Shapes From Pixels

Continuous-domain visual signals are usually captured as discrete (digital) images. This operation is not invertible in general, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image, unless it satisfies certain constraints (\emph{e.g.}, bandlimitedness). In this paper, we study the problem of recovering shape images with smooth boundaries from a set of samples. Thus, the reconstructed image is constrained to regenerate the same samples (consistency), as well as forming a shape (bilevel) image. We initially formulate the reconstruction technique by minimizing the shape perimeter over the set of consistent binary shapes. Next, we relax the non-convex shape constraint to transform the problem into minimizing the total variation over consistent non-negative-valued images. We also introduce a requirement (called reducibility) that guarantees equivalence between the two problems. We illustrate that the reducibility property effectively sets a requirement on the minimum sampling density. One can draw analogy between the reducibility property and the so-called restricted isometry property (RIP) in compressed sensing which establishes the equivalence of the $\ell_0$ minimization with the relaxed $\ell_1$ minimization. We also evaluate the performance of the relaxed alternative in various numerical experiments.Comment: 13 pages, 14 figure

Perceptual modalities guiding bat flight in a native habitat

Flying animals accomplish high-speed navigation through fields of obstacles using a suite of sensory modalities that blend spatial memory with input from vision, tactile sensing, and, in the case of most bats and some other animals, echolocation. Although a good deal of previous research has been focused on the role of individual modes of sensing in animal locomotion, our understanding of sensory integration and the interplay among modalities is still meager. To understand how bats integrate sensory input from echolocation, vision, and spatial memory, we conducted an experiment in which bats flying in their natural habitat were challenged over the course of several evening emergences with a novel obstacle placed in their flight path. Our analysis of reconstructed flight data suggests that vision, echolocation, and spatial memory together with the possible exercise of an ability in using predictive navigation are mutually reinforcing aspects of a composite perceptual system that guides flight. Together with the recent development in robotics, our paper points to the possible interpretation that while each stream of sensory information plays an important role in bat navigation, it is the emergent effects of combining modalities that enable bats to fly through complex spaces

Information of Structures in Galaxy Distribution

We introduce an information-theoretic measure, the Renyi information, to describe the galaxy distribution in space. We discuss properties of the information measure, and demonstrate its relationship with the probability distribution function and multifractal descriptions. Using the First Look Survey galaxy samples observed by the Infrared Array Camera onboard Spitzer Space Telescope, we present measurements of the Renyi information, as well as the counts-in-cells distribution and multifractal properties of galaxies in mid-infrared wavelengths. Guided by multiplicative cascade simulation based on a binomial model, we verify our measurements, and discuss the spatial selection effects on measuring information of the spatial structures. We derive structure scan functions at scales where selection effects are small for the Spitzer samples. We discuss the results, and the potential of applying the Renyi information to measuring other spatial structures.Comment: 25 pages, 8 figures, submitted to ApJ; To appear in The Astrophysical Journal 2006, 644, 678 (June 20th

Automated visual tracking for studying the ontogeny of zebrafish swimming

The zebrafish Danio rerio is a widely used model organism in studies of genetics, developmental biology, and recently, biomechanics. In order to quantify changes in swimming during all stages of development, we have developed a visual tracking system that estimates the posture of fish. Our current approach assumes planar motion of the fish, given image sequences taken from a top view. An accurate geometric fish model is automatically designed and fit to the images at each time frame. Our approach works across a range of fish shapes and sizes and is therefore well suited for studying the ontogeny of fish swimming, while also being robust to common environmental occlusions. Our current analysis focuses on measuring the influence of vertebra development on the swimming capabilities of zebrafish. We examine wild-type zebrafish and mutants with stiff vertebrae (stocksteif) and quantify their body kinematics as a function of their development from larvae to adult (mutants made available by the Hubrecht laboratory, The Netherlands). By tracking the fish, we are able to measure the curvature and net acceleration along the body that result from the fish's body wave. Here, we demonstrate the capabilities of the tracking system for the escape response of wild-type zebrafish and stocksteif mutant zebrafish. The response was filmed with a digital high-speed camera at 1500 frames s–1. Our approach enables biomechanists and ethologists to process much larger datasets than possible at present. Our automated tracking scheme can therefore accelerate insight in the swimming behavior of many species of (developing) fish

FRESH – FRI-based single-image super-resolution algorithm

In this paper, we consider the problem of single image super-resolution and propose a novel algorithm that outperforms state-of-the-art methods without the need of learning patches pairs from external data sets. We achieve this by modeling images and, more precisely, lines of images as piecewise smooth functions and propose a resolution enhancement method for this type of functions. The method makes use of the theory of sampling signals with finite rate of innovation (FRI) and combines it with traditional linear reconstruction methods. We combine the two reconstructions by leveraging from the multi-resolution analysis in wavelet theory and show how an FRI reconstruction and a linear reconstruction can be fused using filter banks. We then apply this method along vertical, horizontal, and diagonal directions in an image to obtain a single-image super-resolution algorithm. We also propose a further improvement of the method based on learning from the errors of our super-resolution result at lower resolution levels. Simulation results show that our method outperforms state-of-the-art algorithms under different blurring kernels

Microrheology with optical tweezers: data analysis

We present a data analysis procedure that provides the solution to a long-standing issue in microrheology studies, i.e. the evaluation of the fluids' linear viscoelastic properties from the analysis of a finite set of experimental data, describing (for instance) the time-dependent mean-square displacement of suspended probe particles experiencing Brownian fluctuations. We report, for the first time in the literature, the linear viscoelastic response of an optically trapped bead suspended in a Newtonian fluid, over the entire range of experimentally accessible frequencies. The general validity of the proposed method makes it transferable to the majority of microrheology and rheology techniques

Minimal Solvers for Monocular Rolling Shutter Compensation under Ackermann Motion

Modern automotive vehicles are often equipped with a budget commercial rolling shutter camera. These devices often produce distorted images due to the inter-row delay of the camera while capturing the image. Recent methods for monocular rolling shutter motion compensation utilize blur kernel and the straightness property of line segments. However, these methods are limited to handling rotational motion and also are not fast enough to operate in real time. In this paper, we propose a minimal solver for the rolling shutter motion compensation which assumes known vertical direction of the camera. Thanks to the Ackermann motion model of vehicles which consists of only two motion parameters, and two parameters for the simplified depth assumption that lead to a 4-line algorithm. The proposed minimal solver estimates the rolling shutter camera motion efficiently and accurately. The extensive experiments on real and simulated datasets demonstrate the benefits of our approach in terms of qualitative and quantitative results.Comment: Submitted to WACV 201