1. Outline Announcement Local operations (continued) Linear filters
Homework #1
Local operations (continued)
Geometric operations
Linear filters

2. Visual Perception Modeling
Announcement
Homework #1
11/8/2018
Visual Perception Modeling

3. Visual Perception Modeling
Geometric Operations
Geometric operations change the spatial relationships among the objects in an image
Have an image on a rubber sheet and then deform the sheet
A geometric operation is more general in that it can move any point in the input image to any point in the output image
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Visual Perception Modeling

4. Geometric Operations – cont.
Two separate algorithms
Spatial transformation
An algorithm that defines the spatial transformation itself
This specifies the motion of each pixel
Pixel value interpolation
Integer pixel positions can map to fractional positions
Nearest neighbor interpolation
Bilinear interpolation
Implementation issues
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Visual Perception Modeling

5. Spatial Transformation
Simple transformations
Rotation
Scaling
Affine transformation
General transformations
Specified by the motion of each pixel
Called “optical flow”
Specified by control points
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Visual Perception Modeling

6. Applications of Geometric Operations
Geometric calibration
Remove the camera-induced geometric distortion from digital images
Image rectification
Transform images of non-rectangular pixel coordinates to display systems
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Visual Perception Modeling

7. Applications of Geometric Operations – cont.
Image registration
Register similar images for purposes of comparison
Motion estimation and video analysis
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Visual Perception Modeling

8. Visual Perception Modeling
Image Mosaicing
Remote sensing of earth and planets, panoramas ....
More on the web
Image mosaics from CMU
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Visual Perception Modeling

9. Applications of Geometric Operations – cont.
Model-based object recognition
Transform an object model to match the input image
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Visual Perception Modeling

10. Applications of Geometric Operations – cont.
Map projection
Project images for purposes of mapping
How to produce photo-mosaic maps of the Earth, moon, or the planets
Cartography
Produce two-dimensional maps of spherical or ellipsoidal bodies
Map properties
Cartographic projections
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Visual Perception Modeling

11. Applications of Geometric Operations – cont.
Image morphing
A technique that allows one object to transform gradually into another
Generate a movie sequence from two images
Image interpolation
How to generate a realistic looking transformation
It has tremendous commercial values
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Visual Perception Modeling

12. Visual Perception Modeling
Image Morphing
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Visual Perception Modeling

13. Visual Perception Modeling
An Example
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Visual Perception Modeling

14. Visual Perception Modeling
Image Morphing
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Visual Perception Modeling

15. More Examples on the Web
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Visual Perception Modeling

16. Visual Perception Modeling
Research Problems
How to create a model very efficiently
Identify important features in one image and the corresponding features in the other image
Deformable templates
Specify the deformation for certain effects
Facial expression modeling
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Visual Perception Modeling

17. Visual Perception Modeling
Linear System Theory
What is a system?
A system is anything that accepts an input and produces an output in response
y[n] = T{x[n]}
where x[n] is the input sequence and y[n] is the output sequence in responses to x[n]
How to represent a sequence?
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Visual Perception Modeling

18. Visual Perception Modeling
Linear System
Linearity
y1[n] = T{x1[n]}
y2[n] = T{x2[n]}
Then
y1[n]+y2[n] = T{x1[n]+x2[n]}
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Visual Perception Modeling

19. Shift-Invariant System
Shift invariance
y[n] = T{x[n]}
y[n-T] = T{x[n-T]}
LSI system
A LSI system is completely characterized by its impulse response h[n]
For any other input, we can obtain the response through convolution
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Visual Perception Modeling

20. Visual Perception Modeling
Filtering
Closely related to convolution
Filter examples
Smoothing by averaging
Smoothing by Gaussian
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Visual Perception Modeling