Histogram equalization

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
of 28

Please download to get full document.

View again

Basis beeldverwerking (8D040) dr. Andrea Fuster Prof.dr . Bart ter Haar Romeny Prof.dr.ir . Marcel Breeuwer dr. Anna Vilanova. Histogram equalization. Contact. d r. Andrea Fuster – A.Fuster@tue.nl Mathematical image analysis at W&I and Biomedical image analysis at BMT
Basis beeldverwerking (8D040)dr. Andrea FusterProf.dr. Bart terHaarRomenyProf.dr.ir. Marcel Breeuwerdr. Anna VilanovaHistogram equalizationContactdr. Andrea Fuster – A.Fuster@tue.nlMathematical image analysis at W&I and Biomedical image analysis at BMT HG 8.84 / GEM-Z 3.108Today
  • Definition of histogram
  • Examples
  • Histogram features
  • Histogram equalization:
  • Continuous case
  • Discrete case
  • Examples
  • Histogram definition
  • Histogram is a discrete function h(rk) = N(rk), where
  • rkis the k-th intensity value, and
  • N(rk)is the number of pixels with intensity rk
  • Histogram normalization by dividing N(rk)by the number of pixels in the image (MN)
  • Normalization turns histogram into a probability distribution function
  • HistogramMN: total number of pixels (image of dimensions MxN) rkWhat do the histograms of these images look like?Bimodal histogramTri- (or more) modal histogramExample histogramsMore examples histogramsMore examples histogramsHistogram Features
  • Mean
  • Variance
  • Mean: image mean intensity, measure of brightnessVariance: measure of contrastQuestions?Any questions so far?Histogram processing Histogram processing Histogram equalizationIdea: spread the intensity values to cover the whole gray scale Result: improved/increased contrast!☺Histogram equalization – cont. caseAssume ris the intensity in an image with L levels:Histogram equalisation is a mapping of the formwith r the input gray value and s the resulting or mapped valueHistogram equalization – cont. case
  • Assumptions / conditions:
  • ① is monotonically increasing function in
  • Make sure output range equal to input range
  • Histogram equalization – cont. caseMonotonically increasing function T(r)Histogram equalization – cont. case
  • Consider a candidate function for T(r) – conditions
  • ① and ② satisfied?
  • Cumulative distribution function (CDF)
  • Probability density function (PDF) p is always non-negative
  • This means the cumulative probability function is monotonically increasing, ① ok!
  • Histogram equalization – cont. caseSo ② ok!Does the CDF fit the second assumption?To have the same intensity range as the input image, scale with (L-1)Histogram equalization – cont. caseWhat happens when we apply the transformation function T(r) to the intensity values? – how does the histogram change? Histogram equalization – cont. caseWhat is the resulting probability distribution?From probability theoryHistogram equalization – cont. caseUniform:What does this mean?Histogram equalization – disc. caseSpreads the intensity values to cover the whole gray scale (improved/increased contrast)Fully automatic method, very easy to implement:Histogram equalization – disc. caseNotice something??Demo of equalization in MathematicaOriginal imageOriginal histogramTransformation function T(r)“Equalised” image“Equalised” histogramEnd of part 1 And now we deserve a break!
    Related Search
    We Need Your Support
    Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

    Thanks to everyone for your continued support.

    No, Thanks

    We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

    More details...

    Sign Now!

    We are very appreciated for your Prompt Action!