1 of 17 thresholding thresholding is usually the first step in any segmentation approach we have...
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Thresholding
Thresholding is usually the first step in any segmentation approach
We have talked about simple single value thresholding already
Single value thresholding can be given mathematically as follows:
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Thresholding Example
Imagine a poker playing robot that needs to visually interpret the cards in its hand
Original Image Thresholded Image
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But Be Careful
If you get the threshold wrong the results can be disastrous
Threshold Too Low Threshold Too High
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Basic Global Thresholding
Based on the histogram of an image
Partition the image histogram using a single global threshold
The success of this technique very strongly depends on how well the histogram can be partitioned
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Basic Global Thresholding Algorithm
The basic global threshold, T, is calculated
as follows:1. Select an initial estimate for T (typically the
average grey level in the image)
2. Segment the image using T to produce two groups of pixels: G1 consisting of pixels with grey levels >T and G2 consisting pixels with grey levels ≤ T
3. Compute the average grey levels of pixels in G1 to give μ1 and G2 to give μ2
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Basic Global Thresholding Algorithm
4. Compute a new threshold value:
5. Repeat steps 2 – 4 until the difference in T in successive iterations is less than a predefined limit T∞
This algorithm works very well for finding thresholds when the histogram is suitable
221
T
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Thresholding Example 1Im
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Thresholding Example 2Im
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Dig
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Pro
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(2
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Problems With Single Value Thresholding
Single value thresholding only works for bimodal histograms
Images with other kinds of histograms need more than a single threshold
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Problems With Single Value Thresholding (cont…)
Let’s say we want to isolate the contents of the bottles
Think about what the histogram for this image would look like
What would happen if we used a single threshold value?
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Wo
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20
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Single Value Thresholding and Illumination
Uneven illumination can really upset a single valued thresholding schemeIm
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Basic Adaptive Thresholding
An approach to handling situations in which single value thresholding will not work is to divide an image into sub images and threshold these individually
Since the threshold for each pixel depends on its location within an image this technique is said to adaptive
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Thresholding T = 4.5
Thresholding T = 5.5
true object boundary
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Split
– Spatially adaptive thresholding– Localized processing
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Thresholding T = 4
Thresholding T = 7
Thresholding T = 4
Thresholding T = 7
spatially adaptive threshold selection
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Thresholding Method
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merge merge
merge merge
merge local segmentation results
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Basic Adaptive Thresholding Example
The image below shows an example of using adaptive thresholding with the image shown previously
As can be seen success is mixed
But, we can further subdivide the troublesome sub images for more success
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Basic Adaptive Thresholding Example (cont…)
These images show the troublesome parts of the previous problem further subdivided
After this sub division successful thresholding can be achieved
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Region-Based Image Segmentation
Region Growing
Split and Merge
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In mathematical sense the segmentation of the image I, which is a set of pixels, is the partition of I into n disjoint sets R1,R2, . . . , Rn, called segments or regions such that their union of all regions equals I.
I =R1 U R2 U….. U Rn
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Region Growing Region growing is a procedure that groups pixels or subregions
into larger regions. The simplest of these approaches is pixel aggregation, which
starts with a set of “seed” points and from these grows regions by appending to each seed points those neighboring pixels that have similar properties (such as gray level, texture, color, shape).
Region growing based techniques are better than the edge-based techniques in noisy images where edges are difficult to detect.
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Region Splitting Region growing starts from a set of seed points. An alternative is to start with the whole image as a single region
and subdivide the regions that do not satisfy a condition of homogeneity.
Region Merging Region merging is the opposite of region splitting. Start with small regions (e.g. 2x2 or 4x4 regions) and merge the
regions that have similar characteristics (such as gray level, variance).
Typically, splitting and merging approaches are used iteratively.
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Bahadir K. Gunturk EE 7730 - Image Analysis I
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Region-Oriented Segmentation
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