CS1674: Homework 6 - Programming

Due: 10/26/2016, 11:59pm

This assignment is worth 50 points.

Part I: Color quantization with K-means (20 points)

For this problem you will write code to quantize a color space by applying k-means clustering to the pixels in a given input image, and experiment with two different color spaces--- RGB and HSV. Use the built-in Matlab function kmeans, or the kmeansML function from HW5P. Include each of the following components in your submission:
  1. [10 pts] Given an RGB image, perform clustering in the 3-dimensional RGB space, and map each pixel in the input image to its nearest k-means center. That is, replace the RGB value at each pixel with its nearest cluster's average RGB value. For example, if you set k=2, you might get:

    Since these average RGB values may not be integers, you should round them to the nearest integer (1 through 255). Use the following form:
    function [outputImg, meanColors, clusterIds] = quantizeRGB(origImg, k)
    where origImg and outputImg are RGB images of type uint8, k specifies the number of colors to quantize to, and meanColors is a kx3 array of the k centers (one value for each cluster and each color channel). clusterIds is a numpixelsx1 matrix (with numpixels = numrows * numcolumns) that says which cluster each pixel belongs to. Matlab tip: if the variable im is a 3d matrix containing a color image with numpixels pixels in each color channel, X = reshape(im, numpixels, 3); will yield a matrix with the RGB features as its rows.

  2. [2 pts] Write a function to compute the Euclidean distance between the original RGB pixel values and the quantized values (this is also called sum-of-squared-differences or SSD error). Use the following form:
    function [error] = computeQuantizationError(origImg, quantizedImg)
    where origImg and quantizedImg are both RGB images of type uint8, and error is a scalar giving the total SSD error across the image.

  3. [8 pts] Write a script colorQuantizeMain.m that calls all the above functions appropriately using the provided image fish.jpg, and displays the results. Illustrate the quantization with at least three different values of k. Label all plots clearly with titles. In a text file explanation.txt, briefly answer the following: How and why does the SSD differ based on the value of k?
Useful Matlab functions: kmeans, kmeansML, reshape, repmat, title. .

Part II: Edge detection and circle detection (30 points)

Implement (1) a simple edge detector, and (2) a Hough Transform circle detector that takes an input image and a fixed radius, and returns the centers of any detected circles of about that size. You are not allowed to use any built-in Matlab functions for finding edges or circles! Include the following:
  1. [10 pts] function [edges] = detectEdges(im, threshold) -- A function to compute edges in an image. im is the input image in uint8 type and in color, and threshold is a user-set threshold for detecting edges. 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.

  2. [15 pts] function [centers] = detectCircles(im, edges, radius, top_k) -- A function to find and visualize circles from an edge map. im, edges are defined as above, radius specifies the size of circle we are looking for, and top_k says how many of the top-scoring circle center possibilities to show. The output centers is an Nx2 matrix in which each row lists the x, y position of a detected circle's center.

  3. [5 pts] Demonstrate the function applied to the provided images jupiter.jpg and egg.jpg. Display the images with detected circle(s), labeling 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.

Acknowledgement: This assignment is adapted from Kristen Grauman.