Get 2D and 3D Image Analysis by Moments PDF

By Jan Flusser, Tomas Suk, Barbara Zitova

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

2D and 3D photograph research by way of Moments, is a special compendium of moment-based photograph research such as conventional tools and in addition displays the most recent improvement of the field.

The booklet offers a survey of 2nd and 3D second invariants with appreciate to similarity and affine spatial changes and to photo blurring and smoothing by way of numerous filters. The e-book comprehensively describes the mathematical historical past and theorems in regards to the invariants yet a wide half can also be dedicated to functional utilization of moments. purposes from quite a few fields of desktop imaginative and prescient, distant sensing, clinical imaging, photograph retrieval, watermarking, and forensic research are verified. awareness is additionally paid to effective algorithms of second computation.

Key features:

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

2D and 3D snapshot research through Moments, is perfect for mathematicians, desktop scientists,   engineers, software program builders, and Ph.D scholars concerned with photo research and popularity. a result of addition of 2 introductory chapters on classifier layout, the ebook can also function a self-contained textbook for graduate collage classes on item recognition.

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Sample text

Such high vulnerability of “pure” differential invariants led to development of semi-differential invariants. This method divides the object into affine-invariant parts. Each part is described by some kind of global invariants, and the whole object is then characterized by a string of vectors of invariants. Recognition under occlusion is again performed by maximum substring matching. Since inflection points of the boundary are invariant to affine (and even projective) deformation of the shape, they have become a popular tool for the definition of the affine-invariant parts.

This is why the Bayesian classifier is sometimes called the “optimal” classifier. Since the posterior probabilities cannot be estimated directly from the training set, we take advantage of the Bayes formula, which express the posterior probability in terms of prior probability and class-conditional probability p(a|????i ) ⋅ p(????i ) . p(????i |a) = ∑C j=1 p(a|????j ) ⋅ p(????j ) Since the denominator is constant over i, maximizing posterior probability is equivalent to maximizing the numerator. The prior probability p(????i ) express the relative frequency with which the class ????i appears in reality.

Such high vulnerability of “pure” differential invariants led to development of semi-differential invariants. This method divides the object into affine-invariant parts. Each part is described by some kind of global invariants, and the whole object is then characterized by a string of vectors of invariants. Recognition under occlusion is again performed by maximum substring matching. Since inflection points of the boundary are invariant to affine (and even projective) deformation of the shape, they have become a popular tool for the definition of the affine-invariant parts.

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