Mesh Scissoring with Minima Rule and Part Salience

Yunjin Lee ,Seungyong Lee , Ariel Shamir,Daniel cohen-Or,

Hans-Peter SeidelComputer Aided Geometric Design, vol. 22, no. 5, pp. 444-465, Elsevier Science, 2005 . (CAGD05).

Outline

• About Atuhor• Definitions• Related work• Main Step• Experimental Results• Summary and Discussion

About Author

Yunjin LeePost-Doc researcher

Computer Graphics Lab. Dept. of Computer Sci. and Eng., POSTECH

Research Interests Mesh parameterization mesh segmentation mesh signal processing surface reconstruction non-photorealistic rendering.

About Author

Seungyong Lee Dept. of Computer Sci. and Eng., POSTECH

Research Interests

Computer Graphics Computer Animation Image Processing

About Author

Ariel ShamirEfi Arazi School of Computer Science

The Interdisciplinary Center

Research Interests Mesh Partitioning Skeleton Based Representations Multi-Resolution Models Object Feature-Space Analysis Digital Typography Visual Succinct Representation of Infor

About Author

Daniel Cohen-Or School of Computer Science, Tel Aviv University

Research Interests

Computer Graphics, in particular, rendering and modeling techniques

Motion and Transformations Visibility Techniques Shapes and Surfaces Point-based Modeling

About Author

Hans-Peter SeidelHead of the Computer Graphics Department

MPII for Computer Science, Saarbrücken

Awarded the “Leibniz Prize” in 2003

Definitions

• Mesh Scissoring• Minima Rule• Part Salience• Feature Contour• Geometric Snake

Mesh Scissoringextracting sub-parts and pieces from exsting meshes part-type segmentation patch-type segmentation

A. Shamir, A formulation of boundary mesh segmentation, in: Proc.2nd International Symposium on 3D Data Processing, Visualization, and Transmission, 2004.

Minima Rule

• defining a framework for how human perception might decompose an object into its constituent parts

• all negative minima of the principal curvatures (along their associated lines of curvature) form boundaries between parts

D. Hoffman, W. Richards, Parts of recognition, Cognition 18 (1984) 65–96.

Part Salience

• the size relative to the whole object• the degree to which it protrudes• the strength of its boundaries.

figure-groundD. Hoffman, M. Signh, Salience of visual parts, Cognition 63 (1997) 29–78.

Geometric Snake

• external energy Emesh: capturing capture nearby features• internal energy Espline: smoothing shape and shorten length

Related Work growing regions merging regions

Overview

Feature Contour Extraction

• extracting feature contours on the mesh • normalization of curvature values• contour connection• selecting a feature contour

normalized values assigned to the vertices of a horse model

Loop Completion• completing the feature contour to a closed loop• distance function• normal function• centricity function• feature function

Part Salience Test

• rejecting the loop if the conditions of part salience are not satisfied

• area: summing the areas of triangles in the segment• protrusion: using a fitting plane obtained from the sample

points on a contour• feature： preventing high feature contours from being reje

cted by the protrusion test.

Snake Movement

• evolving the snake to a loop’s final position for cutting

Experimental Results

Experimental Results

Experimental Results

Experimental Results

Summary and Discussion

• working the best in a semi-automatic setting

• no global search for the best cut

Growing Regions• A. P. Mangan, R. T. Whitaker, Partitioning 3D surface meshes using

watershed segmentation, IEEE Trans. Visualization and Computer Graphics 5 (4) (1999) 308–321.

• A. D. Kalvin, R. H. Taylor, Superfaces: Polygonal mesh simplification with bounded error, IEEE Computer Graphics and Applications 16 (3) (1996) 64–77.24

• O. Sorkine, D. Cohen-Or, R. Goldenthal, D. Lischinski, Bounded-distortion piecewise mesh parameterization, in: Proc. IEEE Visualization 2002, 2002, pp.355–362.

• S. Shlafman, A. Tal, S. Katz, Metamorphosis of polyhedral surfaces using decomposition, Computer Graphics Forum (Proc. Eurographics 2002) 21 (3)(2002) 219–228.

Merging Regions• M. Garland, A. Willmott, P. Heckbert, Hierarchical face clusterin

g on polygonal surfaces, in: Proc. 2001 ACM Symposium on Interactive 3D Graphics, 2001, pp. 49–58.

• T. DeRose, M. Kass, T. Truong, Subdivision surfaces in character animation, ACM Computer Graphics (Proc. of SIGGRAPH ’98) (1998) 85–94.

• O. D. Faugeras, M. Hebert, The representation, recognition, and positioning of 3-D shapes from range data, in: T. Kanade (Ed.), Three-Dimensional Machine Vision, Kluwer Academic Publishers, 1987, pp. 301–353.

same thresholds different meshes

Contour Connection

Approximations

Distance Function

measuring the distances from to other vertices

Normal Function

lower for normals that face opposite directions of

Centricity Function

being perpendicular to the medial axis of a mesh shape.

Feature Function

Area

Protrusion

blue planes are the fitting planes of contours red points indicate the farthest points from the planes

Feature