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# LAPLACE TRANSFORM SUITABILITY FOR IMAGE PROCESSING

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LAPLACE TRANSFORM SUITABILITY FOR IMAGE PROCESSING APPLICATION..BY PRIYANKA RATHORE

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### LAPLACE TRANSFORM SUITABILITY FOR IMAGE PROCESSING

1. 1.  IMAGE PROCESSING  REQUIREMENTS IN IMAGE PROCESSING  LAPLACE TRANSFORM  APPLICATION UNDER LAPLACE TRANSFORM IMAGE SHARPENING BLOB DETECTION EDG EDETECTION  LAPLACE SUITABILITY  DRAWBACK
2. 2.  Image processing is any form of signal processing for which the input is an image, such as a photograph; the output of image processing may be either an image or a set of characteristics or parameters related to the image.  The most requirements for image processing is that the images be available in digitized form, that is, arrays of finite length binary words.  For digitization, the given Image is sampled on a discrete grid and each sample or pixel is quantized using a finite number of bits.
3. 3.  After converting the image into bit information, processing is performed. This processing technique may be  Image enhancement  Image reconstruction  Image compression.  Through various transformation . laplace transformation is one of them.
4. 4. The Laplacian is defined as follows: where the partial 1st order derivative in the x direction is defined as follows: and in the y direction as follows: y f x f f 2 2 2 2 2 ),(2),1(),1(2 2 yxfyxfyxf x f ),(2)1,()1,(2 2 yxfyxfyxf y f
5. 5. So, the Laplacian can be given as follows: ),1(),1([ 2 yxfyxff )]1,()1,( yxfyxf ),(4 yxf
6. 6.  IMAGE SHARPENING/ENHANCEMENT  EDGE DETECTION  BLOB DETECTION
7. 7.  Image enhancement falls into a category of image processing called spatial filtering.  The Laplacian operator is an example of a second order or second derivative method of enhancement.  Any feature with a sharp discontinuity (like noise, ) will be enhanced by a Laplacian operator. Thus, one application of a Laplacian operator is to restore fine detail to an image which has been smoothed to remove noise.
8. 8. Applying the Laplacian to an image we get a new image that highlights edges and other discontinuities Original Image Laplacian Filtered Image Laplacian Filtered Image Scaled for Display
9. 9. The result of a Laplacian filtering is not an enhanced image We have to do more work in order to get our final image Subtract the Laplacian result from the original image to generate our final sharpened enhanced image Laplacian Filtered Image Scaled for Display fyxfyxg 2 ),(),(
10. 10. The entire enhancement can be combined into a single filtering operation ),1(),1([),( yxfyxfyxf )1,()1,( yxfyxf )],(4 yxf fyxfyxg 2 ),(),( ),1(),1(),(5 yxfyxfyxf )1,()1,( yxfyxf
11. 11. This gives us a new filter which does the whole job for us in one step 0 -1 0 -1 5 -1 0 -1 0 agestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
12. 12.  In the field of computer vision, blob detection refers to mathematical methods that are aimed at detecting regions in a digital image that differ in properties, such as brightness or color, compared to areas surrounding those regions.  there are two main classes of blob detectors: (i) differential methods are based on derivatives of the function with respect to position, and (ii) methods based on local extrema are based on finding the local maxima and minima of the function.
13. 13. 1)HISTOGRAM ANALYSIS 2)OBJECT RECOGNITION 3)PEAK DETECTION IN SEGMENTATION 4)TEXTURE ANALYSIS 5)RIDGE DETECTION 6)GATHERING INFORMATION WHICH IS NOT OBTAINED THROUGH CORNER OR EDGE DETECTION.
14. 14.  One of the first and also most common blob detectors is based on the Laplacian of the Gaussian (LoG).  Given an input image , this image is convolved by a Gaussian kernel at a certain scale to give a scale space representation .  The Laplacian operator is computed, which usually results in strong positive responses for dark blobs of extent and strong negative responses for bright blobs of similar size.
15. 15.  Edge Detection: Given an image corrupted by acquisition noise, locate the edges most likely to be generated by scene elements, not by noise.  The laplacian method searches for zero crossing in the second derivative of the image to find edges.  Zero crossing:- an imaginary straight line joining the extreme positive and negative values of the second derivative would cross zero near the midpoint of the edge.
16. 16. Original image Corrupted image with noise
17. 17.  Start with an image  Blur the image. So that only needed feature can be extacted.
18. 18. First gradient of signal Comparison of gradient and thresold  Perform the laplacian on this blurred image through laplacian transformation.  Comparison is done between thresold and gradient. Whenever gradient exceeds the threshold ,edge is detected.
19. 19.  Identification of zero crossing.  Edges are detected.
20. 20.  The laplace operator is a 2nd order derivative operator which means:- i)Stronger response to fine detail such as :- A) Remove blurring from images B) Highlight edges c) Produce a double response at step changes in grey level. ii)Simpler implementation
21. 21. iii) Laplacian measures the change of the slope. i.e simply takes into account the values both before and after the current value whereas other transform such as Sobel/Prewitt measure the slope . iv) Also, a Laplace zero crossing method is more reliable to noise than Sobel or Prewitt.I.E. work well in high noise content
22. 22. v)The laplace filter produces two peaks; the location of the edge corresponds with the zero crossing of the laplace filter result as well as the direction,whereas other filter only provide direction of the edge. vi)Laplace has isotropic i.e. implies identical properties in all directions. It shows identical results when measured along different axes whereas other transform are anisotrophy i.e. they show different in properties and result.
23. 23. vii) We get thinner edges in case of zero crossing laplace method. viii) quite useful for locating the centers of thick edges(zero crossing).
24. 24. ix)Laplacians are computationally faster to calculate (only one kernel vs two kernels) and sometimes produce exceptional results! x) The Laplace Filter weights the difference between the center pixel and its neighbors.
25. 25.  Edges form numerous loops(spheggatti effect).  Complex computation