Shape Analysis and Classification: Theory and Practice by Luciano Da Fontoura Costa, Roberto Marcondes Cesar Jr.

By Luciano Da Fontoura Costa, Roberto Marcondes Cesar Jr.

Advances healthy research influence a variety of disciplines, from arithmetic and engineering to medication, archeology, and paintings. somebody simply coming into the sphere, even though, might locate the few current books on form research too particular or complex, and for college kids drawn to the categorical challenge of form popularity and characterization, conventional books on machine imaginative and prescient are too general.

Shape research and class: conception and perform bargains an built-in and conceptual advent to this dynamic box and its myriad purposes. starting with the elemental mathematical techniques, it offers with form research, from picture catch to development type, and offers some of the so much complex and strong ideas utilized in perform. The authors discover the proper features of either form characterization and popularity, and provides targeted realization to functional concerns, resembling directions for implementation, validation, and assessment.

Shape research and class offers a wealthy source for the computational characterization and type of normal shapes, from characters to organic entities. either scholars and researchers can at once use its state of the art recommendations and strategies to unravel their very own difficulties concerning the characterization and type of visible shapes.

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The concept of parameter can also be extended to techniques, programs and models. 6: The exponential function for several values of its parameter a. 7: The sinc function. Observe that this function crosses the x-axis at x = ±1, ± 2, L . 3, where a is the parameter that controls the smoothness of the transition of the function from –1 to 1. The higher the value of a, the steeper the transition. When a ® ¥ , the sigmoid becomes more and more similar to the signum function (see below). The reader is invited to identify the behavior of the sigmoid function when a<0 and a=0.

9 ) = -8 . This function, which is sometimes represented as ceil( x ) = éxù , can be related to the floor function as ceil( x ) = - floor(- x ) . 20 depicts the ceil function. 19: The floor function. 20: The ceil function. Trunc (or fix): This function produces as result the integer part of its input value. 3 ) = 3 , trunc(2 ) = 2 , trunc(2. 5 ) = 2 , © 2001 by CRC Press LLC trunc(8. 9 ) = 8 , trunc(- 3. 3) = - 3 , trunc(- 2 ) = -2 , trunc(- 2. 9 ) = - 8 . 21 illustrates this function. 21: The trunc function.

It is worth observing that shape similarity criteria, which are fundamental to classifying shapes, are generally dependent on each specific problem. For instance, in a situation where size is an important parameter, two shapes with similar areas can be more similar to each other than two shapes with significantly different areas. Clearly, the shape features adopted for their characterization play a central role with respect to defining how similar two shapes are. Shape similarity is particularly important when trying to match two or more shapes.

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