The detection of dominant points on digital curves by scale-space filtering

-The detection of dominant points is an important preprocessing step for shape recognition. An effective method of scale-space filtering with a Gaussian kernel is introduced to detect dominant points on digital curves. The conventional polygonal approximation algorithms are time-consuming and need input parameter tuning for Gaussian smoothing the noise and quantization error, also they are sensitive to scaling and rotation of the object curve. The above dit~culty can be overcome by finding out the dominant points at each scale by scale-space filtering. By tracing back the dominant point contours in the scale-space image, the stable cardinal curvature points can be detected very accurately. This new method requires no input parameters, and the resultant dominant points do not change under translation, rotation and scaling. Meanwhile a fast convolution algorithm is proposed to detect the dominant points at each scale. Dominant points Scale-space Gaussian smoothing Curvature I. I N T R O D U C T I O N Various representations of two-dimensional shape have been developed in the computational vision literature. (11 It has been suggested from the viewpoint of the human visual system that the dominant points having high curvature are sufficient to characterize the shape of the object. In general, the current existing methods for detecting dominant points are divided into two major groups: one is to detect the dominant points directly through angle or corner detection schemes, (2-7~ and the other is to obtain a piecewise linear polygonal approximation of the digital curve subject to a certain constraint on the goodness of fit.(s-101 The recent Teh-Chin algorithm (7) is a good example of detecting dominant points based on angle detection. The algorithm does not require input parameters and works well on an object curve which is not corrupted with noise. However, it is very sensitive to noise, some false dominant points will be detected due to quantization error and noise effect. On the other hand, the curvature guided polygonal approximation method (1°~ makes use of Gaussian smoothing to reduce the effect of noise, but it requires two input parameters, namely, the width of a Gaussian filter and the collinearity tolerance for doing a split-and-merge algorithm. There is a trade-off in seleoting the width of the Gaussian filter, a larger width will remove small details of the boundary curvature, a smaller width will permit false concavities and convexities. Recently, Ansari and Huang used the advantages of both approaches, they introduced a new method (~11 which was non-parametric with no input parameters and less sensitive to noise. However, this method requires the support region for each contour point to be determined, and then the contour is smoothed by an adaptive Gaussian filter with a width proportional to the support region. This complicates the smoothing procedure a lot and increases the computational efforts and complexities. Mokhtarian and Mackworth "2~ have suggested a number of necessary criteria which any reliable method for curve representation and recognition must satisfy: (11 The feature selection or extraction method must be computed efficiently. (2) The extracted feature should be invariant under translation, rotation and scaling. (3) The feature representation should contain information about the curve at varying levels of detail, and should uniquely specify a single curve. In order to satisfy the above conditions, we introduce the scale-space filtering to find out the relevant dominant points at each scale. Scale-space filtering (~ 31 is a useful signal description method that deals gracefully with the problem about scales by treating the size parameter of the smoothing kernel as a continuous parameter. As the scale parameter is varied, the dominant points of each scale in the smoothed signal in general move continuously. By tracing back the dominant point contour in the scale-space image, we are able to detect the stable cardinal curvature points very accurately. They are extreme curvature points of the digital curve that are stable with respect to Gaussian smoothing for a reasonable wide range of Gaussian filter width, and can represent a unique shape attribute of the curve. Also the resultant dominant points are shown to be invariant under translation, rotation and scaling. Meanwhile a fast convolution algorithm is proposed to extract the dominant points at each scale very efficiently. The arrangement of this paper is organized as follows. In Section 2, we introduce how to detect the dominant points at each scale by scale-space filtering.