3D Shape Similarity: Measuring and Comparing 3D Model Distributions, Study notes of Electrical and Electronics Engineering

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Presented By Ryan Amundsen and Paritosh Gupta University of Michigan EECS 598

 Don’t go to Princeton if you don’t like to write

 3D Shape Similarity is a fundamental task

› Recognition, retrieval, clustering, and classification › Computer Vision, Mechanical Engineering, and Molecular Biology

 3D model databases can expand to a

variety of fields because

› Improved Modeling Tools › World Wide Web spreads availability of 3D models › Hardware and CPU’s are getting faster

 Current Issues

› Different file formats

› Different scanning tools

› Inconsistencies in tagging

› Missing, intersecting, or Overlapping Polygons

› More Complex Parameters

› Pose recognition more difficult

 Previous Works Had Difficulty with 3D

polygon soups

 Classification requires solutions to costly

problems:

› Reconstruction of 3D Models

› Parameterization (e.g. boundary, arc length)

› Registration (e.g. coordinate systems for

alignment)

› Correspondence of features

 A3: Measures the angle between three random

points on the surface of a 3D model.

 D1: Measures the distance between a fixed point

and one random point on the surface. The

centroid of the boundary of the model as the

fixed point.

 D2: Measures the distance between two random

points on the surface.

 D3: Measures the square root of the area

of the triangle between three random points on the surface.

 D4: Measures the cube root of the

volume of the tetrahedron between four random points on the surface.

 Invariance › D2: Rigid motions, mirror imaging with normalization, scaling, rotation › A3: Scaling always invariant  Robustness › Insensitivity to small perturbations  Noise  Blur  Cracks  Dust  Metric › If the distance measure is a metric, then so will be dissimilarity measure  Efficiency - see in results  Generality – independence of color, general for method stored,

 Align maximum magnitudes

 Align mean magnitudes

 Search for most similar scale constant

1. Divide model’s surface into triangles
2. Each triangle is given a probability

proportional to the total surface area of 3D object

3. Select random point from selected triangle

from randomly selected triangle

 The following dissimilarity measures were

used. For the PDF, and CDF measures,

only N= 1,2, ∞ were tested:

 Coded in C++

 3D Models used composed of

independent polygons

 Contained between 20 to 186,

polygons (average = 7000)

 Most models contained cracks, self-

intersections, missing polygons

 Experiments were run on a PC with 400

MHz Pentium II Processor and 256MB of memory

 D2 shape function, MEAN normalization

method, PDF L1 norm

 10 models

 8 Transformations

 90 model library (including original model)

D2 of Seven Variants of the 10 models

 D2 of two models for seven different

tessellations of polygons each.