Transcript Medical Imaging and Pattern Recognition

Medical Imaging and Pattern
Recognition
Lecture 4
Visibility and Noise, Certainty in
Medical Decisions
Oleh Tretiak
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
1
Lecture Overview
• Factors affecting visibility of objects in
images
• Noise as a factor in image quality
• Probability and experimental findings
• Types of errors in medical diagnosis
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
2
How many blobs?
contrast = 1
contrast = 2
contrast = 4
contrast = 8
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
3
How many flowers?
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
4
Visibility of Objects
• If contrast is to small, object can’t be
seen
– Increase contrast!
• If object is too small, it can’t be seen
– Magnify!
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
5
Visual Pathway - Anatomy
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
6
Two-Dimensional Systems
• We would like to have a system model for vision.
x(u,v)
y(u,v)
h
• Input: Image
• Output: Our mind’s perception
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
7
‘Typical’ Visual Spatial Response
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
8
low contrast
high contrast
Mach Bands
Subjective
(perceived) value
Objective value
(intensity)
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
10
The circles have the same objective
intensity.
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
11
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
12
Image Noise
• Variations of intensity that have no
bearing on the information in the image
are called noise
• White noise means that the variation is
uncorrelated from pixel to pixel
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
14
‘White Noise’ Pattern
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
15
Noise Patterns
The standard deviation is a measure of noise
intensity.
White (left), low frequency middle), and high
frequency noises. All have same standard
deviation
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
16
Effect of noise on
image quality: UL ~
original 8-bit image;
UR ~ white noise;
LL ~ low pass
noise; LR ~ high
pass noise. Noise
standard deviation
is equal to 8.
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
17
Effect of noise on
image quaity: UL ~
original 8-bit image;
UR ~ white noise;
LL ~ low pass
noise; LR ~ high
pass noise. Noise
standard deviation
is equal to 32.
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
18
Conclusions
• Object visibility can be improved by
increasing contrast or object size
• This is effective only when object is free
of noise
• All physical systems have noise, and
this places a limit on visibility
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
19
low noise
low noise,
contrast
high noise
high noise,
contrast
Noise Limited Resolution
0.4 photons/pixel
4 photons/pixel
40 photons/pixel
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
21
Noise Tradeoff
• In X-ray and radionuclide systems,
reduced noise produces higher radiation
dose
• In Magnetic Resonance, reduced noise
requires longer time
• Higher resolution produces more noise
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
22
Probability and Decisions
• We poll 100 people about whether they will
vote for Bush of Kerry. 60 say they will vote
for Kerry, 40 for Bush. Will Kerry0 win?
• We give vitamin C to a group of 10 people
who have colds: 6 get better. In a group of 10
people who did not get vitamin C, 4 got
better. Is vitamin C effective against the
common cold?
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
23
Sampling
• Two possible outcomes in a trial
(Bush/Kerry, Healthy/Sick)
• A very large population of individuals
• We select a small number of individuals,
and find their outcomes.
• Can we conclude about the large group
from the small group?
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
24
Bernoulli Trials
• Probability of ‘success’ = p
– In the whole population, the fraction of
‘success’ is p
• Number of observations is n
• Number of successes is k
• Probability of this result is
P(n, k) = (1-p)n-kpk n!/[k!(n-k)!]
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
25
Probability plot, n = 10, p = 0.5
Probability of any specific outcome is pretty low.
The result 6/10 successes with vitamin C, 4/10
successes without could be due to benefit of
vitamin C, or it could be chance. It is not
convincing.
0.3
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
7
8
9
10
26
Probability plot, n = 100, p = 0.5
• Probability of any individual outcome is very low
• Probability of getting 60 or more out of 100 if the
probability were 0.5 is 0.03. That’s unlikely.
• The result does not support that half the voters
support each candidate.
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0
10
20
30
40
50
MIPR
Lecture
4 60
Copyright Oleh Tretiak, 2004
70
80
90
27
100
Probability and Experimental
Conclusions
•
•
•
We would like to predict what will be the
effect of a treatment on a large population
on the basis of a sample.
Chance can give a misleading outcome
Probability theory can tell us if the result of
the test is
1. Strongly supports the apparent outcome
2. Fails to support the outcome (could be due to
chance)
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
28
Medical Diagnosis
• A good test is one that tells us the truth
• In medical tests, there are two kinds of errors
– Predict the patients are healthy when they are sick
– Predict that the patients are sick when they are
healthy
• Both kinds of error are undesirable
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
29
Definition
• SPECIFICITY is accuracy for diagnosing
healthy patients
• SENSITIVITY is accuracy for diagnosing sick
patients
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
30
Comparing Tests
• Method A: Specificity = 0.95, Sensitivity
= 0.80
• Method B: Specificity = 0.90, Sensitivity
= 0.85
– Which is better?
• Cannot conclude which test is better on
the basis of this information
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
31
Diagnostic Decisions
• We can have very high sensitivity by deciding
every piece of data indicates disease
(aggressive treatment). This will lead to low
specificity.
• We can have very high specificity by requiring
very strong evidence of disease (conservative
treatment). This will lead to low sensitivity.
• The goal of improved diagnostic technology is
to improve both sensitivity and specificity.
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
32
Summary
• Probability theory and statistics are important
tools in the study of medical imaging and
pattern recognition.
• Imaging systems require tradeoff between
image resolution, noise, dose, and many
other factors.
• Evaluation of diagnostic systems can only be
done from by using probability theory and
statistics.
MIPR Lecture 4
Copyright Oleh Tretiak, 2004
33