On Using Physical Analogies for Feature and Shape Extraction in Computer Vision

There is a rich literature of approaches to image feature extraction in computer vision. Many sophisticated approaches exist for low- and for high-level feature extraction but can be complex to implement with parameter choice guided by experimentation, but with performance analysis and optimization impeded by speed of computation. We have developed new feature extraction techniques on notional use of physical paradigms, with parametrization aimed to be more familiar to a scientifically trained user, aiming to make best use of computational resource. This paper is the first unified description of these new approaches, outlining the basis and results that can be achieved. We describe how gravitational force can be used for low-level analysis, while analogies of water flow and heat can be deployed to achieve high-level smooth shape detection, by determining features and shapes in a selection of images, comparing results with those by stock approaches from the literature. We also aim to show that the implementation is consistent with the original motivations for these techniques and so contend that the exploration of physical paradigms offers a promising new avenue for new approaches to feature extraction in computer vision

Smooth quasi-developable surfaces bounded by smooth curves

Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not adequate for generating smooth quasi-developable surfaces. We propose the first method which is capable of exploring the full solution space of continuous input curves to compute a smooth quasi-developable ruled surface with as large developability as possible. The resulting surface is exactly bounded by the input smooth curves and is guaranteed to have no self-intersections. The main contribution is a variational approach to compute a continuous mapping of parameters of input curves by minimizing a function evaluating surface developability. Moreover, we also present an algorithm to represent a resulting surface as a B-spline surface when input curves are B-spline curves.Comment: 18 page

Beyond standard benchmarks: Parameterizing performance evaluation in visual object tracking

Object-to-camera motion produces a variety of apparent motion patterns that significantly affect performance of short-term visual trackers. Despite being crucial for designing robust trackers, their influence is poorly explored in standard benchmarks due to weakly defined, biased and overlapping attribute annotations. In this paper we propose to go beyond pre-recorded benchmarks with post-hoc annotations by presenting an approach that utilizes omnidirectional videos to generate realistic, consistently annotated, short-term tracking scenarios with exactly parameterized motion patterns. We have created an evaluation system, constructed a fully annotated dataset of omnidirectional videos and the generators for typical motion patterns. We provide an in-depth analysis of major tracking paradigms which is complementary to the standard benchmarks and confirms the expressiveness of our evaluation approach

Symmetry Detection of Rational Space Curves from their Curvature and Torsion

We present a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric. By using well-known differential invariants of space curves, namely the curvature and torsion, the method is significantly faster, simpler, and more general than an earlier method addressing a similar problem. To support this claim, we present an analysis of the arithmetic complexity of the algorithm and timings from an implementation in Sage.Comment: 25 page

Learning Unitary Operators with Help From u(n)

A major challenge in the training of recurrent neural networks is the so-called vanishing or exploding gradient problem. The use of a norm-preserving transition operator can address this issue, but parametrization is challenging. In this work we focus on unitary operators and describe a parametrization using the Lie algebra $\mathfrak{u}(n)$ associated with the Lie group $U(n)$ of $n \times n$ unitary matrices. The exponential map provides a correspondence between these spaces, and allows us to define a unitary matrix using $n^2$ real coefficients relative to a basis of the Lie algebra. The parametrization is closed under additive updates of these coefficients, and thus provides a simple space in which to do gradient descent. We demonstrate the effectiveness of this parametrization on the problem of learning arbitrary unitary operators, comparing to several baselines and outperforming a recently-proposed lower-dimensional parametrization. We additionally use our parametrization to generalize a recently-proposed unitary recurrent neural network to arbitrary unitary matrices, using it to solve standard long-memory tasks.Comment: 9 pages, 3 figures, 5 figures inc. subfigures, to appear at AAAI-1

Estimating Depth from RGB and Sparse Sensing

We present a deep model that can accurately produce dense depth maps given an RGB image with known depth at a very sparse set of pixels. The model works simultaneously for both indoor/outdoor scenes and produces state-of-the-art dense depth maps at nearly real-time speeds on both the NYUv2 and KITTI datasets. We surpass the state-of-the-art for monocular depth estimation even with depth values for only 1 out of every ~10000 image pixels, and we outperform other sparse-to-dense depth methods at all sparsity levels. With depth values for 1/256 of the image pixels, we achieve a mean absolute error of less than 1% of actual depth on indoor scenes, comparable to the performance of consumer-grade depth sensor hardware. Our experiments demonstrate that it would indeed be possible to efficiently transform sparse depth measurements obtained using e.g. lower-power depth sensors or SLAM systems into high-quality dense depth maps.Comment: European Conference on Computer Vision (ECCV) 2018. Updated to camera-ready version with additional experiment