The local contrast at an image point denotes the (relative) difference between the intensity of the point and the intensity of its neighborhood



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The local contrast at an image point denotes the (relative) difference between the intensity of the point and the intensity of its neighborhood:

  • The local contrast at an image point denotes the (relative) difference between the intensity of the point and the intensity of its neighborhood:



The contrast definition of the entire image is ambiguous

  • The contrast definition of the entire image is ambiguous

  • In general it is said that the image contrast is high if the image gray-levels fill the entire range



How can we maximize the image contrast using the above operation?

  • How can we maximize the image contrast using the above operation?

  • Problems:

    • Global (non-adaptive) operation.
    • Outlier sensitive.


H(k) specifies the # of pixels with gray-value k

  • H(k) specifies the # of pixels with gray-value k

  • Let N be the number of pixels:

  • P(k) = H(k)/N defines the normalized histogram

  • defines the accumulated histogram





The image histogram does not fully represent the image

  • The image histogram does not fully represent the image





The image mean:

  • The image mean:

  • Generally:

  • The image s.t.d. :



The image entropy specifies the uncertainty in the image values.

  • The image entropy specifies the uncertainty in the image values.

  • Measures the averaged amount of information required to encode the image values.



An infrequent event provides more information than a frequent event

  • An infrequent event provides more information than a frequent event

  • Entropy is a measure of histogram dispersion



In many cases histograms are needed for local areas in an image

  • In many cases histograms are needed for local areas in an image

  • Examples:

    • Pattern detection
    • adaptive enhancement
    • adaptive thresholding
    • tracking


Integral histogram: H(x,y) represent the histogram of a window whose right-bottom corner is (x,y)

  • Integral histogram: H(x,y) represent the histogram of a window whose right-bottom corner is (x,y)

  • Construct by can order:

  • H(x,y)= H(x,y-1)+H(x-1,y) – H(x-1,y-1)



Using integral histogram we can calculate local histograms of any window H(x1:x2,y1:y2)

  • Using integral histogram we can calculate local histograms of any window H(x1:x2,y1:y2)



Digitizing parameters

  • Digitizing parameters

  • Measuring image properties:

    • Average
    • Variance
    • Entropy
    • Contrast
    • Area (for a given gray-level range)
  • Threshold selection

  • Image distance

  • Image Enhancement

    • Histogram equalization
    • Histogram stretching
    • Histogram matching


In some optical equipment (e.g. slide projectors) inappropriate lens position creates a blurred (“out-of-focus”) image

  • In some optical equipment (e.g. slide projectors) inappropriate lens position creates a blurred (“out-of-focus”) image

  • We would like to automatically adjust the lens

  • How can we measure the amount of blurring?



Image mean is not affected by blurring

  • Image mean is not affected by blurring

  • Image s.t.d. (entropy) is decreased by blurring

  • Algorithm: Adjust lens according the changes in the histogram s.t.d.











Thresholding is space variant.

  • Thresholding is space variant.

  • How can we choose the the local threshold values?



Segmentation is based on color values.

  • Segmentation is based on color values.

  • Apply clustering in color space (e.g. k-means).

  • Segment each pixel to its closest cluster.



Problem: Given two images A and B whose (normalized) histogram are PA and PB define the distance D(A,B) between the images.

  • Problem: Given two images A and B whose (normalized) histogram are PA and PB define the distance D(A,B) between the images.

  • Example Usage:

    • Tracking
    • Image retrieval
    • Registration
    • Detection
    • Many more ...


Problem: distance may not reflects the perceived dissimilarity:

  • Problem: distance may not reflects the perceived dissimilarity:



Measures the amount of added information needed to encode image A based on the histogram of image B.

  • Measures the amount of added information needed to encode image A based on the histogram of image B.

  • Non-symmetric: DKL(A,B)DKL(B,A)

  • Suffers from the same drawback of the Minkowski distance.



Suggested by Rubner & Tomasi 98

  • Suggested by Rubner & Tomasi 98

  • Defines as the minimum amount of “work” needed to transform histogram HA towards HB

  • The term dij defines the “ground distance” between gray-levels i and j.

  • The term F={fij} is an admissible flow from HA(i) to HB(j)













Constraints:

  • Constraints:

  • Can be solved using Linear Programming

  • Can be applied in high dim. histograms (color).



Define CA and CB as the accumulated histograms of image A and B respectively:

  • Define CA and CB as the accumulated histograms of image A and B respectively:






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