Contour Curve Research Articles

Information Along Contours and Object Boundaries.

F. Attneave (1954) famously suggested that information along visual contours is concentrated in regions of high magnitude of curvature, rather than being distributed uniformly along the contour. Here the authors give a formal derivation of this claim, yielding an exact expression for information, in C. Shannon's (1948) sense, as a function of contour curvature. Moreover, they extend Attneave's claim to incorporate the role of sign of curvature, not just magnitude of curvature. In particular, the authors show that for closed contours, such as object boundaries, segments of negative curvature (i.e., concave segments) literally carry greater information than do corresponding regions of positive curvature (i.e., convex segments). The psychological validity of this informational analysis is supported by a host of empirical findings demonstrating the asymmetric way in which the visual system treats regions of positive and negative curvature.

Contour curvature polarity and surface interpolation

Contour curvature polarity (i.e., concavity/convexity) is recognized as an important factor in shape perception. However, current interpolation models do not consider it among the factors that modulate the trajectory of amodally-completed contours. Two hypotheses generate opposite predictions about the effect of contour polarity on surface interpolation. Convexity advantage: if convexities are preferred over concavities, contours of convex portions should be more extrapolated than those of concave portions. Minimal area: if the area of amodally-completed surfaces tends to be minimized, contours of convex portions should be less extrapolated than contours of concave portions. We ran three experiments using two methods, simultaneous length comparison and probe localization, and different displays (pictures vs. random dot stereograms). Results indicate that contour polarity affects the amodally-completed angles of regular and irregular surfaces. As predicted by the minimal area hypothesis, image contours are less extrapolated when the amodal portion is convex rather than concave. The field model of interpolation [Fantoni, C., & Gerbino, W. (2003). Contour interpolation by vector-field combination. Journal of Vision, 3, 281–303. Available from http://journalofvision.org/3/4/4/] has been revised to take into account surface-level factors and to explain area minimization as an effect of surface support ratio.

Contour-based object identification and segmentation: Stimuli, norms and data, and software tools

We summarize five studies of our large-scale research program, in which we examined aspects of contour-based object identification and segmentation, and we report on the stimuli we used, the norms and data we collected, and the software tools we developed. The stimuli were outlines derived from the standard set of line drawings of everyday objects by Snodgrass and Vanderwart (1980). We used contour curvature as a major variable in all the studies. The total number of 1,500 participants produced very solid, normative identification rates of silhouettes and contours, straight-line versions, and fragmented versions, and quite reliable benchmark data about saliency of points and object segmentation into parts. We also developed several software tools to generate stimuli and to analyze the data in nonstandard ways. Our stimuli, norms and data, and software tools have great potential for further exploration of factors influencing contour-based object identification, and are also useful for researchers in many different disciplines (including computer vision) on a wide variety of research topics (e.g., priming, agnosia, perceptual organization, and picture naming). The full set of norms, data, and stimuli may be downloaded from www.psychonomic.org/archive/.

A Novel Method for Resolving Vehicle Occlusion in a Monocular Traffic-Image Sequence

This paper presents a novel method for resolving the occlusion of vehicles seen in a sequence of traffic images taken from a single roadside mounted camera. Its concept is built upon a previously proposed vehicle-segmentation method, which is able to extract the vehicle shape out of the background accurately without the effect of shadows and other visual artifacts. Based on the segmented shape and that the shape can be represented by a simple cubical model, we propose a two-step method: first, detect the curvature of the shape contour to generate a data set of the vehicles occluded and, second, decompose it into individual vehicle models using a vanishing point in three dimensions and the set of curvature points of the composite model. The proposed method has been tested on a number of monocular traffic-image sequences and found that it detects the presence of occlusion correctly and resolves most of the occlusion cases involving two vehicles. It only fails when the occlusion was very severe. Further analysis of vehicle dimension also shows that the average estimation accuracy for vehicle width, length, and height are 94.78%, 94.09%, and 95.44%, respectively.

Mathematical analysis of tooth and restoration contour using image analysis

The aim of this study was to develop a methodology for comparison of the contour of artificial crowns in the mid bucco-lingual plane with their equivalent natural teeth on the opposing side of the same arch (antimeres) using a novel application of image analysis software. The objective was to determine whether artificial crowns were overcontoured. Specimens consisted of thin sections of silicone putty impressions of the buccal and lingual surfaces of 55 full crown restorations and their natural antimeric teeth. A thin slice of the putty was obtained in the mid-tooth bucco-lingual plane and a digital image was captured and this was analysed to produce a data set (x, y) representing the curvature of the tooth surface. Further analysis was performed in order to describe the profile in optimum mathematical terms. The curves were best represented by three equations: y = a + bx(0.5), ln(y) = a + bx2, and y2 = a + bx. In all equations parameter (b), which expresses the contour curvature, was used as a deciding factor in comparing the degree of contour of the crown restorations with their natural antimeres. Most artificial crowns were found to be either similarly or undercontoured when compared with their natural antimeres. When overcontouring was present in the artificial crowns this tended to occur on the lingual aspects of anterior and posterior crowns. Simplifying tooth contour into a mathematical model can be useful in determining whether restorations are overcontoured. Clinically, particular attention should be directed towards the lingual aspects of restorations which were more likely to be overcontoured.

Region segmentation using information divergence measures

Image segmentations based on maximum likelihood or maximum a posteriori analyses of object textures usually assume parametric models (e.g., Gaussian) for distributions of these features. For real images, parameter accuracy and model stationarity may be elusive, so that model-free inference methods ought to have an advantage over those that are model-dependent. Functions of the relative entropy (RE) from information theory can produce minimum error, model-free inferences, and can detect the boundary of an image object by maximizing the RE between the pixel distributions inside and outside a flexible curve contour. A generalization of the RE – the Jensen–Rényi divergence (JRD) – computes optimal n-way decisions and can contour multiple objects in an image simultaneously. Seed regions expand naturally and multiple contours tend not to overlap. An edge detector based on the JRD, combined with multivariate pixel segmentation, generally improved the error of the segmentation. We apply these functions to contour patient anatomy in X-ray computed tomography for radiotherapy treatment planning.

Electric field in hard superconductors with arbitrary cross section and general critical current law

The induced electric field E(x) during magnetic flux entry in superconductors with arbitrary cross section Ω and general critical current law, has been evaluated by integration along the vortex penetration paths. Nontrivial flux motion streamlines are obtained from a variational statement of the critical state, which takes the form of an optimization problem on the finite element discretization of Ω. The generality of the theory allows one to deal with physical conditions not considered before. In particular, it is shown that the boundary condition to be used for determining E is the knowledge of the locus E=0 within the sample. This is emphasized for anisotropic materials in which the electric field is not parallel to the surface. Both numerical and analytical evaluations are presented for homogeneous materials with different geometries: convex and concave contours, samples with holes, variable curvature contours, and for anisotropic samples. In the isotropic case, discontinuities in the electric current paths are shown to be related to changing curvature of the sample’s surface. Anisotropic samples display the same kind of discontinuities, even for constant surface curvature.

Reflection curves—new computation and rendering techniques

Reflection curves on surfaces are important tools for free‐form surface interrogation. They are essential for industrial 3D CAD/CAM systems and for rendering purposes. In this note, new approaches regarding the computation and rendering of reflection curves on surfaces are introduced. These approaches are designed to take the advantage of the graphics libraries of recent releases of commercial systems such as the OpenInventor toolkit (developed by Silicon Graphics) or Matlab (developed by The Math Works). A new relation between reflection curves and contour curves is derived; this theoretical result is used for a straightforward Matlab implementation of reflection curves. A new type of reflection curves is also generated using the OpenInventor texture and environment mapping implementations. This allows the computation, rendering, and animation of reflection curves at interactive rates, which makes it particularly useful for industrial applications.

Modeling Generalized Cylinders using Direction Map Representation

AbstractFor generalized cylinders (GC) defined by contours of discrete curves, we propose two algorithms to generate GC surfaces (1) in polygonal meshes and (2) in cylindrical type of developable surface patches. To solve the contour blending problem of generalized cylinder, the presented algorithms have adopted the algorithms and properties of LIDM (linear interpolation by direction map) that interpolate geometric shapes based on direction map merging and group scaling operations. Moreover, we propose an algorithm to develop generated developable surface patches on a plane. Proposed algorithms are fast to compute and easy to implement.

Early computation of contour curvature and part structure: evidence from holes.

We used holes to study unilateral border ownership and in particular the information carried by the sign of the curvature along the contour (ie the difference between convex and concave regions). When people perceive a hole, its shape has a reversed curvature polarity (ie a changed sign of curvature) compared to the same region perceived as an object. Bertamini (2001 Perception 30 1295-1310), and Bertamini and Croucher (2003 Cognition 87 33-54) suggested and found evidence to support the hypothesis that, because convex regions are perceived as parts, positional information is more readily available for convex regions. Therefore a change is predicted when a given region is perceived as either a hole or a figure. We confirm that finding in this study, using holes defined by binocular disparity. We conclude that a change from figure to hole always reverses the encoding of curvature polarity. In turn, polarity obligatorily affects perceived part structure and the processing of position.

The Optimal Shifting Strategy for Profile Control

It is a developing technique in hot rolling that the CVC rolls of the down-stands are replaced with shifting conventional rolls. The shifting strategy of conventional rolls will effect on the rolling kilometre and the profile of strip. The article (author) gives a new way that is based on the optimization of contour curve of a strip, to determine the shifting strategy of conventional rolls for reducing the defects of the roll surface and local high spots of the strip.

Visual comparisons within and between object parts: evidence for a single-part superiority effect

Subjects judged whether two marks placed at different positions along a curved contour were physically the same. When targets were separated by a concave curvature extremum––corresponding to a part-boundary––decision latencies were longer than when they straddled an equally curved convex extremum, demonstrating a “single-part superiority effect”. This difference increased with both stimulus duration and the magnitude of contour curvature. However, it disappeared when the global configuration was not consistent with a part-boundary interpretation, suggesting a critical role of global organization in part decomposition.

Computer aided contouring operation for traveling wire electric discharge machining (EDM)

This paper develops a computational method for numerical control (NC) of traveling wire electric discharge machining (EDM) operation from geometric representation of a desired cut profile in terms of its contours. Normalized arc length parameterization of the contour curves is used to represent the cut profile and a subdivision algorithm is developed together with kinematic analysis to generate the required motions of the machine tool axes. In generating the tool motions for cutting sections with high curvatures such as corners with small radii, a geometric path lifting method is presented that increases the machining gap and prevents gauging or wire breakage.

Sketches with curvature: the curve indicator random field and markov processes

While complaints about typical edge operators are common, proposals articulating a notion of the "perfect" edge map are comparatively rare, hindering the improvement of contour enhancement techniques. To address this situation, we suggest that one objective of visual contour computation is the estimation of a clean sketch from a corrupted rendition, the latter modeling noisy and low contrast edge or line operator responses to an image. Our formal model of this clean sketch is the curve indicator random field (CIRF), whose role is to provide a basis for defining edge likelihood models by eliminating the parameter along each curve to create an image of curves. For curves modeled with stationary Markov processes, this ideal edge prior is non-Gaussian and its moment generating functional has a form closely related to the Feynman-Kac formula. This sketch model leads to a nonlinear, minimum mean squared error contour enhancement filter that requires the solution of two elliptic partial differential equations. The framework is also independent of the order of the contour model, allowing us to introduce a Markov process model for contour curvature. We analyze the distribution of such curves and show that its mode is the Euler spiral, a curve minimizing changes in curvature. Example computations using the contour enhancement filter with the curvature-based contour model are provided, highlighting how the filter is curvature-selective even when curvature is absent in the input.

Short‐term visual memory for contour curvature in a delayed discrimination task

Abstract: A two‐interval forced‐choice of constant stimuli was used to measure the point of subjective equality (PSE) and discrimination threshold for standard contour curvature (1.91, 3.24 deg−1) held in short‐term visual memory (STVM). At both standard curvatures, the PSE for remembered curvature was nearly constant for standard curvature from 2 s to 16 s retention intervals, while the discrimination threshold increased as a linear function of retention interval. These results show that the decay in STVM for contour curvature is due to the noisy representation of curvature, neither to fading of the represented curvature nor to converging to the constant curvature. Furthermore, the Weber fraction was nearly constant for both standard curvatures at any delay from 2 to 16 s.

An Efficient Active Contour Model Through Curvature Scale Space Filtering

Active contour models can be successfully used in multimedia database retrieval systems if they have good accuracy and high speed. The majority of existing active contour models do not lock on to interest objects very accurately and quickly especially in complex images. The behavior of the active contour is generally controlled by its internal and external energies. Internal energy is composed of two partss the first part acts to shorten the active contour as it iterates towards the interest object, while the second part is the curvature of the active contour and forces smoothness of active contour during its movement towards interest object. In this paper, first a reformulated internal energy is proposed to improve the computation of curvature at point vi by making use of the three points vi − 1, vi and vi + 1. Second, an accurate and high speed active contour model, SAC is proposed based on reformulating internal energy by removing the curvature part and using Gaussian filtering with low scale of smoothing. The SAC model has only one parameter that affects the internal energy of active contour and as a result of using the Curvature Scale Space (CSS)1 technique for smoothing, the SAC model is more independent of model parameter setting and the initial snake.

Defect Diagnosis Using a Current Ratio Based Quiescent Signal Analysis Model for Commercial Power Grids

Quiescent Signal Analysis (QSA) is a novel electrical-test-based diagnostic technique that uses IDDQ measurements made at multiple chip supply pads as a means of locating shorting defects in the layout. The use of multiple supply pads reduces the adverse effects of leakage current by scaling the total leakage current over multiple measurements. In previous work, a resistance model for QSA was developed and demonstrated on a small circuit. In this paper, the weaknesses of the original QSA model are identified, in the context of a production power grid (PPG) and probe card model, and a new model is described. The new QSA algorithm is developed from the analysis of IDDQ contour plots. A “family” of hyperbola curves is shown to be a good fit to the contour curves. The parameters to the hyperbola equations are derived with the help of inserted calibration transistors. Simulation experiments are used to demonstrate the prediction accuracy of the method on a PPG.

Cellular neural networks and active contours: a tool for image segmentation

In this paper Cellular Neural Networks (CNN) are applied to image segmentation based on active contour techniques. The approach is based on deformable contours which evolve pixel by pixel from their initial shapes and locations until delimiting the objects of interest. The contour shift is guided by external information from the image under consideration which attracts them towards the target characteristics (intensity extremes, edges, etc.) and by internal forces which try to maintain the smoothness of the contour curve. This CNN-based proposal combines the characteristics from implicit and parametric models. As a consequence a high flexibility and control for the evolution dynamics of the snakes are provided, allowing the solution of complex tasks as is the case of the topologic transformations. In addition the proposal is suitable for its implementation as an integrated circuit allowing to take advantages of the massively parallel processing in CNN to reduce processing time.

Self-intersection avoidance and integral properties of generalized cylinders

A generalized cylinder is an object bounded by a surface generated by moving a 2D contour curve along a 3D spine curve, possibly scaling the contour along the spine, and two end planes. Several important properties of such objects are presented. In particular, conditions to avoid local and global self-intersection of generalized cylinders are given, and some of their integral properties, such as area and volume, are discussed.

Analytical parametric analysis of the contact problem of human buttocks and negative Poisson's ratio foam cushions

Analytical investigations on the contact problems between two homogeneous and isotropic soft bodies were performed to simulate the contact of human buttocks and seat cushions. The cushion materials' Poisson's ratio were allowed to be negative. The human buttocks were modeled as an ideal sphere with radius 15 cm, and assumed to have a low Young's modulus and a Poisson's ratio close to 0.5. These parameters were held constant during our analysis. Peak contact pressure was reduced by adjusting the contour curvature of cushions according to Hertz theory, as expected. Moreover, analysis by both the Hertz model and a finite thickness 3D elasticity model showed that using negative Poisson's ratio cushions could further reduce the pressure. Negative Poisson's ratio cushions may be beneficial in the prevention of pressure sores or ulcers in the sick and in reduction of pressure-induced discomfort in seated people.