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This article introduces a partial matching framework, based on set theory criteria, for the measurement of shape similarity. The matching framework is described in an abstract way because the proposed scheme is independent of the selection of a segmentation method and feature space. This paradigm ensures the high adaptability of the algorithm and brings the implementer a wide control over the robustness, the ability to balance between selectivity and sensitivity, and the freedom to deal with more general and arbitrary image transformations required for some particular problem. A strategy to establish a descriptor set obtained from components segmented from the main shape is expounded, and two exclusion measure functions are formulated. Proofs are given to show that it is not required to match the entire descriptor sets to determine that two shapes are similar. The methodology provides a dissimilarity score that may be used for shape-based retrieval and object recognition; this is demonstrated applying the proposed approach in a cattle brand identification system.

Ramanujan Sums (RS) have been found to be very successful in signal processing recently. However, as far as we know, the RS have not been applied to image analysis. In this paper, we propose two novel algorithms for image analysis, including moment invariants and pattern recognition. Our algorithms are invariant to the translation, rotation and scaling of the 2D shapes. The RS are robust to Gaussian white noise and occlusion as well. Our algorithms compare favourably to the dual-tree complex wavelet (DTCWT) moments and the Zernike's moments in terms of correct classification rates for three well-known shape datasets.

Fingerprint identification is one of the most reliable personal identification methods and it plays a very important role in forensic and civilian applications. In this paper, a novel method of fingerprint identification based on the features extracted from the integrated Discrete Wavelet and the Fourier-Mellin Transform (DWFMT) is proposed. Discrete Wavelet transform is used to smooth and preserve the local edges after image decomposition, and hence making the fingerprint images less sensitive to shape distortion whilst Fourier-Mellin transform served to produce a translation, rotation and scale invariant feature. Multiple DWFMT features can be used to form a reference invariant feature through the linearity property of Fourier-Mellin Transform and hence reduce the variability of the input fingerprint images. The experiments show the identification accuracy is over 96% and 99% of identification rate is achieved when multiple DWFMT features are used.