9:00 - 10:00 Keynote talk: Matching images with deformations,
David Jacobs (University of Maryland)
When we match images that come from the same object, we must
often allow for 2D, non-linear deformations. These can model changes in
shape that can occur when an object deforms or an articulated object
moves its parts, differences in shape between different instances of the
same type of object, or variations in apparent shape due to changes in
viewpoint. This talk will provide an overview of several approaches to
matching that stress finding problem formulations that yield
computationally efficient algorithms. First, I will present an
approximation algorithm for computing the Earth Mover's Distance (EMD),
a metric for comparing probability distributions that can be used to
match image descriptors, accounting for deformations. Using a
wavelet-based representation, we construct an accurate, linear time
algorithm for computing the EMD. I will then describe a novel image
descriptor that is invariant to deformations, and a shape descriptor
that is invariant to articulations. We use this shape matching algorithm
in a hand-held device for computer assisted plant species
identification. I will then show that the cost returned by a stereo
matching algorithm can be used for image matching when there deformation
due to pose variation. We use this to construct a face recognition
algorithm that compares 2D gallery and probe images taken from different
viewpoints. This algorithm outperforms all prior work on the CMU PIE
data set for face recognition with pose variation.
10:00 - 10:30 Coffee break
2D shapes and deformable images
- 10:30 - 11:00 Content-aware image resizing by quadratic programming,
Renjie Chen,
Daniel Freedman,
Zachi Karni,
Craig Gotsman,
Ligang Liu
- 11:00 - 11:30 Local pose estimation from a single keypoint
Alberto Del Bimbo,
Fernando Franco,
Federico Pernici
- 11:30 - 12:00 Straight skeletons for binary shapes
Markus Demuth,
Franz Aurenhammer,
Axel Pinz
13:30 - 14:30 Keynote talk: On surface comparison and symmetry,
Yaron Lipman (Princeton University)
In the first part of the talk we will suggest a method for automatic surface
comparison and alignment based on principles from conformal geometry and
optimal mass transportation. One application of the method is automatic
calculation of point correspondences between surfaces. Another application
is a novel distance definition between disc-type surfaces. In the second
part of the talk, we will discuss the relation between symmetry and the
shape matching problem. We will present a recent result of how symmetry can
be understood and/or used in this context.
Shape representation and inverse problems
- 14:30 - 15:00 Continuous Procrustes analysis to learn 2D shape models from 3D objects
Laura Igual,
Fernando De la Torre
- 15:00 - 15:30 Persistence-based segmentation of deformable shapes,
Primoz Skraba,
Maks Ovsjanikov,
Frederic Chazal,
Leonidas Guibas
15:30 - 16:00 Coffee break
16:00 - 17:00 Keynote talk: Metric geometry in shape matching,
Facundo Mémoli (Stanford University)
The problem of object matching under invariances can be studied using
certain tools from Metric Geometry. The central idea is to regard
objects as metric spaces (or measure metric spaces). The type of
invariance one wishes to have in the matching is encoded by the choice
of the metrics with which one endow the objects. The standard example
is matching objects in Euclidean space under rigid isometries: in this
situation one would endow the objects with the Euclidean metric. More
general scenarios are possible in which the desired invariance cannot
be reflected by the preservation of an ambient space metric.
Several ideas due to M. Gromov are useful for approaching this
problem. The Gromov-Hausdorff distance is a natural first candidate
for doing this. However, this metric leads to very hard combinatorial
optimization problems and it is difficult to relate to previously
reported practical approaches to the problem of object matching.
I will discuss different adaptations of these ideas, and in particular
will show a
construction of an L^p version of the Gromov-Hausdorff metric called
Gromov-Wassestein distance which is based on mass transportation ideas. This new
metric leads directly to quadratic optimization problems on continuous
variables with linear constraints. As a consequence of establishing
several lower bounds, it turns out that several invariants of metric
measure spaces are quantitatively stable in the GW sense. These
invariants provide
practical tools for the discrimination of shapes and connect the GW
ideas to several pre-existsting approaches.
After reviewing these constructions I will explain more recent
developments including spectral versions of the GW distance and
connections with persistent topology invariants.
Shape similarity
- 17:00 - 17:30 Bypass information-theoretic shape similarity from non-rigid
points-based alignment
Francisco Escolano,
Miguel Lozano,
Boyan Bonev,
Pablo Suau
- 17:30 - 18:00 Shape matching based on diffusion embedding and on mutual isometric consistency
Avinash Sharma,
Radu Horaud
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