sandeepkonam_statisticalanalysisofimageprocessingtechniques for object counting

Sandeep Konam

Rajiv Gandhi University of Knowledge Technologies,

RK Valley, Andhra Pradesh, India

Motivation

Counting !

Source (Clockwise) :Public domain image (created by the Dartmouth Electron Microscope Facility) ; retrieved from www.bloodwork.com ; Photo by Marty Snyderman

© 2014 Sandeep Konam . All rights reserved.

Related Work

• Hough Transform

• RANSAC

• Neural Network

• Shape Matching


Related Work

Hough Transform


Related Work

Hough Transform

40 out of 50 circles detected as indeed circles© 2014 Sandeep Konam . All rights reserved.

Related Work

• Hough Transform

• RANSAC

• Neural Network

• Shape Matching

How? Randomly chooses pairs of edges to form a line hypothesis and then testhow many other edges fall onto this line

Fallout : Many more hypotheses may need to be generated and tested than those obtained by finding peaks in the accumulator array.


Related Work

• Hough Transform

• RANSAC

• Neural Network

• Shape Matching

How? Through pre-setting of similar shape templates and training them.

Fallout : System needs to be trained with all the variants and discrepanciesassociated with the shapes.


Related Work

• Hough Transform

• RANSAC

• Neural Network

• Shape Matching

How? Requires the shape description and representation based on which the image containing shapes to be detected and the template are compared.

Fallout : Difficult to get a fit descriptor.


Algorithm

Random Image Generation

Introducing random quotient

Coordinate Selection

Drawing shapes based on Mathematical

Properties

Avoid shapes around the corners – Else Distinctness

of the shapes might be lost

Vertices and angles need to be fed for closed

shapes other than line, circle and ellipse


Algorithm

Random Image Generation


Algorithm

Detection and Probability

Find contours

Size of contours

Shape Classification

Image is split into parallel regions

Probability in the vicinity is calculated

Depending on the size, classification of shapes can be

done

Angles and other metrics might be necessary to detect and

classify complex shapes


Algorithm

Detection and Probability


Buffon’s Needle Problem

p(C) = 2lπd

“ Let a needle of length l be thrown at random onto a horizontal plane ruled with parallel straight lines spaced by a distace d from each other, with d > l. What is the probability p that the needle will intersect one of these lines? “

Generalized Buffon’s Needle Problem : p(C) = aπd

• Limiting argument to Circle : p(C) = 2π𝑟πd

= 2𝑟d


Results

Needles

Exp. No. N n p(S) p(C) % Abs. Error1 100 38 0.380 0.455 7.5

2 150 61 0.406 0.455 4.83

3 200 84 0.420 0.455 3.5

4 400 172 0.43 0.455 2.5

5 600 264 0.44 0.455 1.5

6 800 355 0.444 0.455 1.13

7 850 380 0.447 0.455 0.794


Results

Circles

Exp. No. N n p(S) p(C) % Abs. Error1 50 41 0.82 0.857 3.7

2 100 84 0.84 0.857 1.7

3 150 127 0.846 0.857 1.1

4 200 170 0.85 0.857 0.7

5 250 213 0.852 0.857 0.5


Conclusion

• As the number of mathematical shapes increase, results of proposed algorithm converges to that of empirical calculations

Future Scope

• Efficient Algorithm needs to be developed for overlapping images

• Developed algorithms are to be applied on real time images


sandeepkonam_statisticalanalysisofimageprocessingtechniques for object counting

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