MIPR Lecture 4 Copyright Oleh Tretiak, Medical Imaging and Pattern Recognition Lecture 4 Visibility and Noise, Certainty in Medical Decisions Oleh Tretiak

MIPR Lecture 4 Copyright Oleh Tretiak, 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, How many blobs? contrast = 1 contrast = 8contrast = 4 contrast = 2

MIPR Lecture 4 Copyright Oleh Tretiak, How many flowers?

MIPR Lecture 4 Copyright Oleh Tretiak, 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, Visual Pathway - Anatomy

MIPR Lecture 4 Copyright Oleh Tretiak, Two-Dimensional Systems We would like to have a system model for vision. h x(u,v) y(u,v) Input: Image Output: Our mind’s perception

MIPR Lecture 4 Copyright Oleh Tretiak, ‘Typical’ Visual Spatial Response

low contrast high contrast

MIPR Lecture 4 Copyright Oleh Tretiak, Objective value (intensity) Subjective (perceived) value Mach Bands

MIPR Lecture 4 Copyright Oleh Tretiak, The circles have the same objective intensity.

MIPR Lecture 4 Copyright Oleh Tretiak,

MIPR Lecture 4 Copyright Oleh Tretiak, 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, ‘White Noise’ Pattern

MIPR Lecture 4 Copyright Oleh Tretiak, Noise Patterns White (left), low frequency middle), and high frequency noises. All have same standard deviation The standard deviation is a measure of noise intensity.

MIPR Lecture 4 Copyright Oleh Tretiak, 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, 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, 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

low noise low noise, contrast high noise high noise, contrast

MIPR Lecture 4 Copyright Oleh Tretiak, Noise Limited Resolution 0.4 photons/pixel4 photons/pixel 40 photons/pixel

MIPR Lecture 4 Copyright Oleh Tretiak, 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, 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, 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, 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-k p k n!/[k!(n-k)!]

MIPR Lecture 4 Copyright Oleh Tretiak, 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.

MIPR Lecture 4 Copyright Oleh Tretiak, 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 That’s unlikely. The result does not support that half the voters support each candidate.

MIPR Lecture 4 Copyright Oleh Tretiak, 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, 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, Definition SPECIFICITY is accuracy for diagnosing healthy patients SENSITIVITY is accuracy for diagnosing sick patients

MIPR Lecture 4 Copyright Oleh Tretiak, 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, 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, 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.