![Thresholding
• Thresholding can be viewed as an operation
that involves tests against a function T of
the form:
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where p(x,y) denotes
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Thresholding.ppt
- 2. Thresholding • In A: light objects in dark background • To extract the objects: – Select a T that separates the objects from the background – i.e. any (x,y) for which f(x,y)>T is an object point.
- 3. Thresholding • In B: a more general case of this approach (multilevel thresholding) • So: (x,y) belongs: – To one object class if T1<f(x,y)≤T2 – To the other if f(x,y)>T2 – To the background if f(x,y)≤T1
- 4. Thresholding • A thresholded image: T y x f T y x f y x g ) , ( if 0 ) , ( if 1 ) , ( (objects) (background)
- 5. Thresholding • Thresholding can be viewed as an operation that involves tests against a function T of the form: )] , ( ), , ( , , [ y x f y x p y x T T where p(x,y) denotes some local property of this point.
- 6. Thresholding • When T depends only on f(x,y) global threshold • When T depends on both f(x,y) and p(x,y) local threshold • When T depends on x and y (in addition) dynamic threshold
- 7. Role of Illumination • f(x,y) = i(x,y) r(x,y) • A non-uniform illumination destroys the reflectance patterns that can be exploited by thresholding (e.g. for object extraction).
- 8. Role of Illumination Solution g(x,y) = ki(x,y), – Then, for any image f(x,y) = i(x,y) r(x,y), divide by g(x,y). This yields: ) , ( ) , ( ) , ( ) , ( ) , ( y x ki y x r y x i y x g y x f k y x r y x h ) , ( ) , ( if r(x,y) can be segmented by using a single threshold T, then h(x,y) can also be segmented by using a single threshold of value T/k.
- 10. Simple Global Thresholding • To partition the image histogram by using a single threshold T. • Then the image is scanned and labels are assigned. • This technique is successful in highly controlled environments.
- 11. Algorithm
- 15. Optimal Thresholding • The histogram of an image containing two principal brightness regions can be considered an estimate of the brightness probability density function p(z): – the sum (or mixture) of two unimodal densities (one for light, one for dark regions).
- 16. Threshold Selection Based on Boundary Characteristics • The chances of selecting a good threshold are increased if the histogram peaks are: – Tall – Narrow – Symmetric – Separated by deep valleys
- 17. Threshold Selection Based on Boundary Characteristics • One way to improve the shape of histograms is to consider only those pixels that lie on or near the boundary between objects and the background. – Thus, histograms would be less dependent on the relative sizes of objects and the background.
- 20. Thresholds Based on Several Variables • When a sensor makes available more than one variable to characterize each pixel in an image (e.g. color imaging, RGB)
- 21. Thresholds Based on Several Variables • Each pixel is characterized by 3 values, and the histogram becomes 3D. So thresholding now is concerned with finding clusters of points in 3D space. – Instead of the RGB model, the HSI model might be used too.
- 22. – –Ri is a connected region, i = 1, 2, …, n –Ri ∩ Rj = 0 for all i and j, i≠j –P(Ri) = TRUE for i = 1, 2, …, n –P(Ri ⋃ Rj) = FALSE for i≠j Region-Oriented Segmentation • Segmentation is a process that partitions R into n subregions R1, R2, …, Rn such that: R R n i i 1
- 23. Region Splitting and Merging • Subdivide an image initially into a set of arbitrary, disjointed regions and then merge and/or split the regions in an attempt to satisfy the conditions of region-oriented segmentation. • Quadtree-based algorithm
- 24. Region Splitting and Merging • Procedure: – Split into 4 disjointed quadrants any region Ri where P(Ri) = FALSE – Merge any adjacent regions Rj and Rk for which P(Rj ∪ Rk) = TRUE – Stop when no further splitting or merging is possible.