Hough Transform

Image Filtering and Hough Transform

Convolution

Visualize test image 1 with two different kernels

Blur Filter (Box kernel) kernel = ones(15)	Sharping Filter kernel = [0 -1 0; -1 5 -1; 0 -1 0]

Edge detection

Visualize myEdgeFilter results on test image 1&2 edges and edges after threshold

	Image 1	Image 2
Edge
Threshold

Hough Transform

Visualize myHoughTransform results on test image 1&2 hough accumulator

Image 1	Image 2

Finding lines

Here, non maximal suppression was enabled with matlab function imregionalmax, it returns the binary image that identifies the regional maxima in the input image. I use H = imregionalmax(H).* H to then zero out the non-regional maxima which considers all neighbors.

Visualize test image 1&3 result of peak finding

Image 1	Image 3

Fitting line segments for visualization

Visualize test image 1&2 line segment extraction results

Image 1	Image 2

Experiments

Summary

1. Did your code work well on all the images with a single set of parameters?

With one set of parameters, all the images give satisfactory results, though they are not optimal. With customized set of parameters, the performance could visibly be improved.

2. How did the optimal set of parameters vary with images?

I find that, with more details (lines, unregular shapes, and etc.), threshold can be set higher, for example 0.1 to rule out fuzzy and unbounded area so that the edges look neat and clean. It also helps to set thetaRes lower, for example pi/120 to sample more theta values in the range. Sigma = 4 seems to be blur the images well for all cases, though slightly increasing sigma for images with more details can also help to get a clean result. Setting rhoRes to a higher value breaks the hough line segments into smaller intervals and can help to capture short and less obvious boundaries of objects, though the results seems busy due to the small line segments all over the image.

3. Which step of the algorithm causes the most problems?

I think myEdgeFilter caused the most problems, it's mainly because the implementation of non maximum suppression requires complex conditions.

4. Did you find any changes you could make to your code or algorithm that improved performance?

I recognize that vectorization in Matlab often runs more efficiently than the loops. In particular, in myHoughLines.m, I used a loop to iterate (from 1 to nLines) and fill rhos and thetas, though in hindsight, I could use ind2sub vectorized code in Matlab to convert linear indices to subscripts.

A set of intermediate outputs for test image 4

Original	Gaussian Blurred	Sobel Filter	Normalized Sobel Filter
Edge	Threshold	Hough Accumulator	Hough Lines Extraction

More Results on new test images

Vancouver

sigma     = 5;
threshold = 0.1;
rhoRes    = 10;
thetaRes  = pi/90;
nLines    = 45;

Original	Edge	Threshold	Hough Accumulator	Hough Lines Extraction

Mona Lisa

Parameters
sigma     = 2;
threshold = 0.2;
rhoRes    = 8;
thetaRes  = pi/60;
nLines    = 80;

Original	Edge	Threshold	Hough Accumulator	Hough Lines Extraction

Pikachu, Kumamoto

sigma     = 4;
threshold = 0.03;
rhoRes    = 4;
thetaRes  = pi/90;
nLines    = 30;

Pikachu

Original	Edge	Threshold	Hough Accumulator	Hough Lines Extraction

Kumamoto

Original	Edge	Threshold	Hough Accumulator	Hough Lines Extraction