region labelling giving a region a name. image processing and computer vision: 62 introduction...
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Region labelling
Giving a region a name
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Introduction
Region detection isolated regions
Region description properties of regions
Region labelling identity of regions
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Contents
Template matching Rigid Non-rigid templates
Graphical methods Eigenimages Statistical matching Syntactical matching
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Template matching
Define a template a model of the object to be
recognised Define a measure of similarity
between template and similar sized image region
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Measure dissimilarity between image f[i,j] and template g[i,j]
Place template on image and compare corresponding intensities
Need a measure of dissimilarity
Last is best....
i, j Rmax f g f g
i, j R 2
f g i, j R
Similarity
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Expanding
If f and g fixed-fg a good measure of mismatch
fg a good measure of match
Compute match between template and image with cross-correlation
2
f g i, j R 2
f i, j R 2
g 2i , j R fg
i , j R
M i, j g k, l l n
ln
k m
km
f i k, j l
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g is constant, f varies and so influences MNormalisation
C is maximum where f and g are same.Limitations
number of templates required rotation and size changes partial views
C i, j g k, l
l n
ln
k m
k m
f i k, j l
2fl n
ln
k m
km
i k, j l
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Position
No
n-N
orm
alis
ed
Co
rre
lati
on
Template
Input Output
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Flexible Templates
Shapes are seldom constant Variation
in shape itself in image of same shape viewpoint
Non-rigid representations capture variability
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Structure
Flexible image structures Linked by virtual springs
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Recognition Deform image structure
To equate model and image Move image structures
To colocate model and image Matching
externalexternalinternalinternal EWEWEtotal
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Learning the model Accuracy of model determines
success Model
For each control point average, variance of location
To be learnt with minimum external variation
size, orientation, inconsistency of location
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Parametric Models
Parametrically define the shape straight line, circle, parabola, …
Update parameters to match model and object
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Example – Face tracking
Eyes and mouth circles and parabolas locations, sizes, orientations
Templates define image structures
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Flexible templates, EigenImages
Attempt to capture intrinsic variability of data
Mathematical representation of variation
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Take samples from a population plot values of parameters on a
scatter diagram
Mathematical Foundation
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Rotate axes: one axis encodes most of information other axis encodes remainder
Generalise to multiple dimensions
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Images
Use outline co-ordinates image values
As the variables Normalise as much variability
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Hand Eigenimages
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Hand Gestures
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Range of Eigenimages
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Face Eigenimages
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Recognition
Retain n eigenvectors with largest eigenvalues
Form dot product of these with image data
Find nearest neighbour from training set
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Statistical Classification Methods
Derive characteristic feature measurements from image
Form a feature vector that identifies object as belonging to a predefined class
Need decision rules to make classification
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Linear Discriminant Analysis
Samples from different classes occupy different regions of feature space
Can define a line separating them
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Feature 1
Featu
re 2
Class A
Class B
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Decision
d(X) = F2 - mF1 - c
d(X) > 0 for points in class Ad(X) = 0 for points on lined(X) < 0 for points in class B
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height
weight
jockeys
basketball players?
jd 2
iu ijf i1
N
Rd minj1
N
jd
Nearest Neighbour Classifier
Assign the new sample to the population whose centroid is closest.
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Most Likely
Incorporate range of possible class values
2
2
xxCp
A
A
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Take population variation into account
Assume prior probability of observing class j is P(j)
e.g. 10% of population are jockeys
Assume a conditional probability distribution for each feature, x, of each population p(x|j).
height
weight
jockeys
basketball players?
Bayesian Classifiers
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P j | x p x|
j P j p x|
j P j j1
N
Multiply these curves by P(j) to give probability of a measurement belonging to each class.
Divide by total probability of measuring x, to normalise.
This gives the probability of the sample being from each class.
x
p
p(x|1)
p(x|2)
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Syntactic Recognition
Objects’ structure (outline) can be described linguistically Primitive shape elements = words Grammatically correct sentences = a
valid shape
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Shape Grammar A set of pattern primitives
terminal symbols A set of rules that define combinations
of primitives (sentences) the grammar
A start symbol represents a valid object
Non-terminal symbols represent substructures in the shape
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Recognition
Grammar is generative Recognition is degenerative
Recognition uses rules in reverse Terminal symbols are rewritten until a
valid start symbol is attained
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Chromosome Grammar
armpartright
armpartleft
armpartleft pair arm
partright armpair arm
sidepair armpair arm
pair armsidepair arm
pair armpair armchromosomesubmedian
c
c
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Chromosome Grammar
d
b
b
b
a
b
b
side
side
sideside
sideside
arm
armarm
armarm
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The Primitives
a b c d
a bc
b
ab
bb
b
b
b
a
ad
d
c
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Example
a bc
b
ab
bb
b
b
b
a
ad
d
c
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<submedian chromosome>
d b a b c b a b d b a b c b a b
<side><side> <arm><arm> <arm>c <arm>c
<side><side> <arm><arm> <arm>c <arm>cb b
<side><side> <arm> <right part><arm> <right part>
<side> <arm pair><side> <arm pair>
<arm pair><arm pair>
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Evaluation Classification rate Confusion matrix
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Classification Rate How often does the
classifier get the correct answer?
Selection of training and test data must be carefully done.
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Confusion matrix C(i,j) = number of times
pattern i was recognised as class j.
Want off-diagonal elements to be zero.
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Summary
Template matching Deformable templates Flexible templates Statistical classification