Question

a) Briefly describe the two forms of quantization used in image processing 2 marks b) Consider the 1D image fragment below. Give the pixel values after filtering with () 1x3 mean filter (ii) 1x3 median filter. State how you handled the image boundaries and propose one alternative. Give one strength and one weakness for each of the filters 4 marks 210 210 90 90 210 210 c) Draw a rough sketch of what the image histogram for the image of the coins below might look like. 2 marks d) In question 4b how might the histogram be used to segment just the coins? What is this technique known as? 3 marks

Answer 1

Given 1-D Image                              = [210 210 90 90 210 210]

1. 1x3 Mean Filter Output = Pi = (P(i-1) + P(i) + P(i+1) / 3

                  Therefore, Padding the 1-D Input Image with zeros =

                  [0        210,                     210,                    90,                   90,                     210,                      210         0      ]

                  [    (0+210+210)/3, (210+210+90)/3, (210+90+90)/3, (90+90+210)/3, (90+210+210)/3, (210+210+0)/3]

[         140                       170                       130                   170]                  170                        140    ]

2. 1x3 median filter = Median of 3 Pixels

Therefore, Padding the 1-D Input Image with zeros =

                                                         [[0        210,                     210,                    90,                   90,                     210,                      210         0      ]

1x3 Median Filter Image = [(0, 210, 210), (210, 210, 90),     210, 90, 90),     (90, 90, 210),     (90, 210, 210),       (210, 210, 0) ]

                                        = [      210,                   210,                    90,                   90,                   210,                         210]

(iii)

Image boundaries are points where there is sharp change in pixel intensities. Therefore, the image boundaries exists at points (210, 90) and (90, 210) pixel intensity pairs.

Image Histogram is defined as the graph between Gray color intensity and corresponding no. of pixels. The image histogram is basically probability distribution function (PDF). Image histogram provides color profile of the image.

Below is the matlab code for extracting the image histogram:

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close all,
clear all,
clc,

ProjectPath = pwd;
ImagePath = strcat(ProjectPath,'\Coin.jpg');
Orig = imread(ImagePath);
GrayImg = rgb2gray(Orig);
subplot(2,1,1); imshow(Gray); title('Original Input Image');
subplot(2,2,2); imhist(GrayImg); title('Histogram');
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Histogram Original Input Image 4000 3500 3000 2500 2000 1500 1000 500 250 200 150 100