1. - photometric aspects of image formation gray level images
point-wise operations
linear filtering
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2. Image
Brightness values
I(x,y)
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3. Analog intensity function Temporal/spatial sampled function
Image model
Mathematical tools
Analog intensity function
Temporal/spatial sampled function
Quantization of the gray levels
Point sets
Random fields
List of image features, regions
Analysis
Linear algebra
Numerical methods
Set theory, morphology
Stochastic methods
Geometry, AI, logic
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4. What gives rise to images
photometric properties of the environment
geometric properties of the environment
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5. Basic ingredients
Radiance – amount of energy emitted along certain direction
Iradiance – amount of energy received along certain direction
BRDF – bidirectional reflectance distribution
Lambertian surfaces – the appearance depends only on radiance, not
on the viewing direction
Image intensity for a Lambertian surface
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6. Challenges
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7. Computer Vision Visual Sensing Images I(x,y) – brightness patterns
image appearance depends on structure of the scene
material and reflectance properties of the objects
position and strength of light sources
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8. Recovery of the properties of the environment
from single or multiple views
Vision problems
Segmentation
Recognition
Reconstruction
Vision Based Control - Action
Visual Cues
Stereo, motion, shading, texture, contour, brightness
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9. Segmentation – partition image into separate objects
Clustering and search algorithms in the space of visual cues
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10. Recognition – given an image classify what object it represents
Face recognition
Digit recognition
Activity recognition
Patter Recognition and Machine Learning techniques
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11. Computing Stages
Low-level vision (pixels, raw data) - Image processing
Mid-level vision (transformations, measurements, features)
High-level vision (higher level semantic entities)
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12. Computing Stages
Low-level vision (pixels, raw data) - Image processing
Applied operator is linear ->
theory of (discrete) linear systems
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13. Discrete time system maps 1 discrete time signal to another
f[x]
g[x] h
Special class of systems – linear , time-invariant systems
Superposition principle
Shift (time) invariant – shift in input causes shift in output
Examples
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14. Convolution sum:
unit impulse – if x = 0 it’s 1 and zero everywhere else
Every discrete time signal can be written as a sum of scaled
and shifted impulses
The output the linear system is related to the input and the transfer
function via convolution h f g
filter f g
Convolution sum:
Notation:
In matrix form:
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15. Fourier Transform and and FT phase and magnitude definition
FT example gallery
Central theme – approximate a function given a family of
Basis functions
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16. Fourier Transform Examples FT phase and frequency information
Role of the phase information
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17. Filtering - Fourier Transform
Original Image – Band Pass – its FFT
Original - Low Pass – its FFT
Original - High Pass – its FFT
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18. Computing Derivatives
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19. Pointwise Image Operations
Lookup table – match image intensity to the
displayed brightness values
Manipulation of the lookup table – different
Visual effects – mapping is often non-linear
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20. Contrast gamma
Contrast
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Brightness

21. Quantization Thresholding Histogram
Histogram – frequency gray-level -> empirical distribution
h[i] – number of pixels of intensity i
Histogram equalization – making histogram flat
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22. Representation of images at multiple levels of resolution
Image Pyramids
Representation of images at multiple levels
of resolution
Importance – at different resolutions different
features look differently
Over-complete representations
Used for localization properties, motion computation
and matching, biological motivation
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23. Pyramid construction
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24. Pyramid construction/reconstruction
Take an original image – convolve with a blurring
Filter and subsample to get an image at lower
resolution
Reduction – how is the signal at level l+1 related to level l
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25. Pyramid construction/reconstruction
Expansion – how to reconstruct the signal at level l given
related to level l-1 – notation
Signal at level l, expanded k – times
Idea – take the smaller signal fill every second entry
With zero and convolve with the blurring filter
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26. “Drop” vs “Smooth and Drop”
Drop every second pixel
Smooth and Drop every second pixel
Aliasing problems
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27. Gaussian Pyramid
Consecutive smoothing and sub-sampling
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28. Laplacian Pyramid Idea
when we convolve and down-sample some information will get lost i.e. we
reverse the process we cannot get the original image back. Example:
Blurred image of
Lower resolution
(original image - upsampled blurred image)
they are not the same – fine details are lost
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29. Laplacian pyramid Store the fine differences which get lost
Each level of the Laplacian pyramid
difference between two consecutive levels of
gaussian pyramids
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30. Laplacian Pyramid blurred1 image – upsampled blurred2 image
original image – original image smoothed by gaussian
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31. Schematic for construction/reconstruction
Image
blurr/down2
Blurred1
up2/blurr
add
Recon
up2/blurr
subtract
Fine1
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32. Laplacian pyramids
Laplacian pyramids – each level holds the additional information which is needed for better
resolution
We can obtain same image by convolving the image
with difference of Gaussians filter or appropriate
width
Reflects the similarity between difference of
Gaussians DoG and Laplacian operator introduced
in the edge detection stage
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33. Application Texture Synthesis
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