mesh modeling and processing m. ramanathan sttp cad 2011mesh modeling and processing
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Mesh modeling and processing
Mesh modeling and processing
M. Ramanathan
STTP CAD 2011
Mesh modeling and processing
Mesh model• Consists of only {V, E, F}• Boundary meshes – represent 2D surfaces
embed in 3D
STTP CAD 2011
Mesh modeling and processing
Characteristics
• Simple/Concise representation• Aids faster visualization and exchange of
data• No geometry/topology information
available• Created using scanning or modeling
softwares
STTP CAD 2011
Mesh modeling and processing
Mesh processing
• Mesh segmentation/decomposition• Mesh model/shape matching• Correspondence of mesh models
STTP CAD 2011
Mesh modeling and processing
Mesh segmentation• Decomposing a mesh into meaningful
components• Part-type and surface-type are two
prominent approaches
STTP CAD 2011
Mesh modeling and processing
Approaches for mesh segmentation
• Region growing• Hierarchical clustering• Iterative clustering• Spectral analysis• Implicit methods
STTP CAD 2011
Mesh modeling and processing
Mesh attributes
STTP CAD 2011
Minimum curvature Average geodesic distance
Local shape diameter
Difference betweenNormal directions
Mesh modeling and processing
Region Growing Algorithm• Initialize a priority queue Q of elements Loop
until all elements are clustered• Choose a seed element and insert to Q• Create a cluster C from seed• Loop until Q is empty
– Get the next element s from Q– If s can be clustered into C
• Cluster s into C• Insert s neighbours to Q
• Merge small clusters into neighbouring onesSTTP CAD 2011
Mesh modeling and processing
Clustering algorithm using prominent cross-sections
• compute local cross-sections spread over the mesh model
• can be defined as a cross-section of a local sweep passing through that point.
STTP CAD 2011
Mesh modeling and processing
Sectional Gauss map
STTP CAD 2011
Mesh modeling and processing
Algorithm to compute PCS
STTP CAD 2011
Mesh modeling and processing
PCS for different models
STTP CAD 2011
Mesh modeling and processing
Segmentation
STTP CAD 2011
Mesh modeling and processing
Segmentation of CAD models
STTP CAD 2011
(a) Fuzzy clustering (b) Feature point (c) Blowing bubbles (d) Plumber (e) Fitting primitives
Mesh modeling and processing
Problem of matching• Matching is the process of determining how
similar two shapes are.
STTP CAD 2011
Simple Definition
• Retrieve visually similar objects from a database using query object.
…
UserInterface Query Object
Database
…
Output
Mesh modeling and processing
Taxonomy of shape matching methods
STTP CAD 2011
Mesh modeling and processing
D2 Shape distribution
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D2 shape distributions of five tanks (gray curves) and six cars (black curves)
Mesh modeling and processing
Skeletal graph matching
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Skeletal graph matching with colors showing the node-to-node correspondence based uponthe topology and radial distance about the edge
Mesh modeling and processing
View-based similarity
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Extraction of the lightfield descriptor for a chair model
Mesh modeling and processing
Local diameter function
STTP CAD 2011
Mesh modeling and processing
DF, CDF and CF
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DF – Diameter function, CF – Centricity functionCDF – Combined function
Mesh modeling and processing
Temperature distribution descriptor
STTP CAD 2011
Mesh modeling and processing
Spectral embedding
STTP CAD 2011
Compute the affinity matrix and its Eigen decomposition A = VDVT.. D is a diagonal matrix with eigenvalues e1,e2, …, en, along the diagonal and V = [v1| . . . |vn] is an n × n matrix with v1, . . . , vn the corresponding eigenvectors.
Mesh modeling and processing
Database – Accumulation of models
• Princeton shape benchmark (PSB) – 3D graphical models
• Engineering shape benchmark (ESB) – 3D CAD models
• McGill Database – 3D Articulated models
STTP CAD 2011
Mesh modeling and processing
Visualizing the results
STTP CAD 2011
Mesh modeling and processing
Quantitative analysis• First-tier and second-tier values are defined as
percentage of models in the query’s class that appear in top K matches, where K is dependent on the size of the query’s class. The higher values of these statistics indicate better retrieval results.
• Precision–recall (PR) curves. Precision is the ratio of the relevant models retrieved to the retrieval size. Recall is the fraction of the relevant models retrieved for a given retrieval size.
STTP CAD 2011
Mesh modeling and processing
Correspondence problem• The problem can be generally stated as:
given input shapes S1;S2; : : : ;SN, find a meaningful relation (or mapping) between their elements.
STTP CAD 2011
Mesh modeling and processing
Partial correspondence
STTP CAD 2011
Mesh modeling and processing
References• R. Gal, A. Shamir, and D. Cohen-Or. Pose-oblivious shape signature. IEEE Transactions
on Visualization and Computer Graphics, 13(2):261–271, Mar./Apr. 2007.• N. Iyer, S. Jayanti, K. Lou, Y. Kalyanaraman, and K. Ramani. Three-dimensional shape
searching: state-of-the-art review and future trends. Computer-Aided Design, 37(5):509–530, 2005.
• V. Jain and H. Zhang. A spectral approach to shape-based retrieval of articulated 3d models. Comput. Aided Des., 39(5):398–407, 2007.
• R. Osada, T. Funkhouser, B. Chazelle, and D. Dobkin. Shape distributions. ACM Trans. Graph., 21(4):807–832, 2002.
• P. Shilane, P. Min, M. Kazhdan, and T. Funkhouser. The princeton shape benchmark. In Shape Modeling International, June 2004.
• J. Tangelder and R. Veltkamp. A survey of content based 3D shape retrieval methods. In SMI ’04: Proceedings of the Shape Modeling International, pages 145–156, June 2004.
• R. Veltkamp. Shrec home page. http://www.aimatshape.net/event/SHREC• Ariel Shamir. A survey on mesh segmentation techniques. Computer Graphics Forum,
27 (6), pp. 1539-1556,2008.• Oliver van Kaick, Hao Zhang, Ghassan Hamarneh, Daniel Cohen-Or, A survey on shape
correspondence• Subramani S., Ramanathan M., Yagnanarayanan K., Sundar M, Manish, Ramani K, and
Hoffmann C. M., "PCS - Prominent cross-section for mesh models" , Computer Aided Design and Applications (CADA), Volume 7, Number 4, Pages 601-620, 2010.
STTP CAD 2011