Common Image Transforms PDF

Common Image Transforms Hough Transform (HT) The Hough Transform (HT) is an integral feature extraction technique in image processing and computer vision, essential for detecting simple geometric shapes like lines, circles, and ellipses in images. It is especially effective in identifying distor...

Common Image Transforms Hough Transform (HT) The Hough Transform (HT) is an integral feature extraction technique in image processing and computer vision, essential for detecting simple geometric shapes like lines, circles, and ellipses in images. It is especially effective in identifying distorted, incomplete, or partially obscured shapes, making it invaluable when traditional edge detection methods fall short. The HT operates by transforming image space into parameter space, enabling the detection of shapes through pattern identification in this transformed space. Radon Transform The Radon Transform is a mathematical integral transform that maps a function defined on a plane to a function defined on the space of lines in the plane. It is widely used in tomography, such as in CT scans, where it helps reconstruct images from projection data. The transform was introduced by Johann Radon in 1917 and has applications in various fields, including image processing and partial differential equations. Discrete Cosine Transform (DCT) The Discrete Cosine Transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. It is widely used in signal processing and data compression, particularly in digital media such as JPEG images, MPEG videos, and MP3 audio. The DCT was first proposed by Nasir Ahmed in 1972 and is known for its energy compaction properties, making it effective for multimedia compression. Discrete Fourier Transform (DFT) The Discrete Fourier Transform (DFT) converts a finite sequence of equally-spaced samples of a function into a sequence of coefficients of a finite combination of complex sinusoids, ordered by their frequencies. It is used in a wide range of applications, including signal processing, image analysis, and solving partial differential equations. Wavelet Transform The Wavelet Transform is a mathematical technique that decomposes a signal into different frequency components and then studies each component with a resolution matched to its scale. It is used in various applications, including image compression, denoising, and feature extraction. Unlike the Fourier Transform, which uses sine and cosine functions, the Wavelet Transform uses wavelets, which are localized in both time and frequency.