Two-week ISTE workshop on Effective teaching/learning of computer programming Dr Deepak B Phatak Subrao Nilekani Chair Professor Department of CSE, Kanwal Rekhi Building IIT Bombay Lectures 11, Matrices -examples Saturday 3 July 2010 [Several slides courtesy Anirudha Jathar and Wikipedia]

Overview  A quiz  Handling images Representation of digital images Histogram Contrast enhancement  Example program to calculate histogram of a small digital image

A quiz Q. Currently, what activity do you propose to carry out within two weeks of the workshop conclusion, for the mandatory submission A. Design questions and answers for examinations B. Design quiz questions and answers C. Add lecture slides with examples D. Something different

Digital images  Digital images are a collection of pixel values  These are arranged in an array (W x H)  Each pixel value can be represented by 1 bit (m : mono colour, e.g. black and white) 8 bits (g : gray scale 0 – black to 255 – white) 24 bits (c: Red, Blue, Green, each one byte)  One can have 16 million colours! Capacity of a human eye is limited to a small range from 200 to 2000 colours

Digital images...  While storing information about an image in a file, we mainly need values of Width, Height, the type of colours present, and values for each pixel  Images such as black and white fingerprints have small size (500 x 300)  For large images, compression is mandatory to keep the file size within limits 12 M pixel camera can produce 36 M bytes image  Compression can be either lossy or lossless  Several file formats have evolved raw, png, bmp, tiff, giff, jpeg, xmp  Refer to wikipedia (Image_file_formats)

Images and histograms  Pixel values of digital images can be read in a matrix for further processing  Each picture point (pixel) has an associated “tonal” value For grayscale images, the value range is : Black, 255: White  Thus each element of such an image matrix would contain a value which can be of the type/size short int or char (1 byte)  Histogram indicates how many pixels in an image have the same value

A sample image 8 pixel x 8 pixel

Pixel values in the sample image

Histogram values Val n Val n Val n Val n Val n

Cumulative Distribution Function (cdf) V c V c V c V c V c

Histogram equalization  The histogram equalization formula  “Equalization” formula for example image

Histogram equalization …  For example, the cdf of 78 is 46

Pixel values after histogram equalization

Enhancement of Contrast

Original Picture for comparison

Another grayscale picture

Histogram and cdf

“Equalized” histogram and cdf

Picture with enhanced contrast

Original picture for comparison

Program to calculate histogram #include using namespace std; int main(){ int i, j, npix; int image[500][500], histogram[256]; /* we assume that the image data is contained in a text file "image.txt“ in a suitable format Also, we will use command line redirection to read data from this file */

Histogram … cin >> npix; // number of pixels //read image pixel values in the matrix for(i=0; i< npix; i++){ for(j=0; j < npix; j++){ cin >> image[i][j]; cout << image[i][j] << " "; } cout << "\n"; }

Histogram … // set histogram counts to zero // for(i=0 ; i< 256; i++) histogram[i] = 0; // Calculate histogram values for(i=0; i< npix; i++){ for (j = 0; j < npix; j++){ // based on the value of the pixel // increment the corresponding count // in the histogram array histogram[image[i][j]]++; }

Histogram … // print the histogram at non zero values cout << "Histogram at non zero values is:”; cout << "\n"; for (i=0; i<256; i++){ if (histogram[i] !=0) { cout << i << " " << histogram[i] << "\n"; }

Histogram … // find the maximum value in the histogram int imax, max = 0; for (i=0; i<256; i++){ if (histogram[i] > max) max = histogram[i]; } cout << "Maximum histogram value " << max cout << “ occurs at:” << "\n"; // Print the grey levels at which max value occurs for(i=0; i<256; i++){ if (histogram[i]== max) cout << i << " "; } return 0; }

Image of a finger print

THANK YOU

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