Image Transforms
This lecture overviews Image Transforms that are instrumental in image filtering, compression and power spectrum estimation. It covers the following topics in detail: 2D Discrete Space Fourier Transform, 2D Discrete Fourier Transform and their properties. 2D FFT algorithms: Row-column FFT (RCFFT) algorithm, Vector-radix FFT (VRFFT) algorithm, Polynomial Transform FFT (PTFFT). 2D convolution calculation using 2D FFT algorithms. 2D DFT memory problems. 2D Power Spectrum estimation. Discrete Cosine Transform (DCT), 2D DCT and their use in image compression.
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Fast 2D Convolutions Algorithms
This lecture will overview 2D linear and cyclic convolution. Then it will present their fast execution through FFTs, resulting in algorithms having computational complexity of the order O(N^2log2N). Optimal Winograd 2D convolution algorithms will be presented having theoretically minimal number of computations. Parallel block-based 2D convolution/calculation methods will be overviewed. The use of 2D convolutions in Convolutional Neural Networks will be presented.
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2D Digital Filter Design and Implementation
This lecture overviews 2D Digital Filter Design and Implementation that has many applications in digital image filtering, computer vision (template matching) and convolutional neural networks . It covers the following topics in detail: FIR filter design, Direct 2D FIR filter implementation, Digital FIR filter implementation using FFT, Block-based convolution methods, IIR filter design and implementation.
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2D Systems
This lecture overviews 2D Systems, as they are the primary tools for many image processing and analysis operations. It covers the following topics in detail: Two-Dimensional Discrete LTI Systems. 2D convolutions. 2D correlation. 2D Systems Stability. 2D Finite Impulse Response (FIR) systems. 2D Infinite Impulse Response (IIR) systems Two-Dimensional z Transform and its properties. Transfer Function of Two-Dimensional Digital Filters. Implementation of Two-Dimensional Digital Filters.
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Digital Images
This lecture overviews digital image coordinate systems and their mathematical representations (vectors, matrices). Memory allocation issues are presented. Elementary digital image processing and geometrical transformations operations are explained.
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Image Sampling
This lecture overviews spatial image frequency content and image sampling. Rectangular and hexagonal sampling grids are presented. Sampled image frequency content is analyzed and a 2D version of Shannon theorem is presented. Analog image reconstruction from digital images is overviewed.
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