Iterative Identification and Restoration of Images (The by Reginald L. Lagendijk

By Reginald L. Lagendijk

The most fascinating questions in snapshot processing is the matter of getting better the specified or excellent snapshot from a degraded model. generally one has the sensation that the degradations within the photograph are such that appropriate info is as regards to being recognizable, if simply the picture can be sharpened a bit. This monograph discusses the 2 crucial steps in which this is accomplished, particularly the subjects of photo id and recovery. extra in particular the objective of snapshot identifi­ cation is to estimate the houses of the imperfect imaging approach (blur) from the saw degraded photograph, including a few (statistical) char­ acteristics of the noise and the unique (uncorrupted) snapshot. at the foundation of those homes the picture recovery technique computes an estimate of the unique photograph. even though there are various textbooks addressing the picture identity and recovery challenge in a basic snapshot processing environment, there are hardly ever any texts which offer an indepth remedy of the cutting-edge during this box. This monograph discusses iterative systems for choosing and restoring pictures which were degraded by way of a linear spatially invari­ ant blur and additive white remark noise. instead of non-iterative equipment, iterative schemes may be able to resolve the picture recovery challenge whilst formulated as a restricted and spatially variation optimization prob­ during this method recovery effects could be acquired which outperform the lem. result of traditional recovery filters.

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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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