## 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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