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 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 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 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 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 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 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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