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OpenCV
Open Source Computer Vision
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In this tutorial, the basic concept of fuzzy transform is presented. You will learn:
The presented explanation demands knowledge of basic math. All related papers are cited and mostly accessible on https://www.researchgate.net/.
In the last years, the theory of F-transforms has been intensively developed in many directions. In image processing, it has had successful applications in image compression and reduction, image fusion, edge detection and image reconstruction [219] [69] [281] [217] [216] [287]. The F-transform is a technique that places a continuous/discrete function in correspondence with a finite vector of its F-transform components. In image processing, where images are identified by intensity functions of two arguments, the F-transform of the latter is given by a matrix of components.
Let me introduce F-transform of a 2D grayscale image
Let
We say that the
The coefficients
The
where the coefficients are given by
The technique of F-transforms uses two steps: direct and inverse. The direct step is described in the previous section whereas the inverse is as follows
where
The pixels are processed one by one in a way that appropriate basic functions are found for each of them. It will be exactly four, two in each direction. We need some helper structure in the memory for collecting their values. The values will be used in the nominator of the related fuzzy component. Implementation of this approach uses keyword FL
as fast processing (because of more optimizations) and linear basic function.
In this way, image is divided to the regular areas. Each area is processed separately using kernel window. This approach benefits from easy to understand, matrix based processing with straight forward parallelization.
This approach uses kernel