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

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

3.  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.

4.  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.

5. 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

6. So, the Laplacian can be given as follows:
),1(),1([
2
yxfyxff
)]1,()1,( yxfyxf
),(4 yxf

7.  IMAGE SHARPENING/ENHANCEMENT
 EDGE DETECTION
 BLOB DETECTION

8.  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.

9. 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

10. 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
),(),(

12. 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

13. 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)

14.  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.

15. 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.

16.  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.

17.  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.

18. Original image
Corrupted image with
noise

19.  Start with an image
 Blur the image. So that
only needed feature
can be extacted.

20. 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.

21.  Identification of zero
crossing.
 Edges are detected.

22.  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

23. 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

24. 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.

25. vii) We get thinner edges
in case of zero
crossing laplace
method.
viii) quite useful for
locating the centers of
thick edges(zero
crossing).

26. 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.

27.  Edges form numerous loops(spheggatti
effect).
 Complex computation