Searching the Sky with CONFIGR-STARS

SyNAPSE program of the Defense Advanced Projects Research Agency (HRL Laboratories LLC, subcontract #801881-BS under DARPA prime contract HR0011-09-C-0001); CELEST, a National Science Foundation Science of Learning Center (SBE-0354378)CONFIGR-STARS, a new methodology based on a model of the human visual system, is developed for registration of star images. The algorithm first applies CONFIGR, a neural model that connects sparse and noisy image components. CONFIGR produces a web of connections between stars in a reference starmap or in a test patch of unknown location. CONFIGR-STARS splits the resulting, typically highly connected, web into clusters, or "constellations." Cluster geometry is encoded as a signature vector that records edge lengths and angles relative to the cluster’s baseline edge. The location of a test patch cluster is identified by comparing its signature to signatures in the codebook of a reference starmap, where cluster locations are known. Simulations demonstrate robust performance in spite of image perturbations and omissions, and across starmaps from different sources and seasons. Further studies would test CONFIGR-STARS and algorithm variations applied to very large starmaps and to other technologies that may employ geometric signatures. Open-source code, data, and demos are available from http://techlab.bu.edu/STARS/

Four Soviets Walk the Dog-Improved Bounds for Computing the Fr\'echet Distance

Given two polygonal curves in the plane, there are many ways to define a notion of similarity between them. One popular measure is the Fr\'echet distance. Since it was proposed by Alt and Godau in 1992, many variants and extensions have been studied. Nonetheless, even more than 20 years later, the original $O(n^2 \log n)$ algorithm by Alt and Godau for computing the Fr\'echet distance remains the state of the art (here, $n$ denotes the number of edges on each curve). This has led Helmut Alt to conjecture that the associated decision problem is 3SUM-hard. In recent work, Agarwal et al. show how to break the quadratic barrier for the discrete version of the Fr\'echet distance, where one considers sequences of points instead of polygonal curves. Building on their work, we give a randomized algorithm to compute the Fr\'echet distance between two polygonal curves in time $O(n^2 \sqrt{\log n}(\log\log n)^{3/2})$ on a pointer machine and in time $O(n^2(\log\log n)^2)$ on a word RAM. Furthermore, we show that there exists an algebraic decision tree for the decision problem of depth $O(n^{2-\varepsilon})$, for some $\varepsilon > 0$. We believe that this reveals an intriguing new aspect of this well-studied problem. Finally, we show how to obtain the first subquadratic algorithm for computing the weak Fr\'echet distance on a word RAM.Comment: 34 pages, 15 figures. A preliminary version appeared in SODA 201

M\"obius Invariants of Shapes and Images

Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to this problem is to identify the group of possible transformations of the object and to find invariants to the action of that group, meaning that the object has the same values of the invariants despite the action of the group. In this paper we study the invariants of planar shapes and images under the M\"obius group $\mathrm{PSL}(2,\mathbb{C})$, which arises in the conformal camera model of vision and may also correspond to neurological aspects of vision, such as grouping of lines and circles. We survey properties of invariants that are important in applications, and the known M\"obius invariants, and then develop an algorithm by which shapes can be recognised that is M\"obius- and reparametrization-invariant, numerically stable, and robust to noise. We demonstrate the efficacy of this new invariant approach on sets of curves, and then develop a M\"obius-invariant signature of grey-scale images

Vision-Based Localization Algorithm Based on Landmark Matching, Triangulation, Reconstruction, and Comparison

Many generic position-estimation algorithms are vulnerable to ambiguity introduced by nonunique landmarks. Also, the available high-dimensional image data is not fully used when these techniques are extended to vision-based localization. This paper presents the landmark matching, triangulation, reconstruction, and comparison (LTRC) global localization algorithm, which is reasonably immune to ambiguous landmark matches. It extracts natural landmarks for the (rough) matching stage before generating the list of possible position estimates through triangulation. Reconstruction and comparison then rank the possible estimates. The LTRC algorithm has been implemented using an interpreted language, onto a robot equipped with a panoramic vision system. Empirical data shows remarkable improvement in accuracy when compared with the established random sample consensus method. LTRC is also robust against inaccurate map data

Non-Rigid Puzzles

Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non-rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non-rigid multi-part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non-rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario

Water Clouds in Y Dwarfs and Exoplanets

The formation of clouds affects brown dwarf and planetary atmospheres of nearly all effective temperatures. Iron and silicate condense in L dwarf atmospheres and dissipate at the L/T transition. Minor species such as sulfides and salts condense in mid-late T dwarfs. For brown dwarfs below Teff=450 K, water condenses in the upper atmosphere to form ice clouds. Currently over a dozen objects in this temperature range have been discovered, and few previous theoretical studies have addressed the effect of water clouds on brown dwarf or exoplanetary spectra. Here we present a new grid of models that include the effect of water cloud opacity. We find that they become optically thick in objects below Teff=350-375 K. Unlike refractory cloud materials, water ice particles are significantly non-gray absorbers; they predominantly scatter at optical wavelengths through J band and absorb in the infrared with prominent features, the strongest of which is at 2.8 microns. H2O, NH3, CH4, and H2 CIA are dominant opacity sources; less abundant species such as may also be detectable, including the alkalis, H2S, and PH3. PH3, which has been detected in Jupiter, is expected to have a strong signature in the mid-infrared at 4.3 microns in Y dwarfs around Teff=450 K; if disequilibrium chemistry increases the abundance of PH3, it may be detectable over a wider effective temperature range than models predict. We show results incorporating disequilibrium nitrogen and carbon chemistry and predict signatures of low gravity in planetary- mass objects. Lastly, we make predictions for the observability of Y dwarfs and planets with existing and future instruments including the James Webb Space Telescope and Gemini Planet Imager.Comment: 23 pages, 20 figures, Revised for Ap