We present a new method for completing missing parts caused by the removal of foreground or background elements from an image. Our goal is to synthesize a complete, visually plausible and coherent image. The visible parts of the image serve as a training set to infer the unknown parts. Our method iteratively approximates the unknown regions and composites adaptive image fragments into the image. Values of an inverse matte are used to compute a confidence map and a level set that direct an incremental traversal within the unknown area from high to low confidence. In each step, guided by a fast smooth approximation, an image fragment is selected from the most similar and frequent examples. As the selected fragments are composited, their likelihood increases along with the mean confidence of the image, until reaching a complete image. We demonstrate our method by completion of photographs and paintings.

Image segmentation is difficult because objects may differ from their background by any of a variety of properties that can be observed in some, but often not all scales. A further complication is that coarse measurements, applied to the image for detecting these properties, often average over properties of neighboring segments, making it difficult to separate the segments and to reliably detect their boundaries. Below we present a method for segmentation that generates and combines multiscale measurements of intensity contrast, texture differences, and boundary integrity. The method is based on our former algorithm SWA, which efficiently detects segments that optimize a normalized-cutlike measure by recursively coarsening a graph reflecting similarities between intensities of neighboring pixels. In this process aggregates of pixels of increasing size are gradually collected to form segments. We intervene in this process by computing properties of the aggregates and modifying the graph to reflect these coarse scale measurements. This allows us to detect regions that differ by fine as well as coarse properties, and to accurately locate their boundaries. Furthermore, by combining intensity differences with measures of boundary integrity across neighboring aggregates we can detect regions separated by weak, yet consistent edges.

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1 Introduction Traditionally there are two approaches to grouping: region-based methods and contour-based methods. Region-based approaches, such as the Normalized Cut framework [19], have been popular recently. Region-based methods seem to be a natural way to approachthe grouping problem, because (1) regions arise from objects, which are natural entities in grouping; (2) many important cues, such as texture and color, are region-based; (3)region properties are more robust to noise and clutter. Nevertheless, contours, even viewed as boundaries between regions, are themselvesvery important. In many cases boundary contour is the most informative cue in grouping as well as in shape analysis. The intervening contour approach [9] has provided aframework to incorporate contour cues into a region-based framework. However, how to reliably extract contour information, despite years of research, is largely an openproblem. Contour extraction is hard, mainly for the following reasons:

We present ratio contour, a novel graph-based method for extracting salient closed boundaries from noisy images. This method operates on a set of boundary fragments that are produced by edge detection. Boundary extraction identifies a subset of these fragments and connects them sequentially to form a closed boundary with the largest saliency. We encode the Gestalt laws of proximity and continuity in a novel boundary-saliency measure based on the relative gap length and average curvature when connecting fragments to form a closed boundary. This new measure attempts to remove a possible bias toward short boundaries. We present a polynomial-time algorithm for finding the most-salient closed boundary. We also present supplementary preprocessing steps that facilitate the application of ratio contour to real images. We compare ratio contour to two closely related methods for extracting closed boundaries: Elder and Zucker's method based on the shortest-path algorithm and Williams and Thornber's method based on spectral analysis and a strongly-connected-components algorithm. This comparison involves both theoretic analysis and experimental evaluation on both synthesized data and real images.

We introduce a method for unsupervised clustering of images of 3D objects. Our method examines the space of all images and partitions the images into sets that form smooth and parallel surfaces in this space. It further uses sequences of images to obtain more reliable clustering. Finally, since our method relies on a non-Euclidean similarity measure we introduce algebraic techniques for estimating local properties of these surfaces without rst embedding the images in a Euclidean space. We demonstrate our method by applying it to a large database of images. 1

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In this paper we study a variational approach for filling-in regions of missing data in 2D and 3D digital images. Applications of this technique include the restoration of old photographs and removal of superimposed text like dates, subtitles, or publicity, or the zooming of images. The approach presented here, initially introduced in [12], is based on a joint interpolation of the image gray-levels and gradient/isophotes directions, smoothly extending the isophote lines into the holes of missing data. The process underlying this approach can be considered as an interpretation of the Gestaltist's principle of good continuation. We study the existence of minimizers of our functional and its approximation by smoother functionals. Then we present the numerical algorithm used to minimize it and display some numerical experiments. Key words. Disocclusion, Elastica, BV functions, Interpolation, Variational approach, #- convergence AMS subject classifications. 68U10, 35A15, 65D05, 49J99, 47H06, 1.

Motivated by interpolation problems arising in image analysis, computer vision, shape reconstruction and signal processing, we develop an algorithm to simulate curve straightening flows under which curves in R fixed length and prescribed boundary conditions to first order evolve to elasticae, i.e., to (stable) critical points of the elastic energy E given by the integral of the square of the curvature function. We also consider variations in which the length L is allowed to vary and the flows seek to minimize the scaleinvariant elastic energy E inv , or the free elastic energy E # . E inv is given by the product of L and the elastic energy E, and E # is the energy functional obtained by adding a term #-proportional to the length of the curve to E.