Image Segmentation Segmentation is the process of partitioning an - - PowerPoint PPT Presentation

Image Segmentation

• Segmentation is the process of partitioning an

image into regions

– region: group of connected pixels with similar properties

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properties – properties: gray levels, colors, textures, motion characteristics (motion vectors), edge continuity …

• There are two approaches to segmentation

– region segmentation – edge segmentation

Edges and Regions

• In ideal images, a region is bounded by a

closed contour

– the close contours may be obtained from the

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– the close contours may be obtained from the regions by edge detection – the regions may be obtained from the closed contours by boundary+filling

• In real images, it is rare to obtain regions

from contours directly and vice versa

Regions and Objects

• Regions are important for the interpretation of

images because they may correspond to objects in a scene

• An image may contain several objects and each
• bject may contain several regions corresponding

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• An image may contain several objects and each
• bject may contain several regions corresponding

to different parts of an object

• Due to a number of factors (noise, bad

illumination, 3D world etc.) segmentation is usually not perfect

• Image Interpretation requires object specific

knowledge

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• Image with many objects
• Each object consists of several regions

Region Segmentation

• Region Segmentation: the pixels of the

same object are grouped together and are marked to indicate that they form a region

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same object are grouped together and are marked to indicate that they form a region

• Criteria for region segmentation: pixels may

be assigned to the same region if they have similar intensity values and they are close to

• ne another

Edge Segmentation

• Find all pixels on region boundaries
• Canny Operator

– apply Gaussian smoothing – apply edge detection

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– apply edge detection – remove false edges (e.g., noise) – thin the edge boundary is 1 pixel wide – fill the gaps

• recover missing edges

– put boundary pixels in order all pixels in a list

• Ideally closed boundaries

Edge Following

• There may exist gaps and noisy edges in the
• utput of Canny
• Fill gaps and follow the edge in many directions

– there may exist more than one regions meeting each

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– there may exist more than one regions meeting each

• ther

– not all directions are promising

• continuity
• proximity
• intensity
• length
• direction

Edge Following as a Graph Traversal Problem

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Graph Traversal

• Edge following on a graph can be viewed as a

minimization (or maximization) problem

– the most promising path is the one which maximizes a function Φ(i,j)

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function Φ(i,j) – promising paths correspond to strong edges

• Graph search can be hard combinatorial

Can become very slow – Dynamic Programming (DP) – Heuristics

Criterion Φ(C)

• The edge C with maximum Φ is the most

promising

– Φ(C) = Σφ(i,j) over all points on a curve – Σφ(i,j) = average{intensity} + average{angle}

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– Σφ(i,j) = average{intensity} + average{angle} – takes averages over all points on a path

• In places where the curve splits into 2 or more

directions (paths), follow the direction with the maximum φ

– this situation changes after a while and may be necessary to backtrack to an earlier point

5 5 5 5 5 5 7 4 7 4

second path edges directions first path

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7 4 7 4 3 5 3 6 1 6 1 7 1 6 1 6 6 6

promising at 7 φ=17/3+0

φ=14/3+π/(4*3)

φ=22/6+0

φ=33/6+ 2*π/(4*6)

promising at 6

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Using the maximum cost Φ criterion to find the cell boundaries in microscope images a. a stage in the search process

• b. the completed boundary

Region Segmentation

• Analyze the grey value

distribution (histogram) of the image

– assumption: objects are dark against a light background

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dark against a light background – their grey+value distributions can be separated putting thresholds between them – convert a grey+level image into a binary one by applying carefully selected thresholds

Many Regions

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• One threshold two regions

– black pixels: object – white pixels: background

• More than two thresholds more than two regions with

different intensity values

(1) Peakiness Detection Algorithm

1. Find the two highest local maxima gi, gj in the histogram that are at least at distance d apart

• d is user defined

2. Find the lowest point gk in the histogram between gi

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2. Find the lowest point gk in the histogram between gi and gj 3. Peakiness = min{H(gi),H(gj)}/H(gk) 4. Take the combination (gi,gj,gk) with the highest peakiness 5. Threshold the image at T=gk 6. N thresholds: take the N greater peakinesses (Ti=gki)

(2) Iterative Algorithm

• 1. Compute a threshold T

T: mean gray value of image

• 2. Partition the image into R1, R2 using T

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• 2. Partition the image into R1, R2 using T
• 3. Compute the mean values H1,H2 of R1,R2
• 4. Select a new threshold T=1/2(H1+H2)
• 5. Repeat steps 2+4 until H1, H2 do not change

(3) Adaptive Thresholding

• The same threshold is not usable everywhere in

the image

• e.g., uneven illumination

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• 1. Partition the image into mxm subimages
• 2. Select a threshold Tij for each subimage

apply 1st or 2nd threshold selection algorithm

• 3. Compute the union of the thresholded subimages

a.

• riginal image with

uniform illumination

• b. histogram of

c. simulated uneven illumination

• d. image with uneven

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• d. image with uneven

illumination added e. histogram of image f. thresholding at T=72 failed!!

(4) Double Thresholding

1. Select threshold T1 (apply 1st or 2nd algorithm) 2. Set T2 = T1 + ε (ε is user defined) 3. Compute regions R1, R2, R3:

a. R1: pixels with gray values less than T1

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a. R1: pixels with gray values less than T1 b. R2: pixels with gray values between T1 and T2 c. R3: pixels with gray values above T2

4. Visit each pixel of R2: if the pixel has a neighbor in R1, reassign it to R1 5. Repeat step 4 until no pixels of R2 are reassigned 6. Reassign all pixels remaining in R2 to R3