Transcript ppt - Klenot.cz

Texture
Course web page:
vision.cis.udel.edu/cv
March 14, 2003  Lecture 13
Announcements
• HW2 due Monday
• Read Chapter 15.2.1 in Forsyth & Ponce
on least-squares fitting and extra
chapter 1, "An Introduction to
Probability" (through section 1.5) for
Monday
Outline
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Frequency filtering
Oriented pyramids
Texture representation
I’ll talk about texture synthesis on
Monday
Frequency Filtering
courtesy of P. Bourke
I
log(jF(I)j)
Low- and High-Pass Filters
Low-pass
High-pass
I
courtesy of
P. Bourke
Masked log(jF(I)j)
F-1 of mask result
Band-Pass Filters
courtesy of P. Bourke
Masking a specific range of frequencies
emphasizes features at that scale
Ringing
• Spread of frequency spectrum for box image
indicates problem with using it as smoothing filter
– Fourier theorem says that convolving is multiplication
of Fourier transforms, so we are introducing spurious
higher frequencies into the image
• Gaussians are better because Fourier transform is
also a Gaussian ! Frequencies are concentrated
Box kernel & its Fourier transform
Gaussian kernel
Box-filtered image
Laplacian Pyramids as
Band-Pass Filters
courtesy of Wolfram
from Forsyth & Ponce
Each level is the difference of a more smoothed and less
smoothed image ! It contains the band of frequencies in between
Oriented Pyramids
• Laplacian pyramid + direction sensitivity
from Forsyth & Ponce
v
Oriented Pyramids
from Forsyth & Ponce
Gabor Filters
• “Localized Fourier transforms”: Make each kernel
from product of Fourier basis image and Gaussian
Frequency
Odd
Even
Larger scale
Smaller
scale
from Forsyth & Ponce
Texture Representation: Filter
Responses
• Choose a group of filters
– Edge/Bar filters: Something like Gabor
filters at different orientations, scales
– Spot filters: Center-surround filters like a
Gaussian/difference of Gaussians at
multiple scales
• Run filters over image to get a set of
response images—this is analogous to
an oriented pyramid
Example: Filter Responses
Input
image
Filter
bank
from Forsyth & Ponce
Filter responses at one scale
Texture Similarity based on
Response Statistics
• Collect statistics of responses over an
image or subimage
– Mean of squared response
– Mean and variance of squared response
• Euclidean distance between vectors of
response statistics for two images is
measure of texture similarity
Example: Categorizing Textures
Only vertical & horizontal filters in bank; response vector is (v, h)
from Forsyth & Ponce
squared
responses
Dark Grey = Horizontal
Light Grey = Vertical
White = Both
Black = Neither
Application: Texture-based Image Matching
Decreasing
response
vector
similarity
Query image
Ordered list of
best matches
from Forsyth & Ponce