text: Object skeleton is a useful cue for object detection, complementary to the object contour, as it provides a structural representation to describe the relationship among object parts. While object skeleton extraction in natural images is a very challenging problem, as it requires the extractor to be able to capture both local and global image context to determine the intrinsic scale of each skeleton pixel. Existing methods rely on per-pixel based multi-scale feature computation, which results in difficult modeling and high time consumption. In this paper, we present a fully convolutional network with multiple scale-associated side outputs to address this problem. By observing the relationship between the receptive field sizes of the sequential stages in the network and the skeleton scales they can capture, we introduce a scale-associated side output to each stage. We impose supervision to different stages by guiding the scale-associated side outputs toward groundtruth skeletons of different scales. The responses of the multiple scale-associated side outputs are then fused in a scale-specific way to localize skeleton pixels with multiple scales effectively. Our method achieves promising results on two skeleton extraction datasets, and significantly outperforms other competitors.
  @cite_30: 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.
  @cite_15: 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.
  @cite_23: 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.
summary: Some pioneers try to extract skeletons from the gradient intensity maps computed on natural images. The gradient intensity map is generally obtained by applying directional derivative operators to a gray-scale image smoothed by a Gaussian kernel. For instance, in @cite_23 , the author provides an automatic mechanism to determine the best size of the Gaussian kernel used for gradient computation, and he propose to detect skeletons as the pixels for which the gradient intensity assumes a local maximum (minimum) in the direction of the main principal curvature. Jang and Hong @cite_30 extract the skeleton from the pseudo-distance map which is obtained by iteratively minimizing an object function defined on the gradient intensity map. Yu and Bajaj @cite_15 propose to trace the ridges of the skeleton intensity map calculated from the diffused vector field of the gradient intensity map, which can remove the undesirable biased skeletons. Due to the lack of object prior, these methods are only able to handle the images with simple scenes.