special module on media processing and communicationpkalra/siv864/pdf/session-6-18.pdf · new delhi...
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Special Module on Media Processing and
Communication
Dayalbagh Educational Institute (DEI)
Dayalbagh Agra
PHM 961
Indian Institute of Technology Delhi (IITD)
New Delhi
SIV 864
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GeometryCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
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Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Mul1mediaHistorical Perspective: Digital Media
75 80 85 90 95 00 05
Sound
Image
Video
Geometry
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GeometricModels
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Representations
Constructed Solid Geometry
Polygonal Surface
Parametric Surface
Implicit Surface
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GeometricModels
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Applications
Engineering
Topography Art
Medical
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GeometricModels
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
For rendering often object is represented as collection of polygons
Object Surfaces Polygonal Patches
Polygonal Representation
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GeometricModels
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Polygonal Representation Polygonal mesh is a collection of edges, vertices and polygons such that each edge is shared by at most two polygons Vertex: Node Edge: Connects two vertices Polygon: Closed sequence of edges
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GeometricModels
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Polygonal Representation Explicit Representation Each polygon is represented by
P=((x1,y1,z1) (x2,y2,z2) … (xn,yn,zn)) i.e. vertices are stored in the order of traversal Edges connect the successive vertices plus the last one This representation has restrictive manipulation and has multiple storage of points.
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GeometricModels
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Polygonal Representation Pointer to Vertex ListEach vertex is stored once in a list V V=((x1,y1,z1) (x2,y2,z2) … (xn,yn,zn)) Each polygon is represented as P=(V1,V2,V3) e.g. P1=(1,2,4) and P2=(4,2,3)
In this representation it is difficult to find polygons that share an edge.
V4
V2
V3 V1 P1
P2
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GeometricModels
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Polygonal Representation Pointer to Edge List Edge: E = (Vi,Vj,Pm,Pn) Polygon=(Ep,Eq,Er)V = (V1,V2,V3,V4) E1 = (V1,V2,P1,null) E2 = (V2,V3,P2,null) E3 = (V3,V4,P2,null) E4 = (V4,V2,P1,P2) P1= (E1E4E5) E5 = (V4,V1,P1,null) P2= (E2E3E4)
V4
V2
V3 V1 P1
P2 E4
E1
E5 E3
E2
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GeometricModels
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
! Typically, ! Geometry Data: Meshes
l Points l Connectivity
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Connectivity Coding Indexed Face Set
v0
v1 v2
v3 v4
T0
T1
T2
T0 : v0v1v4
T1 : v1v4v3
T2 : v1v2v3
Simple approach Vertex index of 32 bits 3x32 = 96 bits/triangle 3xlog2 (V) bits/triangle =50 bits/triangle (for 100k vertices)
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Connectivity Coding Triangle strip
Triangle fan
Generalized triangle strip
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Connectivity Coding Triangle strip
Triangle fan
Generalized triangle strip
v0 v2
T0
T1
v3 v1
v4
T2
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Connectivity Coding Triangle strips
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Connectivity Coding Spanning Trees
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Geometry Coding Scalar quantization
v0
v1 v2
v3 v4
T0
T1
T2
v0 : x0y0z0
v1 : x1y1z1
v2 : x2y2z2
.
.
Simple approach Each coordinate of 32 bits 3x32 = 96 bits/vertex Quantization: 10 bits =3x10 bits/vertex
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Geometry Coding Uniform quantization
12 bits 8 bits 6 bits
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Geometry Coding Prediction: Exploits correlation between adjacent vertex
coordinates Linear prediction: Linear combination of K previous vertices
Vi-2 Vi-1 Vi P
P = Vi-1+ (Vi-1- Vi-2)
error ei = Vi - P
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Geometry Coding Vertex Coordinates: V1 V2 V3 V4 ...... Using prediction error: V1 V2 e3 e4 ...... Decoding: V1 V2
Vi = P + ei where
Vi-2 Vi-1 Vi P
P = Vi-1+ (Vi-1- Vi-2)
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Geometry Coding Parralelogram prediction:
P
error
v1 v2
v3
vp = v2 + v3 v1 -
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Geometry Coding K-way prediction: Vertex is average of its neighbours
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Geometry Coding Downsampling
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Geometry Coding Downsampling
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Geometry Coding Resolution
Mesh Level of details
Downsampling
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
Multi-resolution Representation Down sample
Subdivide Wavelet
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
• Animation can be modeled as a transformation • Partitioning or clustering of data
• Prediction based method for vertices which move • Measure to preserve time variant geometry features
Animated Mesh Coding
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GeometricCompression
Special Module on Media Processing and Communication http://www.cse.iitd.ac.in/~pkalra/sil864
! References ! Technologies for 3D mesh compression: A survey by J Peng, CS
Kim, CC Jay-Kuo, Journal of Visual Communication Image Representation, 16, 2005, 688-733
! http://imsc.usc.edu/research/project/digitalgeometry/ ! http://www.cs.ubc.ca/~sheffa/dgp/ppts/Geometry.pdf ! 3D mesh compression: survey, comparisons and emerging trends,
ACM Computing Surveys, Vol 9, No 4, Article 39, September 2013.