13,491 research outputs found
Local Descriptors Optimized for Average Precision
Extraction of local feature descriptors is a vital stage in the solution
pipelines for numerous computer vision tasks. Learning-based approaches improve
performance in certain tasks, but still cannot replace handcrafted features in
general. In this paper, we improve the learning of local feature descriptors by
optimizing the performance of descriptor matching, which is a common stage that
follows descriptor extraction in local feature based pipelines, and can be
formulated as nearest neighbor retrieval. Specifically, we directly optimize a
ranking-based retrieval performance metric, Average Precision, using deep
neural networks. This general-purpose solution can also be viewed as a listwise
learning to rank approach, which is advantageous compared to recent local
ranking approaches. On standard benchmarks, descriptors learned with our
formulation achieve state-of-the-art results in patch verification, patch
retrieval, and image matching.Comment: 13 pages, 8 figures. IEEE Conference on Computer Vision and Pattern
Recognition (CVPR), 201
Sliced Wasserstein Kernel for Persistence Diagrams
Persistence diagrams (PDs) play a key role in topological data analysis
(TDA), in which they are routinely used to describe topological properties of
complicated shapes. PDs enjoy strong stability properties and have proven their
utility in various learning contexts. They do not, however, live in a space
naturally endowed with a Hilbert structure and are usually compared with
specific distances, such as the bottleneck distance. To incorporate PDs in a
learning pipeline, several kernels have been proposed for PDs with a strong
emphasis on the stability of the RKHS distance w.r.t. perturbations of the PDs.
In this article, we use the Sliced Wasserstein approximation SW of the
Wasserstein distance to define a new kernel for PDs, which is not only provably
stable but also provably discriminative (depending on the number of points in
the PDs) w.r.t. the Wasserstein distance between PDs. We also demonstrate
its practicality, by developing an approximation technique to reduce kernel
computation time, and show that our proposal compares favorably to existing
kernels for PDs on several benchmarks.Comment: Minor modification
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence
We introduce a new framework for learning dense correspondence between
deformable 3D shapes. Existing learning based approaches model shape
correspondence as a labelling problem, where each point of a query shape
receives a label identifying a point on some reference domain; the
correspondence is then constructed a posteriori by composing the label
predictions of two input shapes. We propose a paradigm shift and design a
structured prediction model in the space of functional maps, linear operators
that provide a compact representation of the correspondence. We model the
learning process via a deep residual network which takes dense descriptor
fields defined on two shapes as input, and outputs a soft map between the two
given objects. The resulting correspondence is shown to be accurate on several
challenging benchmarks comprising multiple categories, synthetic models, real
scans with acquisition artifacts, topological noise, and partiality.Comment: Accepted for publication at ICCV 201
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