Description
Problem 1: Texture Analysis (35%)
In this problem, you will implement texture analysis and segmentation algorithms based on the 5×5 Laws
Filters constructed by the tensor product of the five 1D kernels in Table 1.
a) Texture Classification – Feature Extraction (15%)
48 images of four types of textures are given for the texture classification task. They are split into two
sets, 36 training samples and 12 testing samples. The ground truth labels of the 36 training samples are
known, while the testing samples’ categories are waiting for you to explore. Samples of these images are
shown in Fig. 1.
Figure 1: Examples of Grass, Blanket, Stones, Brick [2]
Please follow steps below to extract features for all texture images provided and do analysis:
1. Filter bank response computation: Use the twenty-five 5×5 Laws Filters in Table 1 to extract
the response vectors from each pixel in the image (use appropriate boundary extensions).
2. Energy feature averaging: Compute the energy feature of each element of the response vector.
Average the energy feature vectors of all image pixels, leading to a 25-D feature vector for each
image. Which feature dimension has the strongest discriminant power? Which has the weakest?
Please justify your answer.
3. Feature reduction: Reduce the feature dimension from 25 to 3 using the principal component
analysis (PCA). Plot the reduced 3-D feature vectors in the 3-D feature space.
Please conduct texture classification using the nearest neighbor rule based on the Mahalanobis distance.
Note: Built-in PCA function can be used.
b) Advanced Texture Classification — Classifier Exploration (20%)
Based on the 25-D and 3-D feature vectors obtained above, conduct both unsupervised and supervised
learning. Please follow the steps below.
1. Unsupervised: K-means clustering is a kind of unsupervised learning algorithm which separates
the textures into different categories without the help of ground truth labels. It will not directly tell
the class for each image but will group similar images together.
a. Apply the K-means algorithm for test images based on the 25-D feature and the reduced 3-
D feature, respectively. Set the hyperparameter K (number of clusters) equal to the number
of possible classes in the dataset (e.g. K=4).
b. Use the test labels to evaluate the purity of each cluster. Specifically, classify the images
in each cluster as the majority class of that cluster. Report the error rate for both methods.
Discuss the effectiveness of the feature dimension reduction over the K-means clustering.
2. Supervised: Use the 3-D feature of training images to train the Random Forest (RF) and the
Support Vector Machine (SVM), respectively. Then predict the test set labels and report the error
rate. Compare the two classifiers.
Note: Built-in K-means function, RF and SVM can be used.
Problem 2: Texture Segmentation (30%)
a) Basic Texture Segmentation (20%)
Segment the texture mosaic Mosaic.raw in Fig. 2 by following the steps below:
1. Filter bank response computation: Use the twenty-five 5×5 Laws Filters in Table 1 to extract
the response vectors from each pixel in the image (use appropriate boundary extensions).
2. Energy feature computation: Use a window approach to compute the energy measure for each
center pixel based on the results from step 1. You may try a couple of different window sizes.
After this step, you will obtain 25-D energy feature vector for each pixel.
3. Energy feature normalization: All kernels have a zero-mean except for �5!�5. Actually, the
feature extracted by the filter �5! �5 is not a useful feature for texture classification and
segmentation. Use its energy to normalize all other features at each pixel.
4. Segmentation: Discard the feature associated with L5T L5. Use the K-means algorithm to perform
segmentation on the composite texture image given in Fig. 2 based on the 24-D energy feature
vectors.
If there are K textures in the image, your output image will be of K colors, with each color represents one
type of texture. Use the following randomly generated color map to represent the K=6 regions. The
ordering does not matter.
0 1 2 3 4 5
R 107 114 175 167 144 157
G 143 99 128 57 147 189
B 159 107 74 32 104 204
Figure 2: Texture mosaic image. [3]
b) Advanced Texture Segmentation (10%)
You may not get good segmentation results for the complicated texture mosaic image in Fig. 2. Please
develop some techniques to improve your segmentation result. Several ideas are sketched below.
1. Use the PCA for feature reduction. Use the dimension reduced features to do texture segmentation
of Fig. 2.
2. Develop a post-processing technique to merge small holes.
3. Enhance the boundary of two adjacent regions by focusing on the texture properties in these two
regions only.
Problem 3: SIFT and Image Matching (35%)
Image feature extractors are useful for representing the image information in a low dimensional form.
(a) Salient Point Descriptor (Basic: 10%)
SIFT is an effective tool to extract salient points in an image. Read the paper in [1] and answer the
following questions.
1. From the paper abstract, the SIFT is robust to what geometric modifications?
2. How does SIFT achieve its robustness to each of them?
3. How does SIFT enhance its robustness to illumination change?
4. What are the advantages of using Difference of Gaussians (DoG) instead of Laplacian of Gaussians
(LoG) in SIFT?
5. What is the SIFT’s output vector size in its original paper?
(b) Image Matching (Basic: 15%)
You can apply SIFT to image matching. Extract and show SIFT features.
1. Find key-points of the Cat_1 and Cat_Dog images in Fig. 3. Pick the key-point with the largest
scale in Cat_1 and find its closest neighboring key-point in Cat_Dog. You can do nearest neighbor
search in the searching database for the query image Cat_1 which is represented as a SIFT
extracted feature vector. Discuss your results, especially the orientation of each key-point. Show
the corresponding SIFT pairs between Cat_1 and Cat_Dog.
2. Perform the same processing with the following three image pairs: a) Dog_1 and Cat_Dog, b)
Cat_1 vs Cat_2, c) Cat_1 vs Dog_1. The matching may not work well between different objects
or against the same object but with a large viewing angle difference. Show and comment on the
matching results. Explain why it works or fails in some cases.
You are allowed to use open source library (OpenCV or VLFeat) to extract features.
(a) Cat_1 (b) Cat_2
EE 569 Digital Image Processing: Homework #4
Professor C.-C. Jay Kuo Page 5 of 6
(c) Dog_1 (d) Cat_Dog
Figure 3: Images for image matching. [4]
(c) Bag of Words (10%)
If we create a codebook with K codewords representing K types of key patterns, each image can be
represented by the codewords. A histogram can be calculated to reflect the occurrence of each codeword
in an image. This representation is called the Bag of Words (BoW).
Apply the K-means clustering to the extracted SIFT features from the four images in part (b) to form a
codebook with K=8 codewords. Each codeword is characterized by the centroid of the SIFT feature
vectors. Generate the BoW representations for Cat_1, Dog_1 and Dog_2 provided in the materials. Match
Dog_2’s BoW representation with Cat_1 and Dog_1, respectively. Which one gives you the better
matching? Show the histograms of these three images and discuss your observations.
Figure 4: Dog_2 image. [4]
Appendix:
Problem 1: Texture Analysis
48 texture images
(./train and ./test)
128×128 8-bit grayscale
Problem 2: Texture Segmentation
Mosaic.raw 512×512 8-bit grayscale
Problem 3: Image Feature Extractors
Cat_1.raw 600×400 24-bit Color (RGB)
Cat_2.raw 600×400 24-bit Color (RGB)
EE 569 Digital Image Processing: Homework #4
Professor C.-C. Jay Kuo Page 6 of 6
Cat_Dog.raw 600×400 24-bit Color (RGB)
Dog_1.raw 600×400 24-bit Color (RGB)
Dog_2.raw 600×400 24-bit Color (RGB)
Reference Images
Images in this homework are taken from SIPI Image Database [2], Prague dataset [3] and Google
images [4].
References
[1] David G. Lowe, “Distinctive image features from scale-invariant keypoints,” International Journal of
Computer Vision, 60(2), 91-110, 2004
[2] https://sipi.usc.edu/database/
[3] https://mosaic.utia.cas.cz/
[4] [Online] http://images.google.com/
