# CS 4640 Assignment A3: Enhancement Filters solved

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## Description

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Q1. Explore the use of Roberts, Prewitt, Sobel, log, | ∇f |, zero crossing and Canny on
the franklin and metro images. These will need preprocessing to convert them to gray level
images. Discuss the differences of the edge detectors, compare their effectiveness for these
images; focus on how they might help delineate words, important shapes, linear features,
etc. Make sure to also include the closed contour option in the Matlab edge function for
the zerocross method. Define performance measures and evaluate the methods with respect
to those. Make sure to provide figures to illustrate your discussion. (No Matlab functions
required for this question.)
Q2. The text says on p. 105 to “look at the gradient of the zero crossing and only keep
zero crossings where this is above a certain threshold (i.e., use the third derivative of the
original image).”
1
Develop filters for ∂
3f
∂x3 and ∂
3f
∂y3 by extending ∂
2f
∂x2 and ∂
2f
∂y2
to the third derivative. These
should be 1×4 and 4×1 filters. The image steps.jpg is provided to explore this and reduces
the problem to just the x dimension. Compute the first derivatives, [x1,y1], (using the Matlab gradient function), second derivatives, [x2,y2], (using gradient on the first derivatives),
and the third derivatives, [x3,y3], (using gradient on the second derivatives). Compare your
third derivative function to the gradient function result. Compare them by over-plotting
steps(21,:), x1(21,:), x2(21,:), and x3(21,:). Modify your third derivative filters to get the
same result as the gradient function. On a second figure, over-plot steps(21,:) and the 21st
row of the results of applying a Laplacian filter to steps, and running the Matlab edge function with the ’log’ method. Explain why the ’log’ method does not line up with the others.
(This question has the CS4640 df3 function.)
Q3. Use all the techniques learned so far to segment:
• line-like features (straight, narrow and long)
• solid rectangular objects
• text objects
Explain the ideas tried for these and provide performance measures. You may want to
demonstrate your results on synthetic images with just a few components. (This question
has the CS4640 shapes function.)
function [dx3,dy3] = CS4640_df3(im)
% CS4640_df3 – third derivative of image in x and y
% On input:
% im (MxN array): input gray level image
% On output:
% dx3 (MxN double array): third derivative in x: dˆ3f/dxˆ3
% dy3 (MxN double array): third derivative in y: dˆ3f/dyˆ3
% Call:
% [dx3,dy3] = CS4640_df3(cells);
% Author:
%
% UU
%
2
function segs = CS4640_shapes(im)
% CS4640_shapes – extract simple shapes from image
% On input:
% im (MxN array): input gray level image
% On output:
% segs (MxN array): labeled image:
% 0: background or unknown
% 1: line object
% 2: circular object
% 3: text object
% Call:
% segs = CS4640_shapes(im);
% Author:
%
% UU