Image Processing

Image ProcessingImage Processing

SegmentationSegmentation

1.1. Process of partitioning a digital Process of partitioning a digital image into multiple segments (sets image into multiple segments (sets of pixels).of pixels).

2. Clustering pixels into salient image regions, i.e., regions corresponding to individual surfaces, objects, or natural parts of objects.


SegmentationSegmentation3.3. Used to locate objects and Used to locate objects and

boundaries (lines, curves, etc.) in boundaries (lines, curves, etc.) in images. images.

4.4. Process of assigning a label to every Process of assigning a label to every pixel in an image such that pixels pixel in an image such that pixels with the same label share certain with the same label share certain visual characteristics.visual characteristics.


SegmentationSegmentation

Two of the most common techniques: Two of the most common techniques:

thresholdingthresholding and and

edgeedge findingfinding


SegmentationSegmentationTwo of the most common techniques: Two of the most common techniques:

thresholdingthresholdingedgeedge findingfinding


B. Detection of discontinuities B. Detection of discontinuities

The objects in image:

Three basic types of gray-level discontinuities in a digital image:

points,lines.edges.

The original image:


The common way The common way run a mask through the image

R = f(x-1, y-1) * M1 + f(x, y-1) * M2 + f(x+1, y-1) * M3

+ f(x-1, y) * M4 + f(x, y) * M5 + f(x+1, y) * M6

+ f(x-1, y+1)* M7 + f(x, y+1)* M8 + f(x+1, y+1)* M9


The common way The common way

run a mask through the image

R = f(x-1, y-1) * M1 + f(x, y-1) * M2 + f(x+1, y-1) * M3

+ f(x-1, y) * M4 + f(x, y) * M5 + f(x+1, y) * M6

+ f(x-1, y+1)* M7 + f(x, y+1)* M8 + f(x+1, y+1)* M9

Select some threshold . If |R(x,y)| then (x,y) to belong to object (background).


ExampleExample

a) b)

Original and segmented images:

a) Mask H8

b) Threshold = 2

If R(x,y) 2 Then g(x,y) = 1

Else g(x,y) = 0

H8=


Line detectionLine detection

A masks are usualy used for detection of isolated points in an image are:


Example of line detectionExample of line detection

The original I image and segmented image Io with horizotal mask



The original I image and segmented image I45 with 45o mask



The original I image and segmented image Iv with vertical mask



The original I image and segmented image I135 with 135o mask



The original I image and segmented image I8 with H8 mask


Formula:Formula:

Set (x,y):

R=0for k=1 to 3for q=1 to 3

R = R + f(x+k-2,y+q-2)*M(k,q)If R Then g(x,y) = 255 (object)

Else g(x,y) = 0 (non-object)

1 x ImageWidth1 y ImageHeight


Egde detection:Egde detection:


Gradient-based procedure:Gradient-based procedure:



The function f(x) is defined as horizontal gray-level of the image.

The first derivative f’(x) is positive at the point of transition into and out of the ramp as moving from left to right along the profile.



A point M is being an edge point if its two-dimention first order derivative is greater than a specified threshold.



If using the second-derivative to define the edge points in an image as the zero crossing of its second derivative.



The signs of second derivative can be used to determine an edge pixel lies on the dark or light side of an edge



The zero crossing property of the second derivative is quite useful for locating the centers of thick edges.



The first is gradient vector of an image f(x, y), and

The second is quantity (magnitude) of gradient vector


The Prewitt gradient vector for detecting x-direction (y-The Prewitt gradient vector for detecting x-direction (y-direction) and direction) and

the Prewitt gradient vectors for detecting diagonal the Prewitt gradient vectors for detecting diagonal edges:edges:

-1 -1 -1 -1 0 1

0 0 0 -1 0 1

1 1 1 -1 0 1

0 1 1 -1 -1 0

-1 0 1 -1 0 1

-1 -1 0 0 1 1

Gx = (W2 + W3 + W6) – (W4 + W7 + W8)

Gy = (W6 + W8 + W9) – (W1 + W2 + W4)

Gx = (W7 + W8 + W9) – (W1 + W2 + W3)

Gy = (W3 + W6 + W9) – (W1 + W4 + W7)


The general formulaThe general formulafor i = 2 to Height-1for i = 2 to Height-1

for j = 2 to Width-1for j = 2 to Width-1

{ {

t1 = 0t1 = 0

t2 = 0t2 = 0

for p = 1 to 3 for p = 1 to 3

for q = 1 to 3for q = 1 to 3

{ {

t1 = t1 + Gt1 = t1 + G11[p, q] * f[i+p-2, j+q-2][p, q] * f[i+p-2, j+q-2]

t2 = t2 + Gt2 = t2 + G22[p, q] * f[i+p-2, j+q-2]}[p, q] * f[i+p-2, j+q-2]}

ts = Abs(t1) + Abs(t2)ts = Abs(t1) + Abs(t2)

if ts > if ts > thenthen Q[i,j] = 1Q[i,j] = 1elseelse Q[i,j] = 0Q[i,j] = 0

}}

}}


ExampleExample

1 1 1 3 1 1

1 1 1 3 1 1

1 1 1 3 1 1

3 3 3 3 3 3

1 1 1 3 1 1

1 1 1 3 1 1W

For the window W from image I, caculating the valueR(3,3) = |Dx*W| + |Dy*W|

= |-6+12| + |-6+12| = 12For all pixels of I, except boundary of I, we have matrix R:

0 8 0 8

8 12 4 12

0 4 0 4

8 12 4 120 0 0 0

0 1 0 1

0 0 0 0

0 1 0 1

If using threshold at 10:


The Prewitt gradient vector for detecting x-direction (y-The Prewitt gradient vector for detecting x-direction (y-direction) and direction) and

the Prewitt gradient vectors for detecting diagonal the Prewitt gradient vectors for detecting diagonal edges:edges:


The Sobel gradient vector for detecting x-The Sobel gradient vector for detecting x-direction and y-direction edges: direction and y-direction edges:

G1= (W2 + 2W3 + W6 ) – (W4 + 2W7 + W8)G2= (W6 + 2W9 + W8 ) – (W2 + 2W1 + W4)

Gx = (W7 + 2W8 + W9) – (W1 + 2W2 + W3)Gy = (W3 + 2W6 + W9 )– (W1 + 2W4 + W7)

-1 -2 -1 -1 0 1

0 0 0 -2 0 2

1 2 1 -1 0 1

The Sobel gradient vector for detecting diagonal edges:

0 1 2 -2 -1 0

-1 0 1 -1 0 1

-2 -1 0 0 1 2


Examples Examples

ofof

Sobel Sobel

filter filter


Second-order derivative: The Second-order derivative: The LaplacianLaplacian

2

2

2

22

y

f

x

ff

0 -1 0 -1 -1 -1

-1 4 -1 -1 8 -1

0 -1 0 -1 -1 -1


Second-order derivative: The Second-order derivative: The LaplacianLaplacian 0 0 -1 0 0

0 -1 -2 -1 0

-1 -2 16 -2 -1

0 -1 -2 -1 0

0 0 -1 0 0

The Laplacian is not used in its original form for edge detection (because of sensitive to noise).The Laplacian is combined with smoothing as a precursor to finding

edges via zero-crossing.

Image Processing

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