IMAGE FORMATION PROCESS
Imaging process maps three-dimensionalscene points onto a two-dimensionalimage plane.
Imaging (Perspective) Transformation
3D-Scene ==============> 2D-Image
Perspective Transformation is key to theImaging Process. It projects 3D-pointsonto a plane.
An analytical model of PerspectiveTransformation can be found byestablishing:
● A world co-ordinate systemrepresenting 3D scene.
● Camera co-ordinate system (x, y, z)which has the image plane.
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IMAGING PROCESS MODEL
For the camera coordinate system (x, y, z)assume:
● Its xy-plane is coincident with theimage plane.
● Its z-axis is along the optical axis ofcamera or line of sight of the observer.
● Centre of camera lens is at (0, 0, λ)where λ is the focal length of lens.
If (X, Y, Z) is the world co-ordinates ofany point in a 3-D scene and (x, y) is itsprojection onto the image plane.
Perspective transformation is the relationbetween (X, Y, Z) and (x, y) which can beobtained by using similar triangles.
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PERSPECTIVE TRANSFORMATION
x/λ = - X/(Z - λ) = X/(λ - Z)y/λ = - Y/(Z - λ) = Y/(λ - Z)
The image plane co-ordinates of theprojected 3-D point are:
x = λX/(λ - Z)y = λY/(λ - Z)
These are non-linear equations. It is oftenconvenient to express them in linearmatrix form.
A point in cartesian world co-ordinatesystem can be represented as a vector incartesian and homogeneous co-ordinates.
| X | | kX |w = | Y | or wh = | kY |
| Z | | kZ || k |
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PERSPECTIVE TRANSFORMATION(cont. 1)
Perspective matrix
| 1 0 0 0 || 0 1 0 0 |
P = | 0 0 1 0 || 0 0 -1/λ 1 |
ch = P wh
| 1 0 0 0 | | kX |= | 0 1 0 0 | | kY |
| 0 0 1 0 | | kZ || 0 0 -1/λ 1 | | k |
| kX |= | kY |
| kZ || -kZ/λ + k |
ch elements are the camera coordinates inhomogeneous form.
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PERSPECTIVE TRANSFORMATION(cont. 2)
The cartesian coordinates of any point inthe camera coordinates system are:
| x | | λX/λ − Z |c = | y | = | λY/λ − Z |
| z | | λZ/λ − Z |
z component is of no interest in termsof image formation model.
It acts as a free variable in the inverseperspective transformation.
The Inverse Perspective Transformationmaps an image point back into 3-D
wh = P−1 ch
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PERSPECTIVE TRANSFORMATION(cont. 3)
| 1 0 0 0 |P−1 = | 0 1 0 0 |
| 0 0 1 0 || 0 0 1/λ 1 |
An image point has co-ordinates (x0, y0, 0)where image plane is located at z = 0.
This point in homogeneous vector ch
| kx0 |ch = | ky0 |
| 0 || k |
wh = P−1 ch
| kx0 |= | ky0 |
| 0 || k |
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PERSPECTIVE TRANSFORMATION(cont. 4)
In cartesian coordinates
| X | | x0 |w = | Y | = | y0 |
| Z | | 0 |
It gives Z = 0 for any 3-D point
☛ Problem
● The problem here is caused bymapping a 3-D scene onto the imageplane.
● It is a many-to-one transformation.
● The image point (x0, y0) correspondsto all the colli near 3-D points that lieon the line passing through (x0, y0, 0)and (0, 0, λ)
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PERSPECTIVE TRANSFORMATION(cont. 5)
The equations of the line joining (x0, y0, 0)and (0, 0, λ) are:
X = (x0/λ)(λ - Z)
Y = (y0/λ)(λ - Z)
They show unless some-thing is knownabout the 3-D scene point, it is notpossible to completely recover the 3-Dpoint from its image.
☛ This is the basic computer visionproblem which every one in this areais researching on.
☛ There are some limited solutions.
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COMPUTER VISION
The purpose of computer vision is toenable a computer to understand itsenvironment from visual information i.e.images using
(grey level, colour, shades, texture etc)
Computer vision is also known as MachineVision and related to:
● Image Processing and Image Analysis
● Image Understanding
● Pattern Recognition
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COMPUTER VISION PROBLEM
Given a 2-D (two-dimensional) image,infer the objects that produce it.
Image I(x, y) is a function of Gray level ateach point in the image.
computer vision processes
I(x, y) ========> Object Information's2-D -------------------> 3-D (three dimensional)
● It is a transformation from 2D to 3D
● A many-to-one transformation. Manysolutions.
● How to identify the correct solution ?
● Third dimension (depth) is missing
● We can not completely recover thethird dimension from a 2-D image.
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COMPUTER VISION PROCESSES
● Sensing
How to get a digital image ?Image Sampling and Quantization
● Video or a TV camera(Monochrome and Colour Images)● IR camera (Thermal Image)● Range finder/Laser etc. (Range Images)
● Preprocessing
● Noise reduction● Filtering● Smoothing● Enhancement etc.
■ Frequency Domain Methods(also known as Image Processing)
■ Spatial Domain Methods
● Segmentation
Partitioning an Image into Objects ofInterest.
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COMPUTER VISION PROCESSES(cont. 1)
● Shape Extraction
Computation of Depth Information by
● Shape from Contours● Shape from Shading● Stereoscopic Imaging● Shape from Motion● Shape from Texture
● Description
Computation of Features
● Recognition
Identifying the Objects
● Interpretation
Assigning meaning to a group ofrecognised objects
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CLASSES OF VISUAL PROCESSING
Three Levels of Visual Processing
They are based on the sophistication ofimplementation and widely known as
Low, Intermediate and High level Vision
● Low Level Vision
It involves preprocessing and low levelfeature extraction
● Requires no intelli gence
● Involves only the data driven processes
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CLASSES OF VISUAL PROCESSING(cont. 1)
● Intermediate Level Vision
It involves image segmentation andimage analysis type processing. Rawshape feature extraction processes arealso its part.
● Very important processing stage
● It combines the data driven and goal driven processes
● High Level Vision
It involves the goal driven processesconsisting of model and knowledgebased vision.
● Recognition
● Interpretation
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IMAGE SEGMENTATIONThe Image Segmentation Process segment an image.
Segmentation:
* Subdivide an image into its constituents parts/objects.
* The level to which this subdivision is carried out depends on the problem being solved.
Constituent Parts:
* Object Boundaries
* Uniform Intensity or colour regions
* Lines, Points and Curves etc.
Image Segmentation is a very important part ofComputer Vision