Download presentation

Presentation is loading. Please wait.

Published byEmanuel Norcott Modified over 2 years ago

1
1/20 Using M-Reps to include a-priori Shape Knowledge into the Mumford-Shah Segmentation Functional FWF - Forschungsschwerpunkt S092 Subproject 7 „Pattern and 3D Shape Recognition“ Grossauer Harald

2
2/20 Outlook Mumford-Shah Mumford-Shah with a-priori knowledge Medial axis and m-reps Statistical analysis of shapes

3
3/20 Original Mumford-Shah functional: For minimizers (u,C) : –u … piecewise constant approximation of f –C … curve along which discontinuities of u are located Mumford-Shah

4
4/20

5
5/20 Replace by d(S ap,S) S ap represents the expected shape (prior) d(S ap,∙) somehow measures the distance to the prior Mumford-Shah with a-priori knowledge How is „somehow“?

6
6/20 Curve representation Curves (resp. surfaces) are frequently represented as –Triangle mesh (easy to render) –Set of spline control points (smoother) –CSG, … Problems: –Local boundary description –No global shape properties

7
7/20 Blum‘s Medial Axis (in 2D) Medial axis for a given „shape“ S : Set of centers of all circles that can be inscribed into S, which touch S at two or more points Medial axis + radius function → Medial axis representation (m-reps)

8
8/20 Information derived from the m-rep (1) Connection graph: –Hierarchy of figure(s) –Main figure, protrusion, intrusion –Topology of surface –Connection and substance edges

9
9/20 Let be a parametrization of, then – is the „principal direction“ of S – describes the „bending“ of S – is the local „thinning“ or „thickening“ of S –Branchings of may indicate singular surface points (edges, corners) Information derived from the m-rep (2)

10
10/20 Problem of m-reps Stability: We never infer the medial axis from the boundary surface!

11
11/20 Discrete representation (in 3D) Approximate medial manifold by a mesh Store radius in each mesh node → Bad approximation of surface → Store more information per node: Medial Atoms

12
12/20 Medial Atoms (in 3D) Stored per node: Position and radius Local coordinate frame Opening angle Elongation (for „boundary atoms“ only)

13
13/20 Shape description by medial atoms One medial atom: Shape consisting of N medial Atoms: + connection graph

14
14/20 A distance between shapes? Current main problem: What is a suitable distance Or maybe even consider

15
15/20 Statistical analysis of shapes Goal: Principal Component Analysis (PCA) of a set of shapes Zero‘th principal component = mean value Problem: is not a vector space

16
16/20 Statistical analysis of shapes Variational formulation of mean value: No vector space structure needed, but not necessarily unique → All S i must be in a „small enough neighborhood“

17
17/20 How to carry over these concepts from the vector space to the manifold ? PCA in For data the k ‘th principal component is defined inductively by: – is orthogonal to – is orthogonal to the subspace, where: has codimension k the variance of the data projected onto is maximal

18
18/20 Principal Geodesic Analysis Vector spaceManifold Linear subspaceGeodesic submanifold Projection onto subspace Closest point on submanifold Problem again: not necessarily unique

19
19/20 Principal Geodesic Analysis Second main problem(s): –Under what conditions is PGA meaningful? –How to deal with the non-uniqueness? –Does PGA capture shape variability well enough? –How to compute PGA efficiently?

20
20/20 The End Comments? Ideas? Questions? Suggestions?

Similar presentations

OK

COMP 175 | COMPUTER GRAPHICS Remco Chang1/6103b – Shapes Lecture 03b: Shapes COMP 175: Computer Graphics February 3, 2015.

COMP 175 | COMPUTER GRAPHICS Remco Chang1/6103b – Shapes Lecture 03b: Shapes COMP 175: Computer Graphics February 3, 2015.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on planet venus Ppt on surface water data Ppt on rc coupled amplifier Ppt on earthquakes and volcanoes Ppt on types of agriculture in india Ppt on principles of peace building institute of africa Ppt on conservation of natural resources Ppt on geothermal energy in india Slideshare ppt on leadership Ppt on care of public property record