# EE 569: Homework #4 solved

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Problem 1: Texture Analysis and Segmentation (60%)
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.
Table 1: 1D Kernel for 5×5 Laws Filters
Name Kernel
L5 (Level) [1 4 6 4 1]
E5 (Edge) [-1 -2 0 2 1]
S5 (Spot) [-1 0 2 0 -1]
W5 (Wave) [-1 2 0 -2 1]
R5 (Ripple) [1 -4 6 -4 1]
(a) Texture Classification — Feature Extraction (Basic: 15%)
48 images of four types 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: Four types of textures: rice, grass, brick, blanket
Please follow steps below to extract features for all texture images provided and do analysis.
1. Feature Extraction: Use the twenty-five 5×5 Laws Filters in Table 1 to extract feature vectors
from pixel in the image (use appropriate boundary extensions).
EE 569 Digital Image Processing: Homework #4
Professor C.-C. Jay Kuo Page 2 of 5
2. Feature Averaging: Average the feature vectors of all image pixels, leading to a 25-D feature
vector for each image. Average feature vectors from pairs such as L5E5/E5L5 to get a 15-D
feature vector. Which feature dimension has the strongest discriminant power? Which has the
3. Feature Reduction: Reduce the feature dimension from 15 to 3 using the principle component
analysis (PCA). Plot the reduced 3-D feature vector in the feature space. (Note that you should
do PCA on train and test separately.)
Built-in PCA function can be used. For those who implement PCA correctly can obtain 5% bonus. Put it
(b) Advanced Texture Classification — Classifier Explore (Basic: 15%)
Based on the 15-D and 3-D feature vectors obtained above, let’s do both unsupervised and supervised
1. Unsupervised: K-means clustering is kind of unsupervised classifier which categorize the
textures without the help of ground truth labels. Use the K-means algorithm for test image
clustering based on the 15-D and 3-D feature. Discuss the effectiveness of feature dimension
reduction over K-means. Report and compare your results with observations (by eyes), give error
rate.
2. Supervised: Use the 3-D feature of training images to train Random Forest (RF) and Support
Vector Machine (SVM) respectively. Then predict the test set labels and give error rate.
Compare the two kinds of classification.
Built-in K-means function, RF and SVM can be used. For those who implement K-means algorithm
correctly can obtain 5% bonus. Show your work!
(c) Texture Segmentation (Basic: 20%)
Segment the textures in Fig. 2 by applying the 15 5×5 Laws Filters. Please follow steps below to
complete this problem.
1. Feature extraction: Apply Laws filters to the input image and get 15 gray-scale images.
2. Energy feature computation: Use a window approach to compute the energy measure for each
pixel based on the results from step 1. You may try a couple of different window sizes. After this
step, you will obtain 15-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 normal all other features at each pixel.
4. Segmentation: Use the K-means algorithm to perform segmentation on the composite texture
images given in Fig. 2 based on the 14-D energy feature vectors.
If there are K textures in the image, your output image will be of K gray levels, with each level represents
one type of texture. For example, you can use (0, 51, 102, 153, 204, 255) to denote six segmented regions
in the output for six textures.
EE 569 Digital Image Processing: Homework #4
Professor C.-C. Jay Kuo Page 3 of 5
Figure 2: Composite texture images
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. Adopt 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.
Brainstorms are welcome!
Problem 2: Image Feature Extractors (40%)
Image feature extractors are useful for representing the image information in a low dimensional form.
(a) Salient Point Descriptor (Basic: 10%)
SIFT are effective tools 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 achieves its robustness to each of them?
3. How does SIFT enhances its robustness to illumination change?
4. What the advantages that SIFT uses Difference of Gaussians (DoG) instead of Laplacian of
Gaussians (LoG)?
5. What is the SIFT’s output vector size in its original paper?
(b) Image Matching (Basic: 20%)
You can apply SIFT to object matching. Extract and show SIFT features.
EE 569 Digital Image Processing: Homework #4
Professor C.-C. Jay Kuo Page 4 of 5
1. Find key-points of the two Husky images in Fig. 3. Pick the key-point with the largest scale in
Husky_3 and find its closest neighboring key-point in Husky_1. You can do nearest neighbor
search in the searching database for the query image which is represented as a SIFT extracted
feature vector. Discuss your results, esp. the orientation of each key-point.
2. Show the corresponding SIFT pairs between the Husky_1 and Husky_3 in Fig. 3. The matching
may not work well between different objects and against the same object but with a large
viewing angle difference. Perform the same job with the following three image pairs: 1)
Husky_3 and Husky_2, 2) Husky_3 and Puppy_1, 3) Husky_1 and Puppy_1. Show and comment
on the matching results. Explain why it works or fails in some cases.
You are allowed to used open source library (OpenCV or VLFeat) to extract features.

(a) Husky_1 (b) Husky_2

(c) Husky_3 (d) Puppy_1
Figure 3: Dog images for image mataching
(c) Bag of Words (Advanced: 10%)
Apply the K-means clustering to extracted SIFT features to form a codebook. The codebook contains 8
bins, where each bin is characterized by the centroid of the SIFT feature vector. In other words, each
image can be represented as histogram of SIFT feature vectors. This representation is called the Bag of
Words (BoW). Create codewords for all four images and match Husky_3’s codewords with other
images. Show the results and discuss your observations.
EE 569 Digital Image Processing: Homework #4
Professor C.-C. Jay Kuo Page 5 of 5
Appendix:
Problem 1: Texture Analysis and Segmentation
Texture1 to 48.raw 128×128 8-bit Gray
Comp.raw 600×450 8-bit Gray
Problem 2: Salient Point Descriptors and Image Matching
Husky_1.jpg 640×420 24-bit Color(RGB)
Husky_2.jpg 640×420 24-bit Color(RGB)
Husky_3.jpg 640×420 24-bit Color(RGB)
Puppy_1.jpg 640×420 24-bit Color(RGB)
Reference Images
Images in this homework are taken from Google images [2], the USC-SIPI image database [3].
References
[1] David G. Lowe, “Distinctive image features from scale-invariant keypoints,” International Journal of
Computer Vision, 60(2), 91-110, 2004.