1. Local Feature Extraction Using Scale-Space Decomposition
Dmitriy Bespalov† Ali Shokoufandeh†
William C. Regli†‡ Wei Sun‡
Department of Computer Science†
Department of Mechanical Engineering & Mechanics‡
College of Engineering
Drexel University
3141 Chestnut Street
Philadelphia, PA 19104

2. Overview Introduction Overview of the approach Experimental results
Current and future work

3. Project Goals
Perform content- , feature- and shape-based retrieval of CAD data
Develop systematic approaches of evaluating matching techniques
Integrate new algorithms with the National Design Repository (

4. Goals of this Work Feature extraction technique
Models in polyhedral representation
Using local information
Tolerance to noise

5. Side Note: Compare Features Scale Space CAD/CAM

6. Selected Related Work
Surface Feature Extraction on Shape Models (Computer Graphics)
Scale-Space features [Bespalov et al., 03]
Multi-resolutional Reeb Graphs [Hilaga et al., 01]
Feature information on range data [Thompson et al., 96,99]
Manufacturing Feature Extraction on Solid Models (Solid Modeling & Engineering)
Feature relationship graphs [Elinson et al. 97; Cicirello and Regli 99,00,01,02]
Automated generation of GT codes [Ames 91; Shah et al., 89 and Ham et al., 86]
Feature Extraction on 2D images (Computer Vision)
Scale-Space features using wavelets and Gaussian filters [Lindeberg, 90 and Shokoufandeh, 99]

7. Traditional CAD Representation
Watertight boundary-representation solid
Implicit surfaces
Analytic surfaces
NURBS, etc
Topologically and geometrically consistent
Produced by kernel modelers and CAD systems

8. Traditional Shape Representation
Usually a mesh or point cloud
Usually an approximate representation
No explicit in/out
Sometimes error prone
STL files, acquired data
Produced by CAD systems, animation tools, laser scanners, etc

9. What is a Scale Space Representation?
Commonly used for Coarse-to-Fine representations of an object
Very popular in computer Vision
Constructed via spatial filters: Gaussian pyramids, Wavelets…
Basic Idea:
At each scale, topologically relevant components will decompose the object into so called salient parts
Recursive application of this paradigm will create the object’s scale space hierarchy

10. Approach to Scale Space Feature Extraction
Obtain polyhedral representation
Convert CAD model or scan physical part
Perform geometry-based decomposition
Singular value decomposition
Construct “feature” graph
Obtain a segmentation into “features”

11. Algorithm Overview (I)
Obtain mesh representation M
Define measurement function: Our d is maximum angle on the shortest path between every two faces on M using angular measure. Distance matrix D is constructed.
d(t1,t2)

12. Algorithm Overview (II)
3. Decompose M into relevant components using a singular value decomposition of distance matrix D Note: this creates a clustering based on the angle between a vector Oti and the basis vectors (ck, ck-1)

13. Algorithm Overview (III)
The Eckart-Young Theorem: Given an n by m matrix X of rank r ≤ m ≤ n, and its singular value decomposition, ULV', where U is an n by m matrix, L is an m by m diagonal matrix of singular values, and V is an m by m matrix such that U'U = In and V'V = VV' = Im with the singular values arranged in decreasing sequence λ1 ≥ λ2 ≥ λ3 ≥ ... ≥ λm ≥ 0 then there exists an n by m matrix B of rank s, s ≤ r, which minimizes the sum of the squared error between the elements of X and the corresponding elements of B when B = UΛsV' where the diagonal elements of the m by m diagonal matrix Λs are λ1 ≥ λ2 ≥ λ3 ≥ ... ≥ λs > λs+1 = λs+2 = ... = λm = 0

14. Algorithm Overview (IV)
Recursive feature decomposition using two principle components creates binary feature trees.
Use leaf nodes as features.

15. Algorithm Overview (V)
Stopping automatic feature decomposition process. Decomposition of M1 into M2 and M3 is significant if:
angle across the border of the cluster is max on the path between most of the pairs of faces in M2 and M3.

16. Algorithmic Complexity
Bisection process:
SVD decomposition takes O(n3).
Polyhedral representation creates a 3D lattice; if only neighboring vertices are used in construction of the distance matrix, SVD decomposition is faster and takes O(n2).

17. Experimental Results

18. Experimental Results – Partial Data

19. Experimental Results – Partial Data

20. Experimental Results – Partial Data

21. Experimental Results – Partial Data

22. Experimental Results – Partial Data

23. Experimental Results – Scanned Data
From Exact Representation
360° Scan
Single Scan

24. Experimental Results – Scanned Data
From Exact Representation
360° Scan
Single Scan
An example of one-to-many correspondence

25. Experimental Results – Scanned Data
From Exact Representation
360° Scan
Single Scan
An example of one-to-one correspondence

26. Experimental Results – Scanned Data
From Exact Representation
360° Scan
Single Scan
An example of one-to-one correspondence

27. Experimental Results – Scanned Data
From Exact Representation
360° Scan
Single Scan
An example of many-to-many correspondence

28. Experimental Results – Scanned Data
From Exact Representation
360° Scan
Single Scan
An example of one-to-many correspondence

29. Experimental Results – Scanned Data
From Exact Representation
360° Scan
Single Scan
An example of one-to-one correspondence

30. Contributions and Future Work
Research Contributions
Surface Feature extraction technique
Performs on models in polyhedral representation
Relatively stable
Does not depend on global structure of the model
Current and Future Work:
Extract approximate B-Rep from polyhedral models
Introduce matching technique for extracted features
Use Scale-Space features for database indexing
Use (partial) scanned data for database queries
Explore techniques for feature extraction that resemble traditional CAD features

31. Q&A
For more information
Sponsored (in part) by: ONR Grant N NSF CAREER Award CISE/IIS