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# CS 4476/6476: PS4 solved

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## Color Quantization with K-Means (25 points)

For this problem you will write code to quantize an image using k-means clustering and experiment with
two different color spaces — RGB and HSV.
Complete the functions defined below in quantization_student.py. Use Qunatization-Student.ipynb
to run your implemented functions and generate quantized images with 3, 5 and 10 clusters. Put these images
1. (5 points) Given an RGB image, quantize 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. Use the following form:
[outputImg, clusterCenterColors] = quantizeRGB(origImg, k)

where origImg and outputImg are MxNx3 matrices of type uint8, k specifies the number of colors to
quantize to, and clusterCenterColors is a k x 3 array of the k centers. (You can use the Scikit-Learn
implementation of the k-means algorithm for this question.)
2. (5 points) Given an RGB image, convert it to HSV, and quantize the 1-dimensional Hue space. Map
each pixel in the input image to its nearest quantized Hue value, while keeping its Saturation and
Value channels the same as the input. Convert the quantized output back to RGB color space. Use
the following form:

[outputImg, clusterCenterHues] = quantizeHSV(origImg, k)
where origImg and outputImg are MxNx3 matrices of type uint8, k specifies the number of clusters, and clusterCenterHues is a k x 1 vector of the hue centers. (You can use the Scikit-Learn
implementation of the k-means algorithm for this question.)
3. (3 points) Write a function to compute the SSD error (sum of squared error) between the original RGB
pixel values and the quantized values, with the following form:
[error] = computeQuantizationError(origImg, quantizedImg)
where origImg and quantizedImg are both RGB images, and error is a scalar giving the total SSD
error across the image. Write down the logarithmic error (base e) for all the generated RGB and HSV
images (3, 5 and 10 clusters) in your report. Note: The function should not return logarithmic error.

sentences of fairly high-level explanations.
(a) How do the results vary with the number of quantization bins?
(b) How are the qualitative results between RGB and HSV color spaces different? How would you
explain this difference?
(c) Name and explain 2 metrics (apart from SSD) used for comparing the generated/modified image(here the modified image is the quantized image) with the original one.
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## 3 Hough Transform on generated images (50 points)

Detecting Traffic Signs and Lights
Learning Objectives
— Use Hough tools to search and find lines and circles in an image.
— Use the results from the Hough algorithms to identify basic shapes.
— Understand how objects can be selected based on their pixel locations and properties.
— Address the presence of distortion and noise in an image.
— Identify what challenges real-world images present over simulated scenes.

## Note:

For all sub-parts in this section, be sure to include the images generated in the IPython notebooks
in the corresponding sections in your report.
how the car would process traffic rules. That is, you are tasked with detection of both traffic lights and
traffic signs. Your job is to design and implement a program that would solve both the objectives.
1. Traffic Light [15 points]:
First off, you are given a generic traffic light to detect from a scene. For the sake of the problem,
assume that traffic lights are shown as below: (with red, yellow, and green) lights that are vertically
stacked. You may also assume that there is no occlusion of the traffic light.
Figure 1: Image of generic traffic light (Left: In order – red, yellow, green light is ON )
It is your goal to find a way to determine the state of each traffic light and position in a scene. Position
is measured from the center of the traffic light. Given that this image presents symmetry, the position
of the traffic light matches the center of the yellow circle.

Complete your python notebook.ipynb such that traffic_light_detection returns the traffic light
center coordinates (x, y) i.e. (col, row) and the color of the light that is activated (‘red’, ‘yellow’, or
‘green’). Read the function description for more details.
Testing:
A traffic light scene that we will test will be randomly generated, like in the following pictures and
examples in the github repo.
Functional assumptions:
For the sake of simplicity, we are using a basic color scheme, but assume that the scene may have
different color objects and backgrounds [relevant for part 2 and 3]. The shape of the traffic light will
not change, nor will the size of the individual lights relative to the traffic light. Size range of the lights
can be reasonably expected to be between 10-30 pixels in radius. There will only be one traffic light
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Figure 2: Example of generated scene
per scene, but its size and location will be generated at random (that is, a traffic light could appear in
the sky or in the road — no assumptions should be made as to its logical position). While the traffic
light will not be occluded, the objects in the background may be.
Deliverables:
(a) Code:

2. Traffic Signs one per scene [25 points]
Now that you have detected a basic traffic light, see if you can detect road signs. Below are five common
road signs that you would see in the United States. Implement a way to recognize these signs:
Figure 3: Traffic Signs
Similar to the traffic light, you are tasked with detecting the sign in a scene and finding the (x, y) i.e
(col, row) coordinates that represent the polygon’s centroid.
Functional assumptions:
Like above, assume that the scene may have different color objects and backgrounds. The size and
location of the traffic sign will be generated at random. While the traffic signs will not be occluded,
objects in the background may be.

## Deliverables:

(a) Code:
Complete the following functions. Read their documentation in notebook.ipynb for more details.
— yield_sign_detection(img_in)
— stop_sign_detection(img_in)
— warning_sign_detection(img_in)
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— construction_sign_detection(img_in)
— do_not_enter_sign_detection(img_in)
3. Multiple signs in a scene [10 points]
The next task is to detect multiple traffic signs and the traffic light in one scene. Find where each sign
is in the scene, Fig. 4 is a randomly generated example:
Figure 4: Generated Scene with Signs

## Functional assumptions:

Like above, assume that the scene may have different color objects and backgrounds. There will be
n instances of each sign and/or traffic light, where n is 0 or 1. The size and location of each will be
generated at random. While the traffic signs will not be occluded, objects in the background may be.
Deliverables:
(a) Code:
Complete traffic_sign_detection(img_in).

## 4 Extra Credit (15 + 10 points)4.1 Hough Transform on Real Images with known radius (10 points code + 5

points report
Let’s try your code using real world images. Implement 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 and the
Hough space used for finding the centers. Include a function with the following form:

where im is the input image, radius specifies the size of circle we are looking for, and useGradient is a
flag that allows the user to optionally exploit the gradient direction measured at the edge points.
The output centers is an N x 2 matrix in which each row lists the (x,y) position of a detected circle’s
center and hough_space is a NumPy array (height x width matrix) of Hough accumulator array (height and
width from the image). Save this function in a file called detectCircles.py.
In Circle Hough Transform, circle candidates are produces by voting in the parameters space and then
finding local maxima in the space. This can be done using techniques like Thresholding, Non-Maximum
Suppression and Mean Shift.
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Experiment with thresholding as a post-processing technique to determine circle parameters from the
accumulator array. In your report include images of the selected circles along with the corresponding Hough
Space for low (≤ 0.4), mid-range (≈0.7) and high (≥ 0.95) thresholds. Explain how your results vary with
increasing thresholds and why that may be the case.

## 4.2 Hough Transform on Real Image with unknown radii (10 points)

Extend your Hough circle detector implementation to detect circles of any radius. Optimize your code for the
image jupiter.jpg. You would be awarded points proportional to the number of circles detected. Detecting
all of the circles gives you the maximum credit. Be sure to include the results generated by the notebook in