Image Processing Math Prob1 1h285u

IMAGE PROCESSING MATHEMATICAL PROBLEM 3/8/17

Koushik Dutta

Department of Computer Science Asutosh College, Kolkata 1

[email protected]

MATHEMATICAL PROBLEM 3/8/17

1. What is the storage requirement for a 1024x1024 binary image and for a 1024x1024 colour image? 2. An image is 2400 pixels high. The image was scanned at 300 dpi. What is the physical size of the image? 3. A medical image has a size of 8 x 8 inches. The sampling resolution is 5 cycles/mm. How many pixels are required? Will an image of size 256 x 256 be enough?  1 2

 4. Assume an image F   5 4  what is the output? 

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 2 2  1 2  . If the threshold value is  2 1  , Assume an image F     5 4 what is the output? 

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MATHEMATICAL PROBLEM

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Let V={0,1}. Compute the De D4 D8 and Dm distances between two pixels p and q. Let the pixel coordinates of p and q be (3,0) and (2,3) respectively.

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MATHEMATICAL PROBLEM Consider the following adjacent regions 3/8/17

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What is the connectivity between these two regions?

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MATHEMATICAL PROBLEM Consider the following image of uint8 type. 3/8/17

 10 40 30    F1   40 100 90   90 80 70   

 40 140 90    F2   140 100 90   90 80 190   

Perform the image addition, multiplication and division operations. Suppose the image is changed to type uint16, will the results change? Also perform image subtraction and image difference? Is there any difference between them?

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MATHEMATICAL PROBLEM Consider the following logical images: 3/8/17

 0 1 0   F1   1 1 1   0 0 0  

 0 1 0   F2   1 1 0   0 0 0  

Perform the logical operations AND, OR, XOR and NAND. Suppose the second row of the image F1 is to be highlighted, what is the mask that is needed?

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MATHEMATICAL PROBLEM 3/8/17

Consider an image point [2,2]. Perform the following operations and show the results of these transforms. 1. Translate the image right by 3 units. 2. Perform a scaling operation in both X-axis and Y-axis by 3 units. 3. Rotate the image in X-axis by 45o . 4. Perform horizontal skewing by 45o . 5. Perform mirroring about X-axis. 6. Perform shear in y-direction by 30 units.

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MATHEMATICAL PROBLEM

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Consider the following binary image. Show the result of Dilation and Erosion operations.

Let the structured element S be [1 1] with coordinates {(0,0), (0,1)}. Show the results of dilation and erosion. 8

MATHEMATICAL PROBLEM  2 1  F    3 1

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1. Consider the image . Apply replication and interpolation techniques and obtain the result. 2.

 2 2   . Calculate mean and entropy of F  Consider the image 3 2  

the image.

3. Find the convolution and correlation of the following stream of data: a) { 1 7 9 6 } and { 1 3 5 } b) { 1 2 3 4 } and { 1 1 }

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MATHEMATICAL PROBLEM

(a)

 7 3 3   F   2 2 2  2 2 1  

(b)

 7 2 3   F   2 2 1  2 1 1  

and

1 1  I    1  1

and

 1 1  I    1 1

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Find the convolution and correlation of the following stream of data:

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MATHEMATICAL PROBLEM 1. A triangle is marked by the points (1,1), (5,5) and (10,10)

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a) Apply translation of δx = 3 and δy = 4 b) Apply rotation with degrees 45, 90, 180 and 270. Consider the image  130 11 67    F   10 10 50   80 90 100    What is the mean, median, mode, IQR, Standard deviation and variance of the image?

3. Consider the following symbol and its probability. Symbols

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What is the image entropy?

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MATHEMATICAL PROBLEM Given a 3-bit 8-level image of size 8x8 pixels. 7

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MATHEMATICAL PROBLEM 3/8/17

1) Draw the histogram of gray level values. 2) Is it possible to find any threshold value for binarization of the image from the histogram. 3) Apply histogram equalization method on this image. 4) Draw the equalized image. 5) Again draw the histogram of the equalized image. 6) Binarize the equalized image using the threshold obtained from the histogram.

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