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

By Jan Flusser, Tomas Suk, Barbara Zitova

ISBN-10: 1119039355

ISBN-13: 9781119039358

Presents fresh major and fast improvement within the box of second and 3D image analysis

2D and 3D photo research through Moments, is a distinct compendium of moment-based snapshot research together with conventional tools and in addition displays the most recent improvement of the field.

The ebook provides a survey of second and 3D second invariants with recognize to similarity and affine spatial adjustments and to snapshot blurring and smoothing by way of numerous filters. The e-book comprehensively describes the mathematical historical past and theorems concerning the invariants yet a wide half is usually dedicated to functional utilization of moments. purposes from quite a few fields of machine imaginative and prescient, distant sensing, scientific imaging, photograph retrieval, watermarking, and forensic research are established. awareness can be paid to effective algorithms of second computation.

Key features:

  • Presents a scientific evaluate of moment-based positive aspects utilized in 2nd and 3D snapshot analysis.
  • Demonstrates invariant houses of moments with admire to numerous 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 creation to classifier design.
  • The accompanying web site comprises round three hundred lecture slides, Matlab codes, whole lists of the invariants, attempt pictures, and different supplementary material.

2D and 3D snapshot research by means of Moments, is excellent for mathematicians, laptop scientists,   engineers, software program builders, and Ph.D scholars excited by photo research and popularity. end result of the addition of 2 introductory chapters on classifier layout, the ebook can also function a self-contained textbook for graduate college 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.

In a supervised classification, the classes are specified beforehand by means of a training set. The training set is a set of objects the class membership of which is supposed to be known. It should contain enough typical representatives of each class including intra-class variations. Selection of the training set is the role of a human expert in the application domain. This is not a mathematical/computer science problem and cannot be resolved by any automatic algorithm because it requires a deep knowledge of the application area.

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. If partition {M1 , · · · , MC } of M is given, then the relation a ≈ b ⇔ a, b lie in the same component Mi is an equivalence on M × M. If we want to abstract away from the properties that may change inside the equivalence classes, we may work with a set of the classes that is called the quotient set and is denoted as (M∕ ≈). Working with quotient sets is very common in mathematics because it helps to 4 We use a notation for finite number of components C because object classification is always to a finite number of classes.

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

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