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
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Mesh modeling and processing
Mesh model• Consists of only {V, E, F}• Boundary meshes – represent 2D surfaces
embed in 3D
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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
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Mesh modeling and processing
Mesh processing
• Mesh segmentation/decomposition• Mesh model/shape matching• Correspondence of mesh models
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Mesh modeling and processing
Mesh segmentation• Decomposing a mesh into meaningful
components• Part-type and surface-type are two
prominent approaches
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Mesh modeling and processing
Approaches for mesh segmentation
• Region growing• Hierarchical clustering• Iterative clustering• Spectral analysis• Implicit methods
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Mesh modeling and processing
Mesh attributes
STTP CAD 2011
Minimum curvature Average geodesic distance
Local shape diameter
Difference betweenNormal directions
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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
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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.
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Mesh modeling and processing
Sectional Gauss map
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Mesh modeling and processing
Algorithm to compute PCS
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Mesh modeling and processing
PCS for different models
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Mesh modeling and processing
Segmentation
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Mesh modeling and processing
Segmentation of CAD models
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(a) Fuzzy clustering (b) Feature point (c) Blowing bubbles (d) Plumber (e) Fitting primitives
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Mesh modeling and processing
Problem of matching• Matching is the process of determining how
similar two shapes are.
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Simple Definition
• Retrieve visually similar objects from a database using query object.
…
UserInterface Query Object
Database
…
Output
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Mesh modeling and processing
Taxonomy of shape matching methods
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Mesh modeling and processing
D2 Shape distribution
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D2 shape distributions of five tanks (gray curves) and six cars (black curves)
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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
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Mesh modeling and processing
View-based similarity
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Extraction of the lightfield descriptor for a chair model
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Mesh modeling and processing
Local diameter function
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Mesh modeling and processing
DF, CDF and CF
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DF – Diameter function, CF – Centricity functionCDF – Combined function
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Mesh modeling and processing
Temperature distribution descriptor
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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.
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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
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Mesh modeling and processing
Visualizing the results
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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.
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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.
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Mesh modeling and processing
Partial correspondence
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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.
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