Three-Dimensional Object Recognition Using Orthogonal Polynomials: An Embedded Kernel Approach

Computer vision seeks to mimic the human visual system and plays an essential role in artificial intelligence. It is based on different signal reprocessing techniques; therefore, developing efficient techniques becomes essential to achieving fast and reliable processing. Various signal preprocessing operations have been used for computer vision, including smoothing techniques, signal analyzing, resizing, sharpening, and enhancement, to reduce reluctant falsifications, segmentation, and image feature improvement. For example, to reduce the noise in a disturbed signal, smoothing kernels can be effectively used. This is achievedby convolving the distributed signal with smoothing kernels. In addition, orthogonal moments (OMs) are a crucial technique in signal preprocessing, serving as key descriptors for signal analysis and recognition. OMs are obtained by the projection of orthogonal polynomials (OPs) onto the signal domain. However, when dealing with 3D signals, the traditional approach of convolving kernels with the signal and computing OMs beforehand significantly increases the computational cost of computer vision algorithms. To address this issue, this paper develops a novel mathematical model to embed the kernel directly into the OPs functions, seamlessly integrating these two processes into a more efficient and accurate approach. The proposed model allows the computation of OMs for smoothed versions of 3D signals directly, thereby reducing computational overhead. Extensive experiments conducted on 3D objects demonstrate that the proposed method outperforms traditional approaches across various metrics. The average recognition accuracy improves to 83.85% when the polynomial order is increased to 10. Experimental results show that the proposed method exhibits higher accuracy and lower computational costs compared to the benchmark methods in various conditions for a wide range of parameter values.