Elsevier

Neural Networks

Volume 24, Issue 2, March 2011, Pages 208-216
Neural Networks

Searching the sky with CONFIGR-STARS

https://doi.org/10.1016/j.neunet.2010.10.007Get rights and content

Abstract

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/.

Introduction

Advances in telescope and camera technology have dramatically increased the ability of amateur astronomers to contribute to star image archives. Professionals and amateurs now create a plethora of quality images which, like historical image libraries, are not necessarily registered. Instruments, weather, and lighting produce substantial variability across observations, and “a vast majority of astronomical data is in disarray” (Romero, 2008, p. 14). New tools for registering star image patches with respect to a standard atlas would help astronomers to add partially documented data to archives and share information.

Through history and across civilizations, humans have cross-referenced star images by clustering salient groups and connecting them to form constellations. Star cluster identification is supported by star-gazing software such as Astrometry.net (http://astronomy.net), Google Earth Sky (http://earth.google.com/sky/index.html), and Stellarium (http://stellarium.org). These programs threshold the brightest stars, then do a template search for characteristic features of known neighborhoods.

The present work introduces a novel method that applies a model of human vision to the star image registration problem. While building a coherent representation of a retinal image, the visual system links spatially separated segments. Early visual areas in the brain—V1–V2–V4—compensate for small and large gaps by completing boundaries and filling in features. CONFIGR (CONtour FIgure and GRound) is a computational model based on principles of biological vision that completes sparse and noisy image figures (Carpenter, Gaddam, & Mingolla, 2007). CONFIGR balances filling-in as figure against complementary filling-in as ground. Originally designed to fill in missing contours in an incomplete image such as a dashed line, the same CONFIGR system connects sparse dots and unifies occluded objects. The model self-scales its completion distances, filling in across gaps of any length, where unimpeded, while limiting connections among dense pixel groups. Code, data, and demos of the general-purpose CONFIGR algorithm, which runs without free parameters, are available from http://techlab.bu.edu/CONFIGR/.

CONFIGR-STARS extends the CONFIGR model to address the star image registration problem. Computational examples demonstrate how the system finds the location of a star test patch that may be rotated or perturbed, with omissions and noise. Various starmaps and test patches illustrate the robustness of the CONFIGR-STARS algorithm.

Romero (2008) describes a related method that maps a test patch with unknown location to a reference map with a billion stars. This algorithm clusters a test patch into groups of four stars. For each quad, the geometry of the stars’ relative positions is translated to a four-dimensional code, which is compared to quad codes in a star catalogue. To define a quad, the two most distant stars form the diameter of a circular neighborhood of interest, within which the relative positions of the other two stars are encoded. This project has now become part of Google Earth Skyview.

The present article constitutes a pilot study of a new method that complements existing methods. In contrast to the Romero method, CONFIGR iterates its connection computations to convergence, with no local neighborhood constraints, and CONFIGR-STARS encodes geometric measures (length ratios and angles) of each cluster. Further studies would explore the marginal utility of the CONFIGR-STARS method on large starmaps.

Fig. 1 shows how CONFIGR-STARS locates an unlabeled test patch (Fig. 1(a)) in a reference starmap. The NASA starmap of the Northern Hemisphere winter evening sky was produced using Star Maps software from the Mount Wilson Observatory. The CONFIGR algorithm computes short-range and long-range connections between test patch stars (Fig. 1(b)). CONFIGR-STARS then splits the resulting web into smaller star clusters (Fig. 1(c)). Geometric signatures of test patch clusters with three or four edges serve as footprints for registration with a starmap, where each CONFIGR-STARS cluster has an associated location (Fig. 1(d)). Note that, in this example, only three of the four test patch cluster edges correspond geometrically to edges in the identified starmap cluster. Given the large space of possible configurations, even partial cluster matches successfully map test patches to clusters in the reference starmap. For visibility, simulation examples show identified starmap areas magnified to the scale of the test patch, and stars are displayed as larger than their one-pixel size.

Starmap A (Fig. 1) includes stars that are brighter than a designated threshold value. The (dimensionless) brightness of astronomical objects is defined as the ratio of brightness as seen by an observer on Earth to brightness in the absence of the atmosphere. With a logarithmic scale that originated in ancient Greece, the smaller the numerical value, the brighter the object, so the brightest stars are “of the first magnitude”. In modern usage (http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980302a.html), an object that is 2.5 times dimmer than another is one magnitude greater, with the bright star Vega close to the baseline magnitude 0.0. The human eye can detect stars from magnitude 6.5 (dimmest), on a dark clear night far from city lights, to −1.5 (the brightest, Sirius). In suburbs or cities, stars may be visible only to magnitudes 2–4. Jupiter may be as bright as −3, and Venus as bright as −4. The full moon is near magnitude −13, and the sun near magnitude −27. Starmap A includes stars of brightness magnitude less than 6, and the visible planets.

The telescope or camera used to capture a test patch is assumed to record the brightness levels of stars and their spatial scales. CONFIGR-STARS projects each star in a test patch or starmap to a single pixel, which is labeled image-figure. For a set of sparsely distributed image-figure pixels (Fig. 2(a)), CONFIGR produces a web of connections. In Fig. 2(b), CONFIGR edges connect six dots to one other dot, 27 to two others, and seven dots to three others. In all, CONFIGR produces 41 figure connections. As Fig. 2(b) indicates, CONFIGR connects pixels across arbitrarily long, but unobstructed, distances, and does so using the same mechanisms as for short-range connections. Although the final connected figure is suggestive of optimization procedures such as those applied to the Traveling Salesman Problem (Flood, 1956), CONFIGR relies on local image-based computations, not the minimization of a global cost function.

CONFIGR-STARS splits the web into clusters that have up to four connected segments, with one to five star vertices (Fig. 2(c)). The geometry of each cluster is encoded as a six-dimensional signature, which records edge lengths and angles relative to a baseline edge. The dictionary of signatures in a reference starmap produces a codebook. For a test patch of unknown location, CONFIGR-STARS computes cluster signatures that are quickly matched to starmap signatures, whose cluster locations are known. Two clusters are defined as matched if all, or all but one, of the edges meet a specified matching criterion.

Section 2 summarizes the CONFIGR model, and Section 3 shows how the CONFIGR-STARS algorithm divides the CONFIGR web into smaller clusters (“constellations”), each with a signature that embodies the cluster geometry. Section 4 describes starmaps with different brightness thresholds, perturbations, and rotations, and illustrates how CONFIGR-STARS locates test patches in a variety of starmaps. Section 5 indicates future directions.

Section snippets

CONFIGR: a vision-based model for figure completion

The following description of the CONFIGR model is adapted from Carpenter et al. (2007).

In the process of recognizing objects, the human visual system encounters long-range featural gaps, derived from physiology, occlusion, and image sparseness. Early visual areas in the central nervous system—areas V1–V2–V4—compensate for such gaps by completing boundaries and filling in features (Pessoa & De Weerd, 2003). Faced with a complex image, the completion mechanism of a visual system needs to solve

Star clusters and geometric signatures

CONFIGR-STARS extends CONFIGR by generating constellation-like star clusters (Fig. 2(c)) whose characteristic signatures are associated with locations in the sky. The edge index is the iteration number at which the CONFIGR algorithm connected the edge endpoints. For an image of sparse random dots, the edge index is approximately equivalent to the L (sup norm) distance.

CONFIGR-STARS breaks up the CONFIGR web into a set of clusters. In order to reduce artifacts from the projection of stars in

CONFIGR-STARS simulations

Fig. 6 shows fragments of Starmap A rotated 5° and 10°. For these patches, CONFIGR-STARS produces clusters that differ geometrically from their corresponding starmap clusters, though the algorithm still finds the correct location. Note that CONFIGR-STARS completions in a test patch typically differ somewhat from completions in a starmap, even if the test patch is an exact subset of the larger image. This is because starmap cluster connections may cross the test patch boundary, as in Fig. 6.

CONFIGR-STARS: future directions

Simulations in this article set the maximum number of cluster edges equal to 4, which produces six-dimensional geometric signatures. Matching clusters may fail to match in at most one edge. The value of the matching parameter (μ) may be determined incrementally, but the default value (μ=0.05) produces good results in most simulations. Further studies of CONFIGR-STARS, which can vary the number of cluster edges as well as the matching criterion, are needed to demonstrate the utility of the

Acknowledgements

This research was supported by the SyNAPSE program of the Defense Advanced Projects Research Agency (HRL Laboratories LLC, subcontract #801881-BS under DARPA prime contract HR0011-09-C-0001) and by CELEST, an NSF Science of Learning Center (SBE-0354378).

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