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This paper proposes a novel method called Wavelet-Sparse-Matrix (WSM) to extract the spatial features of 2-D objects for classifying objects that have subtle differences. The differences between these objects are present in the spatial orientations of the objects, or in the local positions of points on the contours of the objects. The separable wavelets are able to distinguish these differences and to separate them into three sparse subpatterns. Sparse matrix technique has the ability to rearrange nonzero elements in a sparse matrix by moving them as close together as possible. WSM method is a combination of these two techniques which can considerably improve the distinction of slightly dissimilar objects. Experiments are conducted, which include a series of discriminative simulations and comparisons with Fourier descriptor and Zernike moment invariant. These experiments verify the feasibility and effectiveness of the WSM method.

Three-dimensional (3D) model retrieval has gathered great importance in recent years, since the number of available 3D models on the Internet has drastically increased. Many content-based 3D model retrieval approaches have been proposed. Among these methods, visual similarity-based methods have shown higher retrieval accuracy. However, because these methods capture enormous shape features from different viewpoints or locations, a large amount of calculation and comparison is necessary. Furthermore, there is a trade-off between retrieval accuracy and speed. In this paper, a 3D model retrieval method constituting Continuous Principal Component Analysis (CPCA), Fourier descriptors, and Zernike moments is proposed. CPCA is applied to extract significant shape features based on projecting the model along the principal axes. Then, Fourier descriptors and Zernike moments are used to provide shape descriptors with rotation invariants. In addition, a feature integration process combines them. A strategy of similarity measure is proposed to solve the axes switching problem. To conclude, the experimental results show that the approach outperforms SECTORS² and D2,¹⁸ and has slightly better retrieval results than Light Field Descriptor (LFD)⁶ and spin-image signatures.³ Moreover, the approach is more efficient and the storage size is much less.

By generating Fourier descriptors based upon the waveform induced by a pattern's geometric projection, a number of classic difficulties with the Fourier-descriptor methodology are mitigated. Not only are the descriptors invariant with respect to scale, translation, and rotation (as is usually the case), they are also continuous in the Hausdorff metric and robust with respect to both point noise and occlusion. An additional advantage is that they can be computed relative to a thresholded image without first finding an edge, thereby avoiding the difficulties typically present in thinning and orientation determination. The present paper discusses the method of projection-generated Fourier descriptors, as well as a study of the sensitivity to point noise. A companion paper will present the morphological properties and the effect of pattern occlusion.

Fourier descriptors based upon the waveform induced by a pattern's projection overcome a number of classic difficulties with Fourier-descriptor methodology. Not only are the descriptors invariant with respect to scale, translation, and rotation (as is usually the case), they are also continuous in the Hausdorff metric and robust with respect to both point noise and occlusion; insensitivity with respect to minimum occlusions is perhaps their most significant advantage. Continuity in the Hausdorff metric allows prediction of the effect on the descriptors when morphologically filtering a pattern. The effect of occlusion is also predictable.

In this paper, we investigate a novel method for an individual's handwritten Chinese character font generation, using stroke correspondence between the reference character database and the compressed character database, by vector quantization. Chinese characters are composed of a combination of radicals. A radical may be separated into several strokes, with each stroke corresponding to two or more common strokes. By paying attention to the characteristics of Chinese characters and the strokes that form them, we consider each stroke to be a vector and compress the stroke pattern using vector quantization. A compression rate of 1.27% is achieved by the vector quantization. We performed the evaluation experiments using both subjective and objective criteria involving 26 subjects and demonstrated that fonts generated successfully reflect the user's individual handwriting.