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Snakes: Active contour models
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 1988
"... A snake is an energyminimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges. Snakes are active contour models: they lock onto nearby edges, localizing them accurately. Scalespace continuation can be used to enlarge ..."
Abstract

Cited by 3084 (16 self)
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A snake is an energyminimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges. Snakes are active contour models: they lock onto nearby edges, localizing them accurately. Scalespace continuation can be used to enlarge the capture region surrounding a feature. Snakes provide a unified account of a number of visual problems, including detection of edges, lines, and subjective contours; motion tracking; and stereo matching. We have used snakes successfully for interactive interpretation, in which userimposed constraint forces guide the snake near features of interest.
The Curvature Primal Sketch
 Acquisition of Visual Motion Guided Behaviors,” IJCAI'95
, 1984
"... In this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape. Ve call the representation the curvature primgl ,sketch. We describe an implemented algorithn that computes the curvature primal sketch and illustra. te its performan ..."
Abstract

Cited by 188 (3 self)
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In this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape. Ve call the representation the curvature primgl ,sketch. We describe an implemented algorithn that computes the curvature primal sketch and illustra. te its performance on a set of tool shapes. The curvature primal sketch derites ils name from the close analogy to the primal sketch representation advocated ty Mart for descri.bi!)g significant intensity changes. We define a set of primitive parameterized curvature discontinuities, and derive expressions for their convolutions vith the first and second derivatives ot' a Gaussian. The convolved primitives, sorted according to the scale at 'which they are detected, provide us with a multiscaled interpretation of the'contoar of a shape.
The Curve Of Least Energy
, 1983
"... Here we search fi)r the curve which has the smallest integral of the square of curvature, while passing through two given points with given orientation. This is the true shape of a spline used in lofting. In computeraided design, curves have been sought which maximize "smoothness". The curve discus ..."
Abstract

Cited by 72 (2 self)
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Here we search fi)r the curve which has the smallest integral of the square of curvature, while passing through two given points with given orientation. This is the true shape of a spline used in lofting. In computeraided design, curves have been sought which maximize "smoothness". The curve discussed here is the one arising in this way from a commonly used measure of smoothness. The human visual system may use such a curve when it constructs a subjective contour.
Extracting Salient Curves from Images: An Analysis of the Saliency Network
, 1998
"... The Saliency Network proposed by Shashua and Ullman (1988) is a wellknown approach to the problem of extracting salient curves from images while performing gap completion. This paper analyzes the Saliency Network. The Saliency Network is attractive for several reasons. First, the network generally ..."
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Cited by 27 (3 self)
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The Saliency Network proposed by Shashua and Ullman (1988) is a wellknown approach to the problem of extracting salient curves from images while performing gap completion. This paper analyzes the Saliency Network. The Saliency Network is attractive for several reasons. First, the network generally prefers long and smooth curves over short or wiggly ones. While computing saliencies, the network also fills in gaps with smooth completions and tolerates noise. Finally, the network is locally connected, and its size is proportional to the size of the image. Nevertheless, our analysis reveals certain weaknesses with the method. In particular, we show cases in which the most salient element does not lie on the perceptually most salient curve. Furthermore, in some cases the saliency measure changes its preferences when curves are scaled uniformly. Also, we show that for certain fragmented curves the measure prefers large gaps over a few small gaps of the same total size. In addition, we analyze the time complexity required by the method. We show that the number of steps required for convergence in serial implementations is quadratic in the size of the network, and in parallel implementations is linear in the size of the network. We discuss problems due to coarse sampling of the range of possible orientations. Finally, we consider the possibility of using the Saliency Network for grouping. We show that the Saliency Network recovers the most salient curve efficiently, but it has problems with identifying any salient curve other than the most salient one.
Rethinking Classical Internal Forces for Active Contour Models
 in Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition
, 2001
"... The classical active contour model has two basic internal forces: tension and curvature. These forces are included to provide cohension, equal control point spacing, and locally smooth shape. These classical internal forces have undesirable attributes that am in conflict with these original desired ..."
Abstract

Cited by 14 (4 self)
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The classical active contour model has two basic internal forces: tension and curvature. These forces are included to provide cohension, equal control point spacing, and locally smooth shape. These classical internal forces have undesirable attributes that am in conflict with these original desired characteristics. Tension evenly spaces the control points, but also causes the models to collapse in weak image gradients. Curvature produces locally smooth curvature, but it does so by foming the model toward a straight line. This paper roturns to the original active contour model motivations to reformulate these internal forces. The desired properties am achieved without the introduction of unwanted model behavior A new spacing force and a new constant change in curvature force am introduced and their performance characteristics am discussed. The paper includes experimental results that demonstrate the efficacy and performance of the proposed re formulations.
O.: Minimum length in the tangent bundle as a model for curve completion
 In: Proc. CVPR. (2010) 2384 – 2391
"... The phenomenon of visual curve completion, where the visual system completes the missing part (e.g., due to occlusion) between two contour fragments, is a major problem in perceptual organization research. Previous computational approaches for the shape of the completed curve typically follow formal ..."
Abstract

Cited by 7 (5 self)
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The phenomenon of visual curve completion, where the visual system completes the missing part (e.g., due to occlusion) between two contour fragments, is a major problem in perceptual organization research. Previous computational approaches for the shape of the completed curve typically follow formal descriptions of desired, imagebased perceptual properties (e.g, minimum total curvature, roundedness, etc...). Unfortunately, however, it is difficult to determine such desired properties psychophysically and indeed there is no consensus in the literature for what they should be. Instead, in this paper we suggest to exploit the fact that curve completion occurs in early vision in order to formalize the problem in a space that explicitly abstracts the primary visual cortex. We first argue that a suitable abstraction is the unit tangent bundle R 2 × S 1 and then we show that a basic principle of “minimum energy consumption ” in this space, namely a minimum length completion, entails desired perceptual properties for the completion in the image plane. We present formal theoretical analysis and numerical solution methods, we show results on natural images and their advantage over existing popular approaches, and we discuss how our theory explains recent findings from the perceptual literature using basic principles only. 1.
Extracting Salient Curves from Images: An Analysis of the Saliency Network
, 1995
"... The Saliency Network proposed by Shashua and Ullman is a wellknown approach to the problem of extracting salient curves from images while performing gap completion. This paper analyzes the Saliency Network. Although the network is attractive for a number reasons, our analysis reveals certain weakne ..."
Abstract
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The Saliency Network proposed by Shashua and Ullman is a wellknown approach to the problem of extracting salient curves from images while performing gap completion. This paper analyzes the Saliency Network. Although the network is attractive for a number reasons, our analysis reveals certain weaknesses with the method. In particular, we show cases in which the most salient element does not lie on the perceptually most salient curve. Furthermore, the saliency measure may change its preferences when curves are scaled uniformly. Also, for certain fragmented curves the measure prefers large gaps over a few small gaps of the same total size. We analyze the time complexity required by the method and discuss problems due to coarse sampling of the range of possible orientations. We show that with proper sampling the complexity of the network becomes cubic in the size of the network. Finally, we consider the possibility of using the Saliency Network for grouping. We show that the Saliency Netw...
Grasping and Tracking Using . . .
, 2003
"... In this paper we present our constant curvature dynamic contours (snakes) and three applications of these: visual servoing and grasping, occluding contour depth extraction, and localization of miniature mobile robots. For the first application, a novel deformable contour model is implemented for the ..."
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In this paper we present our constant curvature dynamic contours (snakes) and three applications of these: visual servoing and grasping, occluding contour depth extraction, and localization of miniature mobile robots. For the first application, a novel deformable contour model is implemented for the automatic determination of plausible grasp axes of unknown objects using an eyeinhand robotic system. The system finds potential grasp point pairs, ranks them based upon measurements taken from the contour, and executes a visionguided grasp using the highest ranked grasp point pair to determine the gripper alignment. Our method is based upon statistical active deformable models. We have developed a new snake model that is applicable to realtime vision problems. The grasping method is experimentally verified using both simple and complex unknown grasping targets. These experiments demonstrate the effectiveness of using the