Computing object skeletons in natural images is challenging, owing to large variations in object appearance and scale, and the complexity of handling background clutter. Many recent methods frame object skeleton detection as a binary pixel classification problem, which is similar in spirit to learning-based edge detection, as well as to semantic segmentation methods. In the present article, we depart from this strategy by training a CNN to predict a two-dimensional vector field, which maps each scene point to a candidate skeleton pixel, in the spirit of flux-based skeletonization algorithms. This "image context flux" representation has two major advantages over previous approaches. First, it explicitly encodes the relative position of skelet al pixels to semantically meaningful entities, such as the image points in their spatial context, and hence also the implied object boundaries. Second, since the skeleton detection context is a region-based vector field, it is better able to cope with object parts of large width. We evaluate the proposed method on three benchmark datasets for skeleton detection and two for symmetry detection, achieving consistently superior performance over state-of-the-art methods.
 In this paper we describe a method for skeletonization of gray-scale images without segmentation. Our method is based on anisotropic vector diffusion. The skeleton strength map, calculated from the diffused vector field, provides us a measure of how possible each pixel could be on the skeletons. The final skeletons are traced from the skeleton strength map, which mimics the behavior of edge detection from the edge strength map of the original image. A couple of real or synthesized images will be shown to demonstrate the performance of our algorithm. In this paper we introduce a new tool, called a pseudo-distance map (PDM), for extracting skeletons from grayscale images without region segmentation or edge detection. Given an edge-strength function (ESF) of a gray-scale image, the PDM is computed from the ESF using the partial differential equations we propose. The PDM can be thought of as a relaxed version of a Euclidean distance map. Therefore, its ridges correspond to the skeleton of the original gray-scale image and it provides information on the approximate width of skeletonized structures. Since the PDM is directly computed from the ESF without thresholding it, the skeletonization result is generally robust and less noisy. We tested our method using a variety of synthetic and real images. The experimental results show that our method works well on such images. Centerline detection and line width estimation are important for many computer vision applications, e.g., road network extraction from high resolution remotely sensed imagery. Radon transform-based linear feature detection has many advantages over other approaches: for example, its robustness in noisy images. However, it usually fails to detect the centerline of a thick line due to the peak selection problem. In this paper, several key issues that affect the centerline detection using the radon transform are investigated. A mean filter is proposed to locate the true peak in the radon image and a profile analysis technique is used to further refine the line parameters. The thetas-boundary problem of the radon transform is also discussed and the erroneous line parameters are corrected. Intensive experiments have shown that the proposed methodology is effective in finding the centerline and estimating the line width of thick lines When computing descriptors of image data, the type of information that can be extracted may be strongly dependent on the scales at which the image operators are applied. This article presents a systematic methodology for addressing this problem. A mechanism is presented for automatic selection of scale levels when detecting one-dimensional image features, such as edges and ridges. A novel concept of a scale-space edge is introduced, defined as a connected set of points in scale-space at which: (i) the gradient magnitude assumes a local maximum in the gradient direction, and (ii) a normalized measure of the strength of the edge response is locally maximal over scales. An important consequence of this definition is that it allows the scale levels to vary along the edge. Two specific measures of edge strength are analyzed in detail, the gradient magnitude and a differential expression derived from the third-order derivative in the gradient direction. For a certain way of normalizing these differential descriptors, by expressing them in terms of so-called γ-normalized derivatives, an immediate consequence of this definition is that the edge detector will adapt its scale levels to the local image structure. Specifically, sharp edges will be detected at fine scales so as to reduce the shape distortions due to scale-space smoothing, whereas sufficiently coarse scales will be selected at diffuse edges, such that an edge model is a valid abstraction of the intensity profile across the edge. Since the scale-space edge is defined from the intersection of two zero-crossing surfaces in scale-space, the edges will by definition form closed curves. This simplifies selection of salient edges, and a novel significance measure is proposed, by integrating the edge strength along the edge. Moreover, the scale information associated with each edge provides useful clues to the physical nature of the edge. With just slight modifications, similar ideas can be used for formulating ridge detectors with automatic selection, having the characteristic property that the selected scales on a scale-space ridge instead reflect the width of the ridge. It is shown how the methodology can be implemented in terms of straightforward visual front-end operations, and the validity of the approach is supported by theoretical analysis as well as experiments on real-world and synthetic data. In this paper, the algorithm for thinning of grey-scale images is proposed that is based on a pseudo-distance map (PDM). The PDM is a simplified distance map of gray-scale image and uses only that features of image and objects that are necessary to build a skeleton. The algorithm works fast for large gray-scale images and allows constructing a high quality skeleton Symmetry is a powerful shape regularity that's been exploited by perceptual grouping researchers in both human and computer vision to recover part structure from an image without a priori knowledge of scene content. Drawing on the concept of a medial axis, defined as the locus of centers of maximal inscribed discs that sweep out a symmetric part, we model part recovery as the search for a sequence of deformable maximal inscribed disc hypotheses generated from a multiscale super pixel segmentation, a framework proposed by LEV09. However, we learn affinities between adjacent super pixels in a space that's invariant to bending and tapering along the symmetry axis, enabling us to capture a wider class of symmetric parts. Moreover, we introduce a global cost that perceptually integrates the hypothesis space by combining a pair wise and a higher-level smoothing term, which we minimize globally using dynamic programming. The new framework is demonstrated on two datasets, and is shown to significantly outperform the baseline LEV09.  Scale-invariant interest points have found several highly successful applications in computer vision, in particular for image-based matching and recognition. This paper presents a theoretical analy ...  Skeletonization algorithms typically decompose an object's silhouette into a set of symmetric parts, offering a powerful representation for shape categorization. However, having access to an object's silhouette assumes correct figure-ground segmentation, leading to a disconnect with the mainstream categorization community, which attempts to recognize objects from cluttered images. In this paper, we present a novel approach to recovering and grouping the symmetric parts of an object from a cluttered scene. We begin by using a multiresolution superpixel segmentation to generate medial point hypotheses, and use a learned affinity function to perceptually group nearby medial points likely to belong to the same medial branch. In the next stage, we learn higher granularity affinity functions to group the resulting medial branches likely to belong to the same object. The resulting framework yields a skelet al approximation that is free of many of the instabilities that occur with traditional skeletons. More importantly, it does not require a closed contour, enabling the application of skeleton-based categorization systems to more realistic imagery. We introduce a method for segmenting a shape from an image and simultaneously determining its symmetry axis. The symmetry is used to help the segmentation and in turn the segmentation determines the symmetry. The problem is formulated as one of minimizing a goodness of fitness function and Dijkstra's algorithm is used to find the global minimum of the cost function. The results are illustrated on real images.