EE 569 Digital Image Processing: Homework #3

EE 569: Homework #3

General Instructions:

1. Read Homework Guidelines and MATLAB Function Guidelines for the information about homework

programming, write-up and submission.

2. If you make any assumptions about a problem, please clearly state them in your report.

In the first two problems, you will apply geometric modification and spatial warping techniques to do

some interesting image processing tricks. During this process, you may need to solve some linear

equations to get the matrix parameters.

Problem 1: Geometric Image Modification (25%)

Design and implement a spatial warping technique that transforms an input square image into an output

image of a star-shaped image, out of the square image. An example is given in Figure 1.

Figure 1: Warp the original image to star-shaped image.

The warped image should satisfy the following requirements:

• Pixels that lie on boundaries of the square should still lie on the boundaries of the star.

• Pixels on the two diagonals of the square should remain where they are.

• The thickness (height) of each black arc region is 64 pixels.

Apply the same developed spatial warping algorithm to Forky and Twenty-two images in Figure 2.

EE 569 Digital Image Processing: Homework #3

Professor C.-C. Jay Kuo Page 2 of 6

Figure 2: Forky and Twenty-two images.

(1) Describe your approach as clearly as possible and show the resulting images.

(2) Apply the reverse spatial warping to each warped image to recover its original image.

(3) Compare the recovered square image with the original square image. Is there any difference between

two images? If any, explain sources of distortion in detail.

Problem 2: Homographic Transformation and Image Stitching (25%)

One can use homographic transformation and image stitching techniques to create panorama that

consisting of multiple images. One example (Taken from MATLAB examples [1]) is shown in Figure 3.

The left images were taken with an uncalibrated smart phone camera by sweeping the camera from left to

right along the horizon to capture all parts of the building. The right panorama is the desired output by

stitching transformed images.

Figure 3: An example of image stitching to make panorama [1].

EE 569 Digital Image Processing: Homework #3

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This example involves five images. However, the basic principle is to process in

terms of consecutive pair of images. It could be achieved by following these steps:

• Select control points from both images. You can use SIFT/SURF to detect control points. You

are allowed to use OpenCV or other open source code for selecting control points, online source

refer to [2].

• Apply homographic transformation to find a homograph mapping (described below).

• Warp one image onto the other using the estimated transformation.

• Create a new image big enough to hold the panorama and composite the warped image into it.

You can composite by simply averaging the pixel values where the two images overlap.

The homographic transformation procedure is stated below. Images of points in a plane, from

two different camera viewpoints, under perspective projection (pin hole camera models) are

related by a homography:

where 𝐻 is a 3×3 homographic transformation matrix, 𝑃1 and 𝑃2 denote the corresponding image

points in homogeneous coordinates before and after the transform, respectively. Specifically, we

have

To estimate matrix 𝐻, you can proceed with the following steps:

• Fix 𝐻33 = 1 so that there are only 8 parameters to be determined.

• Select four-point pairs in two images to build eight linear equations.

• Solve the equations to get the 8 parameters of matrix 𝐻.

• After you determine matrix 𝐻, you can project all points from one image to another by

following the backward mapping procedure and applying the interpolation technique.

Implement above homographic transformation and stitching techniques to composite the scenery

images in Figure 4. Show the results and make discussion on the following questions.

(1) How many control points were used? Show the corresponding control points between left and

middle pair, middle and right pair.

(2) How did you select control points? Clearly specify how you use matched feature from

SURF/SIFT to create panorama.

EE 569 Digital Image Processing: Homework #3

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Figure 4. The scenery images (left, middle, right) (credit to Zhiruo Zhou)

Problem 3: Morphological processing (50%)

In this problem, you will implement the morphological processing operation: thinning. A pattern table

(patterntables.pdf) is attached for your reference. For shrinking and skeletonizing, you can use Matlab

or OpenCV functions if needed. Please show outputs for all following parts in your report and discuss

them thoroughly. Please state any assumptions you make in your solution.

Note: the provided greyscale images may not be binary images. You need to binarize them before doing

morphological processing. Binarize the image in the following way: suppose the maximum pixel intensity

is 𝑥, then any locations with original intensity greater than 0.5𝑥 are labeled as 1 in the binary image.

Otherwise, 0.

(a) Basic morphological process implementation (15%)

Please apply the “thinning” filter to the pattern images (spring, flower, jar) below. Show your results,

including intermediate processing result (around the 20th iteration) and give reasonable explanation.

Figure 5: flower, jar, spring (modified from [3])

(b) Defect detection and counting (20%)

A greyscale image of a deer is shown in Figure 6. The deer image is supposed to be all white; however,

there are black defects of different sizes all over the deer. Suppose that black holes whose sizes are smaller

than 50 pixels are defects. Please apply morphological processing algorithm for automatic defect counting

EE 569 Digital Image Processing: Homework #3

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and detection. For each question, please explain your method and include intermediate results if there are

any:

(1) Count the total number of defects in the image.

(2) How many different defect sizes are present in the image? What is the frequency of these defect

sizes?

(Hint: The defect size is the number of pixels in a defect. Please state any further assumption you

take regarding defect size.)

(3) Correct the defects and show the clear deer image.

Figure 6: deer with defect.

(c) Object Segmentation and Analysis (15%)

Figure 7 displays different types of beans.

Figure 7: beans (modified from [4])

For each question, please explain your method and include intermediate results if there are any:

(1) Count the total number of beans via morphological processes.

(2) Generate the segmentation mask for different types of beans. Then compare the size of different

types of beans. Rank the bean’s size from small to large in terms of type.

Note: You need to convert the incoming RGB image to grayscale image first and then apply

morphological processes. Some pre-processing or post-process may be needed to deal with unwanted

dots and holes.

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Appendix:

Problem 1&2: Geometric Image Modification

Forky.raw 328×328 24-bit color (RGB)

22.raw 328×328 24-bit color (RGB)

left.raw 576×432 24-bit color (RGB)

middle.raw 576×432 24-bit color (RGB)

right.raw 576×432 24-bit color (RGB)

Problem 3: Morphological processing

spring.raw 252×252 8-bit greyscale

flower.raw 247×247 8-bit greyscale

jar.raw 252×252 8-bit greyscale

deer.raw 550×691 8-bit greyscale

beans.raw 494×82 24-bit color (RGB)

Note: “550×691” means “width=550, height=691”.

References

[1] Matlab panorama example: https://www.mathworks.com/help/vision/ug/feature-based-panoramicimage-stitching.html

[2] OPENCV feature matching example: https://docs.opencv.org/3.4/d5/d6f/tutorial_feature_flann_matcher.html

[3] MPEG-7 Shape dataset: http://www.dabi.temple.edu/~shape/MPEG7/dataset.html

[4] https://wdrfree.com/stock-vector/download/beans-legumes-set-vector-illustration-397505954