In this paper, we analyze some properties of the orthogonal Gaussian-Hermite moments and propose a new method to detect the moving objects using the orthogonal Gaussian-Hermite moments. For the segmentation of moving objects in such moment images, we propose the fuzzy relaxation method (FRM) and 3D morphological relaxation method (3DMRM). The experiment results are reported, which show the robustness of our methods.

Moments are widely used in pattern recognition, image processing, computer vision and multiresolution analysis. To clarify and to guide the use of different types of moments, we present in this paper a study on the different moments and compare their behavior. After an introduction to geometric, Legendre, Hermite and Gaussian–Hermite moments and their calculation, we analyze at first their behavior in spatial domain. Our analysis shows orthogonal moment base functions of different orders having different number of zero-crossings and very different shapes, therefore they can better separate image features based on different modes, which is very interesting for pattern analysis and shape classification. Moreover, Gaussian–Hermite moment base functions are much more smoothed, they are thus less sensitive to noise and avoid the artifacts introduced by window function discontinuity. We then analyze the spectral behavior of moments in frequency domain. Theoretical and numerical analyses show that orthogonal Legendre and Gaussian–Hermite moments of different orders separate different frequency bands more effectively. It is also shown that Gaussian–Hermite moments present an approach to construct orthogonal features from the results of wavelet analysis. The orthogonality equivalence theorem is also presented. Our analysis is confirmed by numerical results, which are then reported.

We propose a fast calculation to characterise images by Legendre moments. We first propose the recursive calculation of 1D Legendre moments. The fast algorithm is then generalized to 2D cases. With our algorithm, the computational complexity to calculate the Legendre moments is much reduced, and it is independent of the window size.

In the paper, a novel method is proposed to calculate three-dimensional (3-D) moments. First, a discrete Gaussian theorem is proposed to convert the summation in a 3-D volume domain to that on a 2-D plane region, which decreases computational complexity from O(N/sup 3/) to O(N/sup 2/). Second, a Pascal triangle transform, a Pascal triangle matrix, and a systolic structure are proposed to calculate the monomials on a 3-D object boundary surface, which simplifies the monomial calculation. Third, a range-image measurement system is used to implement the new method. Finally, a comparison of the authors' method with the known ones is provided, showing that the authors' method is much simpler.>

The authors deduce the first and second directional derivative operators for 2-D and 3-D images for a symmetric exponential filter and realize them by a first-order recursive algorithm. The edges are detected according to the gradient maxima or the zero crossing of the second derivative along the gradient direction. Experimental results show that the new methods are less sensitive to noise and have a much better precision of edge localization. Theoretical and experimental studies comparing the performances of the filters were performed, showing that the exponential filter is superior to other current filters. >

The magnitude-distance and maximum-value-distance filters are analyzed, and fast realizations are proposed to implement a DRF cascade for edge detection. It is shown that the maximum-value-distance filter is well adapted to parallel processing and works two times as fast as the magnitude-distance filter. It is shown also that the adaptive gradient is an optimal estimate for edge-pixel verification after zero-crossing detection. The efficiency of the proposed algorithms is confirmed by experimental results.>

In stereo vision, it is important to find the correspondence between the stereopair images. In the present paper, we propose a method based on the geometric feature analysis to find the correspondence between the straight lines and the planes in the stereopair images. We suppose that the stereopair images have been processed separately and some polygons are thus obtained as composed of their edges. We propose the necessary and sufficient conditions which the edge parameters of two corresponding polygons respectively in the two images should satisfy, and note that these conditions are independent of the camera parameters and of the distance between the cameras.

In a previous paper, we proposed a photometric method for the first order specular surfaces. In the present paper, we propose a photometric method for n-order specular surfaces (where n describes the sharpness of the specular property of the surface), when the incident light intensity and direction are unknown. The image is considered as a perspective projection and the Image-Surface Orientation Equation (ISEO) is proposed. One can calculate the surface normal from the ISEO. The constraint is that the surface is rather planar in a small region. Our algorithm is implemented and tested for artificial data created by computer and the results, which are given in the paper, are encouraging.

In structural pattern recognition, the errors in primitive recognition have an important effect on the recognition rate of object. This paper proposes a method using models with fuzzy primitives. It provides a simple and effective approach which can, by utilizing the knowledge about the universe and the context of the primitives, correct possible errors in primitive recognition and therefore improve the ability of the recognition system. In order to apply this method to the on line recognition of handwritten chinese ideographs, a method for feature extraction of graphisms, i.e. MLG method, is developed. Our system is implemented on a micro-computer Apple-II, the experiments for 200 chinese ideographs give satisfactory results.