After studying this chapter you will be able to understand: Analyze the computational complexity of image transform operations, the separable transformation, computational complexity reduction of the separable transformation. | Digital Image Processing CSC331 Image transformation 1 Summery of previous lecture Image Interpolation explanation Interpolation operation Unitary matrix and its equation Unitary matrix with 1D signal Unitary matrix with 2D signal 2 Todays lecture Analyze the computational complexity of image transform operations The separable transformation computational complexity reduction of the separable transformation 3 4 5 6 7 8 9 Basis image 10 11 12 13 14 Discrete cosine trasformatine Basis Image Basis images of dimension 8 by 8 in total 64 basis images. One is the real component, other one is the imaginary component. 15 Discrete cosine trasformatine Basis Image The row of this represents the index k The column indicates the index l. We have 64 images, each of these 64 images is of size 8 by 8 pixels. 16 Basis images for other transformations The purpose of showing these basis images is to represent an input image as linear combination of the set of basis images Each of basis images will be weighted by the corresponding coefficient in the transformation coefficient v (k, l) v (k, l) is the inner product of k, l’th basis image. 17 Summery of the lecture Analyze the computational complexity of image transform operations The separable transformation computational complexity reduction of the separable transformation 18 References Prof .P. K. Biswas Department of Electronics and Electrical Communication Engineering Indian Institute of Technology, Kharagpur Gonzalez R. C. & Woods . (2008). Digital Image Processing. Prentice Hall. Forsyth, D. A. & Ponce, J. (2011).Computer Vision: A Modern Approach. Pearson Education. . | Digital Image Processing CSC331 Image transformation 1 Summery of previous lecture Image Interpolation explanation Interpolation operation Unitary matrix and its equation Unitary matrix with 1D signal Unitary matrix with 2D signal 2 Todays lecture Analyze the computational complexity of image transform operations The separable transformation computational complexity reduction of the separable transformation 3 4 5 6 7 8 9 Basis image 10 11 12 13 14 Discrete cosine trasformatine Basis Image Basis images of dimension 8 by 8 in total 64 basis images. One is the real component, other one is the imaginary component. 15 Discrete cosine trasformatine Basis Image The row of this represents the index k The column indicates the index l. We have 64 images, each of these 64 images is of size 8 by 8 pixels. 16 Basis images for other transformations The purpose of showing these basis images is to represent an input image as linear combination of the set of basis images Each of basis images will be weighted by the corresponding coefficient in the transformation coefficient v (k, l) v (k, l) is the inner product of k, l’th basis image. 17 Summery of the lecture Analyze the computational complexity of image transform operations The separable transformation computational complexity reduction of the separable transformation 18 References Prof .P. K. Biswas Department of Electronics and Electrical Communication Engineering Indian Institute of Technology, Kharagpur Gonzalez R. C. & Woods . (2008). Digital Image Processing. Prentice Hall. Forsyth, D. A. & Ponce, J. (2011).Computer Vision: A Modern Approach. Pearson Education. 19
