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![Gholamreza Anbarjafari, PhD
Video Lecturers on Digital Image Processing
Histogram Processing
Histogram : is the discrete function h(rk)=nk , where rk is the kth
gray level in the range of [0, L-1] and nk is the number of pixels
having gray level rk.
Normalized histogram : is p(rk)=nk/n, for k=0,1,…,L-1 and p(rk)
can be considered to give an estimate of the probability of
occurrence of ray level rk.](https://image.slidesharecdn.com/vidlecture06fin-220414192808/85/DIGITAL-IMAGE-PROCESSING-2-320.jpg)
DIGITAL IMAGE PROCESSING
- 1. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Digital Image Processing Contrast Enhancement: Part II
- 2. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Histogram Processing Histogram : is the discrete function h(rk)=nk , where rk is the kth gray level in the range of [0, L-1] and nk is the number of pixels having gray level rk. Normalized histogram : is p(rk)=nk/n, for k=0,1,…,L-1 and p(rk) can be considered to give an estimate of the probability of occurrence of ray level rk.
- 3. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Histogram Equalization Histogram equalization : is a method which increases the dynamic range of the gray-levels in a low-contrast image to cover full range of gray-levels. How-to-Do: is achieved by having a transformation function which is the Cumulative Distribution Function (CDF) of a given PDF of gray-levels in a given image.
- 4. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Histogram Equalization Histogram equalization : the new intensity value of pixel x is calculated by: min round 1 1 min cdf x cdf I x L cdf
- 5. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Histogram Equalization Histogram equalization : the probability function of the output levels is uniform. Note : the transformation function is simply the CDF.
- 6. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Histogram Equalization 0 2 4 6 8 10 12 14 16 x 10 4 0 50 100 150 200 250 0 2 4 6 8 10 12 14 16 x 10 4 0 50 100 150 200 250 Histogram Equalization
- 7. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Histogram Equalization (a) A face image from the CALTECH face database, (b) its histogram, (c) the equalized face image using HE, (d) and its respective histogram.
- 8. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Singular Value Equalization Singular value decomposition : any matrix, A, can be written as multiplication of two orthogonal square matrices, U and V, and a matrix containing the sorted singular values on its main diagonal, Σ. A=UΣVT
- 9. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Singular Value Equalization Note : as σ1 is much bigger than other σs then changing it will affect on the reconstructed image, i.e. changing σ1 will directly change the luminance of the image.
- 10. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Singular Value Equalization G(0.5, 1) : is a synthetic intensity matrix whose pixel values have Gaussian distribution with mean of 0.5 and variance of 1 with the same size of the original image. ξ: is ratio of the largest singular value of the generated normalized matrix over a normalized image. 0.5, 1 max max G A
- 11. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Singular Value Equalization Im T A A A Equalized age U V
- 12. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Singular Value Equalization Low contrast Histogram equalization Singular value equalization
- 13. Gholamreza Anbarjafari, PhD VideoLecturers on Digital Image Processing Summary •We have looked at: – How histogram equalization works. – What is SVD? – How SVE works •Next time we will continue our talk about image enhancement in spatial domain