Abstract
Orthogonal moments are beneficial tools for analyzing and representing images and objects. Different hybrid forms, which are first and second levels of combination, have been created from the Tchebichef and Krawtchouk polynomials. In this study, all the hybrid forms, including the first and second levels of combination that satisfy the localization and energy compaction (EC) properties, are investigated. A new hybrid polynomial termed as squared Tchebichef–Krawtchouk polynomial (STKP) is also proposed. The mathematical and theoretical expressions of STKP are introduced, and the performance of the STKP is evaluated and compared with other hybrid forms. Results show that the STKP outperforms the existing hybrid polynomials in terms of EC and localization properties. Image reconstruction analysis is performed to demonstrate the ability of STKP in actual images; a comparative evaluation is also applied with Charlier and Meixner polynomials in terms of normalized mean square error. Moreover, an object recognition task is performed to verify the promising abilities of STKP as a feature extraction tool. A correct recognition percentage shows the robustness of the proposed polynomial in object recognition by providing a reliable feature vector for the classification process.
Highlights
Shape descriptors and features are considered substantial tools in computer vision applications, such as pattern recognition [1], face recognition [2], shot boundary detection [3], [4], and information hiding [5]
For noisy environments, the correct recognition percentage (CRP) value is 98.75%, when squared Tchebichef–Krawtchouk polynomial (STKP) is used for Gaussian with σ 2 = 0.01, whereas the best CRP for other polynomials is 98.27% when Krawtchouk–Tchebichef polynomial (KTP) is used for feature extraction
In this study, a new separable polynomial and their moments based on the second level of combination of Tchebichef polynomial (TP) and Krawtchouk polynomial (KP) are proposed
Summary
Shape descriptors and features are considered substantial tools in computer vision applications, such as pattern recognition [1], face recognition [2], shot boundary detection [3], [4], and information hiding [5]. Continuous and discrete moments are orthogonal and can reconstruct signals (1D and 2D); they solve the problem of information redundancy. The TKP and their discrete transform coefficients (moments) have a remarkable localization property, but a special type of window for signal framing is required for signal processing [12]. Idan et al.: New Separable Moments Based on Tchebichef-Krawtchouk Polynomials of orthogonal polynomials (OPs). It is performed by multiplying two OPs, each resulting from the hybrid OPs (TKP and KTP) [13]. A mathematical analysis of the different combinations of hybrid OPs is performed. These combinations are discussed in terms of localization and EC properties.
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