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 object may contain several regions corresponding

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• An image may contain several objects and each object 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 one 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 output 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 other

– 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 pathedges

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=17/3-0φ=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 µ1,µ2 of R1,R2

4. Select a new threshold T=1/2(µ1+µ2)

5. Repeat steps 2-4 until µ1, µ2 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. original image with

uniform illumination

b. histogram of a

c. simulated uneven

illumination

d. image a with uneven

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d. image a with uneven

illumination added

e. histogram of image d

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