Image Processing: The Fundamentals by Maria Petrou

By Maria Petrou

Following the good fortune of the 1st version, this completely up to date moment version of Image Processing: The Fundamentals will make sure that it continues to be the precise textual content for an individual looking an creation to the basic innovations of picture processing. New fabric contains photograph processing and color, sine and cosine transforms, self reliant part research (ICA), part congruency and the monogenic sign and several new subject matters. those updates are mixed with assurance of vintage subject matters in snapshot processing, akin to orthogonal transforms and photograph enhancement, making this a very complete textual content at the subject.

Key features:

  • Presents fabric at degrees of hassle: the most textual content addresses the elemental techniques and offers a large view of photo processing, when extra complicated fabric is interleaved in containers through the textual content, delivering additional reference if you desire to learn every one approach in depth.
  • Contains lots of totally labored out examples.
  • Focuses on an realizing of ways photograph processing tools paintings in practice.
  • Illustrates advanced algorithms on a step by step foundation, and lists not just the great practices but additionally identifies the pitfalls in each one case.
  • Uses a transparent query and resolution structure.
  • Includes a CD containing the MATLAB® code of a few of the examples and algorithms provided within the publication. there's additionally an accompanying web site with slides on hand for obtain for teachers as a educating resource.

Image Processing: the basics, moment Edition is a perfect educating source for either undergraduate and postgraduate scholars. it's going to even be of price to researchers of assorted disciplines from medication to arithmetic with a qualified curiosity in photo processing

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Example text

8 You are U; given an image: g = . Compute the eigenvectors of ggT and v; of gTg. Then SST = 001111 The eigenvalues of ggT will be computed from the characteristic equation: l-X 2 0 2 6-X 1 0 1 l-X + (1- X)[(6 - X)(1 - X) - l] - 2[2(1- = 0 + (1- X)[(6 - X)(1 - X) - 1- 41 = 0 X)] = 0 32 Image Processing: Fundamentals The One eigenvalue is X = 1. 146 be the eigenvector which corresponds to eigenvalue 21 Xi. 23). So wehavereallyonlytwoindependent equations for the three unknowns. W e choose the value of x1 to be 1.

E. 319 v3 = What is the singular value decomposition of an image? 27) i=l since the only non-zero terms are those with i = j . How can we approximate an image using SVD? 9 1 A 256 X 256 grey image with 256 grey levels is to be transmitted. How many terms can be kept in its SVD before the transmission of the transformed image becomes too inefficient in comparison withthe transmission of the original image? ) 1 Assume that X7 is incorporated into one of the vectors. When term of the SVD expansion of the image we must transmit: we transmit one 35 Image 2 X 32 X 256 bits.

That is whywe chose subscripts T and c to denote these matrices ( r = rows, c = columns). 41) m=l n=l H is a ( N 2X N 2 ) matrix. We may think of it as partitioned inN X N submatrices stacked together. Then it can beshown that NKHN, is the H,, such submatrix. 43) m=l n=l The product V n V z is the product between an ( N X 1) matrix with the only non-zero element at position n , with a (l X N ) matrix, with the only non-zero element at position m. So, it is an N X N square matrix with the only non-zero element at position ( n ,m ) .

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