LAPLACE TRANSFORM SUITABILITY FOR IMAGE PROCESSING APPLICATION

BY PRIYANKA RATHORE 1014313037 IT 3RD YEAR IMSEC(GHAZIABAD)

IMAGE PROCESSING REQUIREMENTS IN IMAGE PROCESSING LAPLACE TRANSFORM APPLICATION UNDER LAPLACE TRANSFORM IMAGE SHARPENING BLOB DETECTION EDG EDETECTION LAPLACE SUITABILITY DRAWBACK

CONTENT

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.

IMAGE PROCESSING

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.

reqiurements ( cont….)

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:

The LAPLACE TRANSFORM

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So, the Laplacian can be given as follows:

The Laplacian

),1(),1([2 yxfyxff )]1,()1,( yxfyxf

),(4 yxf

IMAGE SHARPENING/ENHANCEMENT

EDGE DETECTION

BLOB DETECTION

APPLICATION OF LAPLACE TRANSFORM

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.

IMAGE ENHANCEMENT

Applying the Laplacian to an image we get a new image that highlights edges and other discontinuities

HOW IMAGE ENHANCEMENT IS DONE??

OriginalImage

LaplacianFiltered Image

LaplacianFiltered Image

Scaled for Display

The result of a Laplacian filtering is not an enhanced imageWe have to do more work in order to get our final imageSubtract the Laplacian result from the original image to generate our final sharpened enhanced image

But That Is Not Very Enhanced!

LaplacianFiltered Image

Scaled for Display

fyxfyxg 2),(),(

Laplacian Image Enhancement

The entire enhancement can be combined into a single filtering operation

Simplified Image Enhancement

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This gives us a new filter which does the whole job for us in one step

Simplified Image Enhancement (cont…)

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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.

BLOB DETECTION

USE OF BLOB DETECTION1)HISTOGRAM ANALYSIS2)OBJECT RECOGNITION3)PEAK DETECTION IN SEGMENTATION4)TEXTURE ANALYSIS5)RIDGE DETECTION6)GATHERING

INFORMATION WHICH IS NOT

OBTAINED THROUGH CORNER OR EDGE DETECTION.

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.

BLOB DETECTION BY LAPLACE OPERATOR

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.

EDGE DETECTION METHOD

EDGE DETECTION

Original image Corrupted image with noise

EDGE DETECTION STEPS Start with an image

Blur the image. So that only needed feature can be extacted.

EDGE DETECTION STEPS

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.

EDGE DETECTION STEPS Identification of zero

crossing.

Edges are detected.

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

LAPLACE SUITABILITY

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

LAPLACE SUITABILITY

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.

LAPLACE SUITABILITY

LAPLACE SUITABILITYvii) We get thinner

edges in case of zero crossing laplace method.

viii) quite useful for locating the centers of thick edges(zero crossing).

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.

LAPLACE SUITABILITY

Edges form numerous loops(spheggatti effect).

Complex computation

DRAWBACKS

THANK YOU!!!