Image Enhancement

References Gonzalez and Woods, “ Digital Image Processing,” 2nd Edition, Prentice Hall, 2002. Jahne, “Digital Image Processing,” 5th Edition, Springer 2002. Jain, “Fundamentals of Digital Image Processing,” Prentice Hall 1989 9/19/2018

Overview Human perception (focus of this discussion) Machine perception (ocr) Application specific Heuristic based: result better than the original image – subjective assessment Spatial vs frequency domain 9/19/2018

Spatial Domain Based on the collection of pixels in the image Enhancement techniques will yield Noise reduction Neighborhood smoothing Highlighting of desired feature 9/19/2018

Spatial Domain – Math Framework From [1] Typically, spatial domain based enhancement involves: g(x,y) = T [f(x,y)], where f = input image; g = output image; T = operator defined on f based on a neighborhood of x,y. If the neighborhood is 1x1 pixel, then the output intensity is dependent on the current intensity value of the pixel, and can be represented as s = T( r ) where r and s are gray level values of f(x,y) and g(x,y) at location x,y. In such situations T is a gray-level transformation function. 9/19/2018

Examples of Gray level Transformation Functions (Point Processing) From [1] Contrast Stretching Best if input is 0 outside a range of values. Thresholding: Result is a binary Image 9/19/2018

Larger Neighborhoods Objective – determine g(x,y) based on input intensity (gray level) values f(x,y) in the neighborhood of x,y. Mask processing or filtering Each of the elements in the neighborhood has an associated weight g(x,y) depends on f(a,b)|a,b є N(x,y) 9/19/2018

Basic Gray Level Transformations Light From [1] Dark Dark Light 9/19/2018

Image Negatives From [1] In this example, using the image negative, it is easier to analyze the breast tissue. 9/19/2018

Log transformations s = c log (1 + r) r >= 0; hence 1 + r > 0; log 0 = ? Log transformations are useful, when there is a large dynamic range for the input variable ( r ). From [1] 9/19/2018 Range: 0 to 1.5*106 Range: 0 to 6.2

Power law transformation From [1] Stretch higher (lighter) gray levels Many display devices (e.g. CRT) respond like the power law, i.e intensity – voltage relationship is power law based gamma 1.8 to 2.5. The display will tend to produce images darker than intended. So the display is distorted. Gamma correction is used to correct for this distortion. Stretch lower (ldarker) gray levels 9/19/2018

Display distortion correction Gamma correction can also fix the distortions in color. More important with the internet. Many viewers, variety of monitors. Gamma of view station is not known. Preprocess using an average gamma. From [1] 9/19/2018

Power law – contrast manipulation (c) better than (b). (d) Background is better than (c) but washed out effect. From [1] 9/19/2018

Piece-wise Linear Transformation Contrast Stretching From [1] Mean gray level value of the image 9/19/2018

Gray level Slicing From [1] 9/19/2018

Bit plane Slicing MSb (bit 7) From [1] 9/19/2018 LSb (bit 0)

Histograms Histogram - frequency of occurrence of a gray level value Normalizing histograms with rest to the total number of pixels converts these into probability density like function Histogram processing yields robust image processing results Histograms are NOT unique 9/19/2018

Histograms for 4 images From [1] For high contrast, it is best to have a larger range of gray level values. If we could transform an image with a resulting change in histogram, then that may yield more contrast. We need to study the rules for transforming histograms, and study the resulting impact on images. 9/19/2018 From [1]

Transformation From [1] s s1 r r s1 s Applying transformations to histograms, can use results from probability. Consider the transformation S = T( r ); 0 <= r <=1 which has the following properties: T( r ) is single-valued and monotonically increasing in [0,1] 0 <= T( r ) <= 1 for r in [0,1] Single valued condition ensures that an inverse transformation exists, and the monotonic condition ensures the increasing order of the pixels from black to white. (a) and (b) do not ensure that the inverse transform is single valued. s1 r r s1 s 9/19/2018

Histogram Equalization 9/19/2018 From [1]

Transformation Functions From [1] 9/19/2018

Mapping for Histogram Specification From [1] 9/19/2018

Example of Histogram Specification From [1] 9/19/2018

Continued From [1] 9/19/2018

Localized Histogram Equalization From [1] 9/19/2018

From [1] 9/19/2018

Histogram Stats From [1] 9/19/2018