SCCS 4761 Point Processing Basic Image Processing Operations Arithmetic Operations Histograms

SCCS 4762 Basic Image Processing Operations Transforms –process entire image as one large block Neighborhood processing –process the pixel in a small neighborhood of pixels around the given pixel. Point operations –process according to the pixel’s value alone (single pixel). Image-Processing operations may be divided into 3 classes based on information required to perform the transformation.

SCCS 4763 Schema of Image Processing Image Transformed Image Transform Output Image Inverse Transform Processed Transformed Image Image-processing operation

SCCS 4764 Arithmetic Operations Addition Subtraction Multiplication Division Complement

SCCS 4765 Arithmetic Operations (cont) Addition: y = x + c Subtraction: y = x - c Multiplication: y = cx Division: y = x/c Complement: y= x Let x is the old gray value, y is the new gray value, c is a positive constant.

SCCS 4766 Arithmetic Operations (cont) Addition: y = x + c Subtraction: y = x - c Multiplication: y = cx Division: y = x/c Complement: y= x To ensure that the results are integers in the range [0, 255], the following operations should be performed Rounding the result to obtain an integer Clipping the result by setting y = 255 if y > 255 y = 0 if y < 0

SCCS 4767 Arithmetic Operations (cont) MATLAB functions –Addition: imadd(x,y) Add two images or add constant to image –Subtraction: imsubstract(x,y) Subtract two images or subtract constant to image –Multiplication: immultiply(x,y) Multiply two images or multiply image by constant –Division: imdivide(x,y) Divide two images or divide image by constant –Complement: imcomplement(x)

SCCS 4768 Addition & Subtraction Lighten/darken the image Some details may be lost MATLAB: –commands: x = imread(‘filename.ext’); y = uint8(double(x) + c); or y = uint8(double(x) - c); –function: x = imread(‘filename.ext’); y = imadd(x, c); or y = imsubtract(x, c);

SCCS 4769 Ex: Addition & Subtraction Added by 128 Subtracted by 128 Draw graphs of the transformation functions !!!

SCCS Multiplication & Division Lighten/darken the image Some details may be lost (but less than addition/subtraction) MATLAB: –commands: x = imread(‘filename.ext’); y = uint8(double(x)*c); or y = uint8(double(x)/c); –functions: x = imread(‘filename.ext’); y = immultiply(x, c); or y = imdivide(x, c);

SCCS Ex: Multiplication & Division Multiplied by 2 Divided by 2 Draw graphs of the transformation functions !!!

SCCS Comparison: Addition VS Multiplication

SCCS Comparison: Subtraction VS Division

SCCS Complement Create the negative image MATLAB: –commands: x = imread(‘filename.ext’); y = uint8(255 - double(x)); –function: x = imread(‘filename.ext’); y = imcomplement(x);

SCCS Ex: Complement Draw a graph of the transformation function !!!

SCCS Histogram Graph showing the number of pixels for each intensity Normalized histogram: histogram where the number of pixel is divided by the total number of pixel so the range is [0,1] Cumulative histogram: histogram which shows the number of pixels whose intensity is less or equal to each intensity.

SCCS Histogram Example >> p = imread(‘pout.tif’) >> inshow(p) >> figure;imhist(p)

SCCS What Histogram Describes? Brightness –dark image has gray levels (histogram) clutered at the lower end. –bright image has gray levels (histogram) clutered at the higher end. Contrast –well contrasted image has gray levels (histogram) spread out over much of the range. –low contrasted image has gray levels (histogram) clutered in the center.

SCCS Contrast Enhancement by Spreading Out Histogram Histogram Stretching (Contrast Stretching) Histogram Equalization

SCCS Histogram Stretching 0 max I I #pixel IminImax

SCCS Steps of Histogram/Contrast Stretching Create the histogram of the image Gray level ( i ) No. of gray value ( n i ) 0…………………………………………….15 1…………………………………………….. 0 2…………………………………………….. 0 3……………………………………………..0 4…………………………………………….. 0 5…………………………………………….70 6……………………………………………110 7…………………………………………….45 8……………………………………………70 9…………………………………………….35 10……………………………………… ………………………………………… ………………………………………… …………………………………………… 0 14…………………………………………… 0 15………………………………………….. 15 Draw the histogram.

SCCS Steps of Histogram/Contrast Stretching (cont) From the histogram, stretch out the gray levels in the center of the range by applying the piecewise linear function –Ex: [5,9]  [2,14] – y = [(14 – 2)/(9 – 5)](x – 5) + 2, Draw a graph of transformation Gray levels outside this range are either left as original values or transforming according to the linear function at the ends of the graph. xy

SCCS Steps of Histogram/Contrast Stretching (cont) Change the old gray values to the new gray values by using the piecewise linear function from the previous step as a mapping function. Create the histogram from the new image

SCCS Histogram Stretching: Example originaloutput

SCCS Histogram before/after Adjustment Before After

SCCS Histogram Mapping: Piecewise Linear I #pixel IminImax I #pixel IminImax Mapping function: Ix1 Ix2 Iy1 Iy2

SCCS MATLAB: Histogram/Contrast Stretching Command: imadjust Syntax: imadjust(x, [ a,b], [c,d]); imadjust(x, [ a,b], [c,d],  ); –convert intensity x  a to c –convert intensity x  b to d –values of a,b,c,d must be between 0 and 1 –  : positive constant (describe the shape of the function, 1 concave upward)

SCCS Transformation Function with Gamma (Power –Law Transformation) Brighten image Linear mapping Darken image

SCCS Example of Adjusting by the Power- Law Transformation Original Adjust by using Gamma = 0.5

SCCS MATLAB: Piecewise Linear A MATLAB function for applying a piecewise linear-stretching function (see Figure 4.15) Command: find Syntax: find(condition) Ex pix = find(im >= a(i) & im < a(i+1)); pix holds the index for members in im having intensity between a(i) and a(i+1) include a(i).

SCCS Histogram Equalization The trouble with the methods of histogram stretching is that they require user input. Histogram equalization is an entirely automatic procedure. Idea: Each gray level in the image occurs with the same frequency. Give the output image with uniform intensity distribution.

SCCS Histogram Equalization (cont) Mapping function: where p(i) is the PDF of the intensity level i, obtained from cumulative histogram.

SCCS Histogram Equalization: Procedure Example: Suppose a 4-bit grayscale image has the histogram associated with a table of the numbers n i of gray values. (page 78)

SCCS Histogram Equalization: Example BEFOREAFTER

SCCS MATLAB: Histogram Equalization Command: histeq Syntax: histeq(image, target_hist) histeq(image, #bin) histeq(indexed_im, #bin, target_hist) histeq(indexed_im, map, #bin) Default: #bin = 64 Output: output_im, [output_im, transform], new_map, [new_map, transform]

SCCS Lookup Tables Improve the performance of point processing Why? –one intensity is always mapped to the same value –reduce the computing time Lookup table: array Input intensity: index in the array Output intensity: value of the member

SCCS Ex: Lookup Table (1) Function: output = input/2; MATLAB >> T = uint8(floor(0:255)/2); >> output = T(input);

SCCS Ex: Lookup Table in MATLAB (2) Function: MATLAB >> T1 = *[0:95]; >> T2 = 2*[96:160] – 128; >> T3 = *[161:255] ; >> T = uint8(floor([T1 T2 T3]));