x-DTT: A package for calculating real and Integer Discrete Tchebichef Transform kernels based on orthogonal polynomials

Abstract

This paper presents a MATLAB implementation of the exact real Discrete Tchebichef Transform (DTT) and Integer Discrete Tchebichef Transform (IDTT) with their inverse functions. It is a simple and scalable package that is the first of its kind for MATLAB. This software provides an efficient way to advance research related to DTT, IDTT, and their inverses. It is applicable to all domains where Chebyshev moments are employed, including feature extraction, image and video compression, and other related image processing. The package supports matrix generation of any size, from 2 × 2 to any desired size, which makes it scalable. The presented software is easy to use and generates the exact DTT transformation kernel, integer IDTT kernel, and diagonal matrix. The performance of DTT and IDTT-based JPEG compression compared to DCT-based JPEG compression was evaluated using standard metrics. Overall, this package is a valuable tool for researchers and practitioners working in the field of image and video processing.

Keywords

• Discrete Tchebichef Transform
• Integer Discrete Tchebichef Transform
• Image compression
• Features extraction