify the decoded 3D model.
• default_coord_bbox This 1 -bit unsigned integer indicates whether a default bounding box is used for the entire 3D model's geometry. 0 means using another bounding box and 1 means using the default bounding box.
• coord_bbox This data field contains the bounding box of the entire 3D model's geometry.
• the geometry bounding box is defined by (x min , y min , z min , x max , y max , z max ).
• QP_coord This 5-bit unsigned integer indicates the quality parameter of the 3D model geometry. The minimum value of QP_coord is 3 and maximum is 31 .QP_coord may correspond to QB_Pattern in Eq. (10) or QB_EntireModel in Eq. (15).
• normal binding This 2-bit unsigned integer indicates the binding of normals to the 3D model. The admissible values are described in the following table.
• default_normal_bbox This 1 -bit unsigned integer should always be ⁇ ', which indicatesthat a default bounding box is used for the normal of the entire 3D model.
• QP_normal This 5-bit unsigned integer indicates the quality parameter of the 3D model geometry.
• the minimum value of QP_normal is 3 and maximum is 31 .
• default_color_bbox This 1 -bit unsigned integer indicates whether a default bounding box is used for the color of the entire 3D model. 0 means using another bounding box and 1 means using the default bounding box.
• color_bbox This data field contains the bounding box of the color of the entire 3D model.
• the color bounding box is defined by (r min , g min , b min , r max , b max ).
• QP_color This 5-bit unsigned integer indicates the quality parameter of the color.
• the minimum value of QP_color is 3 and maximum is 31 .
• multi_texCoord_num This 5-bit unsigned integer gives the number of texture coordinates per vertex/corner.
• texCoord_binding This 2-bit unsigned integer indicates the binding of texture coordinates to the 3D model.
• the following table shows the admissible values. 2 forbidden
• default_texCoord_bbox This 1 -bit unsigned integer indicates whether a default bounding box is used for the texture coordinates. 0 means using another bounding box and 1 means using the default bounding box.
• texCoord_bbox This data field contains the bounding box of the texture coordinate of the entire 3D model.
• the texture coordinate bounding box is defined by (u min , v min , u max , v max ).
• QP_texCoord This 5-bit unsigned integer indicates the quality parameter of texture cooridinates.
• the minimum value of QP_texCoord is 3 and maximum is 31 .
• default_attribute_bbox This 1 -bit unsigned integer indicates whether a default bounding box is used for the attributes. 0 means using another bounding box and 1 means using the default bounding box.
• attribute_max[1 ..attribute_dim] 1 .0.
• attribute_bbox This data field contains the bounding box of the attribute.
• the texture coordinate bounding box is defined by (attribute_min[1..attribute_dim], attribute_max[1..attribute_dim]).
• QP_attribute This 5-bit unsigned integer indicates the quality parameter of the attribute.
• the minimum value of QP_attribute is 3 and maximum is 31 .
• compr_uni_comp_data This data field contains the compressed geometry, connectivity and properties of all unique components, which is encoded by the compression method indicated by 3d_model_compr_mode. All unqiue components are translated to the origin before compression.
• compr_uni_comp_transl This data field contains the compressed translation vectors for all unique components. The unique component translation vectors are compressed by first quantization and then entropy coding. This data field use the same order of unique component with compr_uni_comp_data.
• bit_num_uni_comp_transl() This function computes the number of bits used for quantizing each unique component translation vector based on QP_coord.
• compr_pattern_data This data field contains the compressed geometry, connectivity and properties of all patterns, which is encoded by the compression method indicated by 3d_model_compr_mode.
• compr_pattern_transl This data field contains the compressed translation vectors for all pattern components. The pattern translation vectors are compressed by first quantization and then entropy coding. This data field uses the same order of patterns with compr_pattern_data.
• compr_insta_elementary_data This data field contains the compressed transformation data for all instances using the "elementary instance transformation mode". It is compressed in a manner that is byte aligned.
• compr_insta_grouped_data This data field contains the compressed transformation data for all instances using the "grouped instance transformation mode". It is compressed in a manner that is byte aligned.
• bit_num_pattern_transl() This function computes the number of bits used for quantizing translation vector of each pattern component based on QP_coord.
• insta_transl_bbox This data field contains the bounding box of all translation vectors so that quantization can be used when compressing instance translation information.
• the bounding box is defined by insta_transl_x min , insta_transl_y min , insta_transl_z min , insta_transl_x max , insta_transl_y max , insta_transl_z max .
• compr_elem_insta_patternlD This data field contains the compressed pattern ID of i th instance.
• elem_insta_filp_flag Thisl -bit unsigned integer indicates whether or not the i th instance is flipped compared with the corresponding pattern.
• a flipped instance means the instance triangle normals are in the opposite diection of the correspoonding pattern triangles. 0 means i instance is not flipped and 1 i th instance is flipped.
• elem_insta_reflection_flag This 1 -bit unsigned integer indicates whether the transformation of i th instance includes reflection. 0 means the transformation of i th instance doesn't include reflection and 1 means the transformation of i th instance includes reflection.
• This data field contains the attribute header of i th instance.
• compr_elem_insta_transl This data field contains the compressed translation vector of i th instance.
• compr_elem_insta_rotat_spherical This data field contains the compressed rotation transformation of i th instance in spherical mode.
• compr_elem_insta_scaling This data field contains the compressed scaling factor of i th instance.
• compr_elem_insta_error_compen_data This data field contains the compressed coding errorcompensation data of i th instance.
• compr_elem_insta_attribute_data This data field contains the compressed attribute data of i th instance.
• bit_num_insta_transl() This function computes the number of bits used for quantizing instance translation vectors based on QP_coord.
• bit_num_vertex_coding_error() This function adaptively computes the number of bits used for quantizing the coding error of each vertex of i th instance based on QP_coord.
• the rotation of the i th instance in a spherical mode is represented by three angles: alpha, beta and gamma.
• compr_elem_insta_rotat_alpha This data field contains the compressed alpha of i instance's rotation.
• compr_elem_insta_rotat_beta This data field contains the compressed beta of i th instance's rotation.
• compr_elem_insta_rotat_gamma This data field contains the compressed gamma of i instance's rotation.
• bit_num_rotat_alpha() This function adaptively computes the number of bits for the alpha value of i th instance's rotation based on QP_coord and the scale of the corresponding pattern.
• bit_num_rotat_beta() This function computes the number of bits for the beta value of i th instance's rotation based on QP_coord and the scale of the corresponding pattern.
• bit_num_rotat_gamma() This function computes the number of bits for the gamma value of i th instance's rotation based on QP_coord and the scale of the corresponding pattern.
• the implementations 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 such as, 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, such as, for example, computers, cell phones, portable/personal digital assistants ("PDAs"), and other devices that facilitate communication of information between end-users.
• PDAs portable/personal digital assistants
• 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 the specification are not necessarily all referring to the same embodiment.
• Accessing the information may include one or more of, for example, receiving the information, retrieving the information (for example, from memory), 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.
• 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).
• “receiving” is typically involved, in one way or another, during operations such as, 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.
• 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.
• 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.

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