Multidimensional signal, image, and video processing and by John W. Woods

By John W. Woods

Electronic photographs became mainstream of past due significantly inside HDTV, cellphones, own cameras, and lots of scientific functions. The processing of electronic photos and video contains adjusting illumination, production enlargements/reductions, and growing distinction. This improvement has made it attainable to take lengthy forgotten, badly broken photographs and cause them to new back with snapshot estimation. This totally revised and accelerated moment edition, will supply you the worthwhile knowing of picture and video processing suggestions to give a contribution to this sizzling technology's destiny advances. very important new issues contain introductory random methods, snapshot enhancement and research, and the hot MPEG scalable video coding typical. simply R&D point educational that provides an built-in remedy of photograph and video processing - subject matters which are interconnected. New chapters on introductory random approaches, info thought, and photo enhancement and research assurance and dialogue of the newest criteria in video coding: H.264/AVC and the recent scalable video general (SVC)

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9. In general, the Fourier transform of a product of 2-D sequences corresponds through Fourier transformation to the periodic convolution of their transforms: x(n1 , n2 )y(n1 , n2 ) ⇔ X(ω1 , ω2 ) Y(ω1 , ω2 ). However, if the product is a separable product, then the product of 1-D sequences corresponds through Fourier transformation to the product of their Fourier transforms: x(n1 )y(n2 ) ⇔ X(ω1 )Y(ω2 ). Reconcile these two facts by writing x(n1 ) and y(n2 ) as 2-D sequences, taking their 2-D Fourier transforms, and showing that the resulting periodic convolution in the 2-D frequency domain reduces to the product of two 1-D Fourier transforms.

1–7 A basic cell, indicated by heavy lines, for diagonal analog Fourier transform support. 1 Sampling Theorem—Rectangular Case From this last example, we see that, more so than in one dimension, there is a wider variety of the support or shape of the incoming analog Fourier-domain data, and it is this analog frequency domain support that, together with the sampling rates, determines whether the resulting discrete-space data are aliased or not. 1–6, we see that aliasing will not occur if we use this new basic cell.

2–2, we get the following two transform pairs: xe (n1 , n2 ) ⇔ Re X(ω1 , ω2 ), xo (n1 , n2 ) ⇔ j Im X(ω1 , ω2 ). Similarly, the conjugate symmetric and antisymmetric parts in the 2-D frequency are defined. 2–3: The conjugate symmetric part of X is 1 X(ω1 , ω2 ) + X ∗ (−ω1 , −ω2 ) . 2 The conjugate antisymmetric part of X is Xe (ω1 , ω2 ) Xo (ω1 , ω2 ) 1 X(ω1 , ω2 ) − X ∗ (−ω1 , −ω2 ) . 2 Using these symmetry properties, we get the following two general transform pairs: Re x(n1 , n2 ) ⇔ Xe (ω1 , ω2 ), j Im x(n1 , n2 ) ⇔ Xo (ω1 , ω2 ).

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