Comparison of Discrete Curvature Estimators and Application to Corner Detection

International audienceSeveral curvature estimators along digital contours were pro- posed in recent works [1-3]. These estimators are adapted to non perfect digitization process and can process noisy contours. In this paper, we compare and analyse the performances of these estimators on several types of contours and we measure execution time on both perfect and noisy shapes. In a second part, we evaluate these estimators in the con- text of corner detection. Finally to evaluate the performance of a non curvature based approach, we compare the results with a morphological corner detector [4]

Curvature based corner detector for discrete, noisy and multi-scale contours

International audienceEstimating curvature on digital shapes is known to be a difficult problem even in high resolution images 10,19. Moreover the presence of noise contributes to the insta- bility of the estimators and limits their use in many computer vision applications like corner detection. Several recent curvature estimators 16,13,15, which come from the dis- crete geometry community, can now process damaged data and integrate the amount of noise in their analysis. In this paper, we propose a comparative evaluation of these estimators, testing their accuracy, efficiency, and robustness with respect to several type of degradations. We further compare the best one with the visual curvature proposed by Liu et al. 14, a recently published method from the computer vision community. We finally propose a novel corner detector, which is based on curvature estimation, and we provide a comprehensive set of experiments to compare it with many other classical cor- ner detectors. Our study shows that this corner detector has most of the time a better behavior than the others, while requiring only one parameter to take into account the noise level. It is also promising for multi-scale shape description

A new Edge Detector Based on Parametric Surface Model: Regression Surface Descriptor

In this paper we present a new methodology for edge detection in digital images. The first originality of the proposed method is to consider image content as a parametric surface. Then, an original parametric local model of this surface representing image content is proposed. The few parameters involved in the proposed model are shown to be very sensitive to discontinuities in surface which correspond to edges in image content. This naturally leads to the design of an efficient edge detector. Moreover, a thorough analysis of the proposed model also allows us to explain how these parameters can be used to obtain edge descriptors such as orientations and curvatures. In practice, the proposed methodology offers two main advantages. First, it has high customization possibilities in order to be adjusted to a wide range of different problems, from coarse to fine scale edge detection. Second, it is very robust to blurring process and additive noise. Numerical results are presented to emphasis these properties and to confirm efficiency of the proposed method through a comparative study with other edge detectors.Comment: 21 pages, 13 figures and 2 table

Terrain analysis using radar shape-from-shading

This paper develops a maximum a posteriori (MAP) probability estimation framework for shape-from-shading (SFS) from synthetic aperture radar (SAR) images. The aim is to use this method to reconstruct surface topography from a single radar image of relatively complex terrain. Our MAP framework makes explicit how the recovery of local surface orientation depends on the whereabouts of terrain edge features and the available radar reflectance information. To apply the resulting process to real world radar data, we require probabilistic models for the appearance of terrain features and the relationship between the orientation of surface normals and the radar reflectance. We show that the SAR data can be modeled using a Rayleigh-Bessel distribution and use this distribution to develop a maximum likelihood algorithm for detecting and labeling terrain edge features. Moreover, we show how robust statistics can be used to estimate the characteristic parameters of this distribution. We also develop an empirical model for the SAR reflectance function. Using the reflectance model, we perform Lambertian correction so that a conventional SFS algorithm can be applied to the radar data. The initial surface normal direction is constrained to point in the direction of the nearest ridge or ravine feature. Each surface normal must fall within a conical envelope whose axis is in the direction of the radar illuminant. The extent of the envelope depends on the corrected radar reflectance and the variance of the radar signal statistics. We explore various ways of smoothing the field of surface normals using robust statistics. Finally, we show how to reconstruct the terrain surface from the smoothed field of surface normal vectors. The proposed algorithm is applied to various SAR data sets containing relatively complex terrain structure

Direct occlusion handling for high level image processing algorithms

Many high-level computer vision algorithms suffer in the presence of occlusions caused by multiple objects overlapping in a view. Occlusions remove the direct correspondence between visible areas of objects and the objects themselves by introducing ambiguity in the interpretation of the shape of the occluded object. Ignoring this ambiguity allows the perceived geometry of overlapping objects to be deformed or even fractured. Supplementing the raw image data with a vectorized structural representation which predicts object completions could stabilize high-level algorithms which currently disregard occlusions. Studies in the neuroscience community indicate that the feature points located at the intersection of junctions may be used by the human visual system to produce these completions. Geiger, Pao, and Rubin have successfully used these features in a purely rasterized setting to complete objects in a fashion similar to what is demonstrated by human perception. This work proposes using these features in a vectorized approach to solving the mid-level computer vision problem of object stitching. A system has been implemented which is able extract L and T-junctions directly from the edges of an image using scale-space and robust statistical techniques. The system is sensitive enough to be able to isolate the corners on polygons with 24 sides or more, provided sufficient image resolution is available. Areas of promising development have been identified and several directions for further research are proposed

Robust statistical approaches for local planar surface fitting in 3D laser scanning data

This paper proposes robust methods for local planar surface fitting in 3D laser scanning data. Searching through the literature revealed that many authors frequently used Least Squares (LS) and Principal Component Analysis (PCA) for point cloud processing without any treatment of outliers. It is known that LS and PCA are sensitive to outliers and can give inconsistent and misleading estimates. RANdom SAmple Consensus (RANSAC) is one of the most well-known robust methods used for model fitting when noise and/or outliers are present. We concentrate on the recently introduced Deterministic Minimum Covariance Determinant estimator and robust PCA, and propose two variants of statistically robust algorithms for fitting planar surfaces to 3D laser scanning point cloud data. The performance of the proposed robust methods is demonstrated by qualitative and quantitative analysis through several synthetic and mobile laser scanning 3D data sets for different applications. Using simulated data, and comparisons with LS, PCA, RANSAC, variants of RANSAC and other robust statistical methods, we demonstrate that the new algorithms are significantly more efficient, faster, and produce more accurate fits and robust local statistics (e.g. surface normals), necessary for many point cloud processing tasks.Consider one example data set used consisting of 100 points with 20% outliers representing a plane. The proposed methods called DetRD-PCA and DetRPCA, produce bias angles (angle between the fitted planes with and without outliers) of 0.20° and 0.24° respectively, whereas LS, PCA and RANSAC produce worse bias angles of 52.49°, 39.55° and 0.79° respectively. In terms of speed, DetRD-PCA takes 0.033 s on average for fitting a plane, which is approximately 6.5, 25.4 and 25.8 times faster than RANSAC, and two other robust statistical methods, respectively. The estimated robust surface normals and curvatures from the new methods have been used for plane fitting, sharp feature preservation and segmentation in 3D point clouds obtained from laser scanners. The results are significantly better and more efficiently computed than those obtained by existing methods

Curvature-Based Environment Description for Robot Navigation Using Laser Range Sensors

This work proposes a new feature detection and description approach for mobile robot navigation using 2D laser range sensors. The whole process consists of two main modules: a sensor data segmentation module and a feature detection and characterization module. The segmentation module is divided in two consecutive stages: First, the segmentation stage divides the laser scan into clusters of consecutive range readings using a distance-based criterion. Then, the second stage estimates the curvature function associated to each cluster and uses it to split it into a set of straight-line and curve segments. The curvature is calculated using a triangle-area representation where, contrary to previous approaches, the triangle side lengths at each range reading are adapted to the local variations of the laser scan, removing noise without missing relevant points. This representation remains unchanged in translation or rotation, and it is also robust against noise. Thus, it is able to provide the same segmentation results although the scene will be perceived from different viewpoints. Therefore, segmentation results are used to characterize the environment using line and curve segments, real and virtual corners and edges. Real scan data collected from different environments by using different platforms are used in the experiments in order to evaluate the proposed environment description algorithm