Download 2D and 3D Image Analysis by Moments by Jan Flusser, Tomas Suk, Barbara Zitova PDF

By Jan Flusser, Tomas Suk, Barbara Zitova

Presents fresh major and quick improvement within the box of 2nd and 3D image analysis

2D and 3D picture research by means of Moments, is a special compendium of moment-based snapshot research such as conventional equipment and likewise displays the most recent improvement of the field.

The ebook provides a survey of 2nd and 3D second invariants with appreciate to similarity and affine spatial changes and to photo blurring and smoothing by means of a number of filters. The ebook comprehensively describes the mathematical historical past and theorems in regards to the invariants yet a wide half can also be dedicated to sensible utilization of moments. purposes from a number of fields of machine imaginative and prescient, distant sensing, clinical imaging, picture retrieval, watermarking, and forensic research are proven. recognition is additionally paid to effective algorithms of second computation.

Key features:

  • Presents a scientific evaluate of moment-based positive factors utilized in 2nd and 3D snapshot analysis.
  • Demonstrates invariant houses of moments with recognize to numerous spatial and depth transformations.
  • Reviews and compares numerous orthogonal polynomials and respective moments.
  • Describes effective numerical algorithms for second computation.
  • It is a "classroom prepared" textbook with a self-contained creation to classifier design.
  • The accompanying web site includes round three hundred lecture slides, Matlab codes, entire lists of the invariants, try out pictures, and different supplementary material.

2D and 3D photo research by way of Moments, is excellent for mathematicians, desktop scientists,   engineers, software program builders, and Ph.D scholars curious about photo research and popularity. end result of the addition of 2 introductory chapters on classifier layout, the publication can also function a self-contained textbook for graduate collage classes on item recognition.

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Additional info for 2D and 3D Image Analysis by Moments

Example text

While ????2 again leads to a Voronoi tessellation the seeds of which are the class centers, the use of ????1 generates complex curved decision boundaries. 13). We can find two versions of this algorithm in the literature. Version 1 1. Unknown feature vector a is given. 2. Find k training samples which are the closest (in the sense of metric d) to sample a. 3. Check for each class how many times it is represented among the k samples found in Step 1. 4. Assign a to the class with the maximum frequency.

A typical choice of k in practice is from 2 to 10, depending on the size and reliability of the training set. The k-NN classifier is relatively time expensive, especially for high k. Several efficient implementations can be found in the literature, and some are even available on the internet. 2 Support vector machines Classifiers called the Support vector machines (SVMs) are generalizations of a classical notion of linear classifiers. The SVMs were invented by Vapnik [72]. In the training stage, the SVM classifier looks for two parallel hyperplanes which separate the training samples such that the distance (which is called margin) between these hyperplanes is maximized.

Any equivalence on M × M unambiguously determines a partition of M and vice versa. The components Mi are then called equivalence classes. Clearly, if equivalence ≈ is given on M × M, we can choose an arbitrary a ∈ M and find a set Ma = {x ∈ M|a ≈ x}. This is our first partition component. Then we find b ∈ M such that b ∉ Ma and construct the partition component Mb . We repeat this process until the whole M is covered. The sets Ma , Mb , · · · fulfill the definition of the partition. The backward implication is even more apparent.

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