CS1674: Homework 5

• function [edges] = detectEdges(im, threshold) -- A function to compute edges in an image. Converts to grayscale first, computes gradients, then computes the gradient magnitude and orientation at each pixel, and only returns those (x, y) locations with magnitude that is higher than the threshold. The function also displays the final thresholded edge image.
  
  Inputs:
  • im is the RGB input image of class uint8, and
  • threshold is a user-set threshold for detecting edges (which can be omitted if you want to use the default threshold-- to use that, only supply the first input to the function).
  
  Output:
  • edges is an Nx4 matrix containing 4 numbers for each of N detected edge points: N(i, 1) is the x location of the point, N(i, 2) is the y location of the point, N(i, 3) is the gradient magnitude at the point, and N(i, 4) is the gradient orientation (non-quantized) at the point.

1. [20 pts] function [centers] = detectCircles(im, edges, radius, top_k) -- A function to find and visualize circles given an edge map.
   
   Inputs:
   • im, edges are defined as above,
   • radius specifies the size of circle we are looking for (use impixelinfo to hover over the image and visually approximate the radius), and
   • top_k says how many of the top-scoring circle center possibilities to show and output.
   
   Output:
   • centers is an Nx2 matrix in which each row lists the x, y position of a detected circle's center.
   
   Tips:
   • Since we use atand to compute gradient orientation in degrees, make sure you use cosd and sind to detect circles.
   • Consider using ceil(a / quantization_value) and ceil(b / quantization_value) (where, for example, quantization_value can be set to 5) to easily figure out quantization/bins in Hough space. Don't forget to multiply by quantization_value once you've figured out the Hough parameters with most votes, to find out the actual x, y location corresponding to the selected bin.
   • You can use this line at the end of your function to visualize circles: figure; imshow(im); viscircles(centers, radius * ones(size(centers, 1), 1));.
   • You can ignore circles whose centers are outside the image.


2. [10 pts] Demonstrate the function applied to the provided images jupiter.jpg and egg.jpg. Display the images with detected circle(s), label the figure with the radius, save your image outputs, and include them in your submission. You can use impixelinfo to estimate the radius of interest manually.

1. [15 pts] function [outputImg, meanColors, clusterIds] = quantizeRGB(origImg, k) which performs clustering in the 3-dimensional RGB space, and "quantizes" the image. Use the built-in Matlab function kmeans (and read the documentation to see how to use it, including what data types it expects). At the end of your function, show the (1) original and (2) quantized image, in a 1x2 subplot. Make sure to label the figure with the value of k that was used.
   
   Inputs:
   • origImg is an RGB image of class uint8, and
   • k specifies the number of colors to quantize to (i.e. the number of clusters).
   
   Outputs:
   • outputImg is an RGB image of class uint8 and the same size as the original image,
   • meanColors is a kx3 array of the k centers (one value for each cluster and each color channel), and
   • clusterIds is a numpixelsx1 matrix (with numpixels = numrows * numcolumns) that says to which cluster each pixel belongs.
   
   Tip: If the variable origImg is a 3d matrix (numrowsxnumcolsx3) containing a color image with numpixels pixels (first two dimensions) in each color channel (third dimension), then X = reshape(origImg, [numpixels, 3]); will yield a matrix with the RGB features as its rows. It is in this space (samples = rows, features = columns) that you want to apply k-means.


2. [5 pts] Run your function on the provided image fish.jpg. Use three different values of k; display and submit the results. For example, if you set k=2, you might get the following as part of your subplot:
   
   
   
   

• detectCircles.m
• demonstrations of your circle detection on the provided images jupiter.jpg and egg.jpg, for one radius (can be different for the two images), named jupiter_circles.png and egg_circles.png, respectively
• quantizeRGB.m
• 3 different images with different k applied on fish.jpg, named k?.png, k??.png, k???.png, where the question marks are replaced with the values of k you used