IMAGE ANALYSIS CHAPTER 6 Histogram Manipulation A Dermanis

IMAGE ANALYSIS CHAPTER 6 Histogram Manipulation A. Dermanis

The image histogram x = 1, 2, …, 2 p-1 Pixel values for a p-bit digital image: x = 1, 2, …, 255 (e. g. p = 8, 8 -bit) x=0 Frequency of value x : fx = nx N = preserved as “no data” code no of pixels having the value x total number of image pixels Image histogram: A. Dermanis

The image histogram x Number of pixels having value x : Nx = Cumulative frequency of value x : Fx = Image cumulative histogram: Fx Nx N = n z =1 z no of pixels having the value x total number of image pixels 1 x 0 1 128 255 A. Dermanis

Histogram Equalization Image with optimal contrast: all values of gray equally present Corresponding histogram f (x) : f (x) = constant = 1 2 p-1 p = 8 (8 -bit): f (x) = 1 255 homogeneous histogram ! Corresponding cumulative histogram F (x) : F (x) = x 2 p-1 p = 8 (8 -bit): F (x) = x 255 A. Dermanis

Histogram Equalization Contrast Enhancement: Transformation of histogram to homogeneous one Continuous case: homogeneous cumulative histogram original cumulative histogram Each pixel value x is replaced with a new value x such that F(x) = F (x ) Corresponding realistic discrete case A. Dermanis

Histogram Equalization Problems appearing in discrete histogram equalization: no values are mapped into some particular values of the new equalized histogram Different values are mapped into the same value A. Dermanis

Histogram Equalization Original image and histogram Resulting image and histogram Note departure from ideal homogeneous histogram ! A. Dermanis

Histogram matching Modifying an image so that its histogram F(x) is transformed into a prescribed histogram F (x ) (usually that of another image – Result: images of similar contrast) “target” cumulative histogram original cumulative histogram Each pixel value x is replaced with a new value x such that F(x) = F (x ) Same as histogram equalization with homogeneous histogram replaced by a given histogram A. Dermanis

Histogram matching The original image and its histogram The resulting image and its histogram The target image and its histogram Note that histograms are not exactly identical A. Dermanis

Linear streching Original image with pixel values limited to an interval xmin x xmax Application of a linear transformation x x = Ax + B A & B values, selected so that xmin 1 & xmax L x = (xmax – x) + L (x – xmin) xmax – xmin Resulting image with pixel values covering all possible values 0 x L A. Dermanis

Linear streching Original 3 bands of a Landsat TM image The same 3 bands after linear stretching of their histograms A. Dermanis

Saturated linear streching Linear transformation with (a > xmin) 1 and (b < xmax) L instead of xmin 1 and xmax L Saturation: (values 1 x < a) 1 (values b < x L) L A. Dermanis

Saturated linear streching Use of saturated linear stretching for the enhancement of particular features: Boat identification Original Resulting Bathymetry determination Original Resulting A. Dermanis