Simon Korman

Coherency Sensitive Hashing

Coherency Sensitive Hashing (CSH) extends Locality Sensitivity Hashing (LSH) and PatchMatch to quickly find matching patches between two images. LSH relies on hashing, which maps similar patches to the same bin, in order to find matching patches. PatchMatch, on the other hand, relies on the observation that images are coherent, to propagate good matches to their neighbors, in the image plane. It uses random patch assignment to seed the initial matching. CSH relies on hashing to seed the initial patch matching and on image coherence to propagate good matches. In addition, hashing lets it propagate information between patches with similar appearance (i.e., map to the same bin). This way, information is propagated much faster because it can use similarity in appearance space or neighborhood in the image plane. As a result, CSH is at least three to four times faster than PatchMatch and more accurate, especially in textured regions, where reconstruction artifacts are most noticeable to the human eye. We verified CSH on a new, large scale, data set of 133 image pairs.

FasT-Match: Fast Affine Template Matching

Fast-Match is a fast algorithm for approximate template matching under 2D affine transformations that minimizes the Sum-of-Absolute-Differences (SAD) error measure. There is a huge number of transformations to consider but we prove that they can be sampled using a density that depends on the smoothness of the image. For each potential transformation, we approximate the SAD error using a sub linear algorithm that randomly examines only a small number of pixels. We further accelerate the algorithm using a branch-and-bound scheme. As images are known to be piecewise smooth, the result is a practical affine template matching algorithm with approximation guarantees, that takes a few seconds to run on a standard machine. We perform several experiments on three different datasets, and report very good results. To the best of our knowledge, this is the first template matching algorithm which is guaranteed to handle arbitrary 2D affine transformations.

Inverting RANSAC: Global model detection via inlier rate estimation

This work presents a novel approach for detecting inliers in a given set of correspondences (matches). It does so without explicitly identifying any consensus set, based on a method for inlier rate estimation (IRE). Given such an estimator for the inlier rate, we also present an algorithm that detects a globally optimal transformation. We provide a theoretical analysis of the IRE method using a stochastic generative model on the continuous spaces of matches and transformations. This model allows rigorous investigation of the limits of our IRE method for the case of 2D-translation, further giving bounds and insights for the more general case. Our theoretical analysis is validated empirically and is shown to hold in practice for the more general case of 2D-affinities. In addition, we show that the combined framework works on challenging cases of 2D-homography estimation, with very few and possibly noisy inliers, where RANSAC generally fails.

Probably Approximately Symmetric: Fast Rigid Symmetry Detection With Global Guarantees

We present a fast algorithm for global rigid symmetry detection with approximation guarantees. The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user‐specified threshold, with very high probability. Our method uses a carefully designed sampling of the transformation space, where each transformation is efficiently evaluated using a sublinear algorithm. We prove that the density of the sampling depends on the total variation of the shape, allowing us to derive formal bounds on the algorithms complexity and approximation quality. We further investigate different volumetric shape representations (in the form of truncated distance transforms), and in such a way control the total variation of the shape and hence the sampling density and the runtime of the algorithm. A comprehensive set of experiments assesses the proposed method, including an evaluation on the eight categories of the COSEG data set. This is the first large‐scale evaluation of any symmetry detection technique that we are aware of.

DCSH - Matching Patches in RGBD Images

We extend patch based methods to work on patches in 3D space. We start with Coherency Sensitive Hashing (CSH), which is an algorithm for matching patches between two RGB images, and extend it to work with RGBD images. This is done by warping all 3D patches to a common virtual plane in which CSH is performed. To avoid noise due to warping of patches of various normals and depths, we estimate a group of dominant planes and compute CSH on each plane separately, before merging the matching patches. The result is DCSH - an algorithm that matches world (3D) patches in order to guide the search for image plane matches. An independent contribution is an extension of CSH, which we term Social-CSH. It allows a major speedup of the k nearest neighbor (kNN) version of CSH - its runtime growing linearly, rather than quadratic ally, in k. Social-CSH is used as a subcomponent of DCSH when many NNs are required, as in the case of image denoising. We show the benefits of using depth information to image reconstruction and image denoising, demonstrated on several RGBD images.

Fast-Match: Fast Affine Template Matching

Fast-Match is a fast algorithm for approximate template matching under 2D affine transformations that minimizes the Sum-of-Absolute-Differences (SAD) error measure. There is a huge number of transformations to consider but we prove that they can be sampled using a density that depends on the smoothness of the image. For each potential transformation, we approximate the SAD error using a sublinear algorithm that randomly examines only a small number of pixels. We further accelerate the algorithm using a branch-and-bound-like scheme. As images are known to be piecewise smooth, the result is a practical affine template matching algorithm with approximation guarantees, that takes a few seconds to run on a standard machine. We perform several experiments on three different datasets, and report very good results.

Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays

Understanding the local behaviour of structured multi-dimensional data is a fundamental problem in various areas of computer science. As the amount of data is often huge, it is desirable to obtain sublinear time algorithms, and specifically property testers, to understand local properties of the data. We focus on the natural local problem of testing pattern freeness: given a large

Tight Approximation of Image Matching

d

Testing Pattern-Freeness.

-dimensional array

Peeking Template Matching for Depth Extension

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