Lecture 5

Question 1

Methods to quantify segmentation performances

Answer 1

• ROC analysis
• F-measure
• JSC
• DSC

Question 2

Sensitivity

Answer 2

True positive rate:

TPR=TP/(TP+FN)

Question 3

Specificity

Answer 3

True negative rate:

TNR = TN/(TN+FP)

Question 4

ROC analysis

Answer 4

Plot of the TPR vs the FPR (1-specificity) of a method as a function of its free parameters.
The higher the area under the curve, the better

Question 5

Precision vs accuracy

Answer 5

High accuracy implies that the mean of repeated estimates has low bias
High precision implies that the variance of repeated estimates is low.

Question 6

True postive, true negative, false positive and false negative

Answer 6

• True positive: TP=intersection S&T
• True negative: TN=Intersection Sc and Tc
• False positive: FP = intersection S and Tc
• False negative: FN=intersection Sc and T

Question 7

F-measure

Answer 7

F= 2(RP)/(R+P)

Question 8

JSC

Answer 8

Fraction of teh union of the segmented object and the true object that is correctly segmented:
JSC=Intersec(S&T)/Union(S&T)=TP/(FP+TP+FN)

Question 9

DSC

Answer 9

Fraction of the segmented oject set joined with the true object set that is correctly segmented:
DSC=2Intersec(S&T)/(S+T)=2TP/(FP+2TP+FN)

Question 10

Basic measures to quantify binary object properties

Answer 10

• Position: Center of mass as an estimate of object position
• Area: count pixels
• Perimeter
• Moments: m= sumover x sumover y((x^p * y^q)I(x,y))
• Orientation: second order moments analysis
• Major &minor axes

Question 11

Perimeter

Answer 11

Boundary chain code analysis to estimate object parameter

Question 12

Major & minor axes

Answer 12

For a matrix that is real, symmetric and positive, the eigenvalues are positive real valued, the eignevectors u are orthogonal.
Major axis: U2/sq(lambda2) *2

Question 13

Advanced measures to quantify binary object shape

Answer 13

• Eccentricity
• Circularity
• Convex hull
• Convex defiency
• Curvature measures

Question 14

Eccentricity

Answer 14

How much a conic section varies from being circular. Circle has eccentricity zero.
E=major axis length/minor axis length= sqrt(lambda1/lambda2)

Question 15

Circularity

Answer 15

C=4piA/P^2
with P=2pir as the circle perimeter
C=1 for circles

Question 16

Convex hull

Answer 16

object is convex if the straight line between any two point in the object is contained in object.
Concave hull is the smallest convex set that contains the object

Question 17

Convex deficiency

Answer 17

Set difference betwee the convex hull and the object

Question 18

Curvature measures

Answer 18

Boundary is parametrized as C=[x(s),y(s)]
Tangent is the rate of change of the difection. The higher the curvature, the smaller the radius.
Convex parts have positive curvatures, concave negative.

Question 19

Measures to quantify image intensities and structures

Answer 19

• Histogram based properties
• Gradient tensor analysis
• Orientation
• Anistropy

Question 20

Histogram based properties

Answer 20

from the normalized histogram you can figure out the mean, mode, median, moments, variance, skewness, kurtosis, engergy and entropy

Question 21

Gradient tensor analysis

Answer 21

Can create local gradient scales which form gradient vectors towards largest distance.
Gradient tensor S:
Ix^2 IxIy
IxIy Iy^2
-> [s1 s2] * [lambda1 0 [s1^T
0 lambda2] s2^T]

Question 22

Orientation

Answer 22

&=(1/2)arctan(2Ix*Iy/(Ix^2-Iy^2)

Question 23

Anisotropy

Answer 23

Alpha=(lambda1-lambda2)/(lambda1+lambda2)

Question 24

Quantitative colocalization measures

Answer 24

Degree to which different species of objects are present in the same spatial locations.
Co-occurence: Counting number of common spatial locations
Correlation: Computing relationship between intensity distributions
- Pearson
- Manders

Question 25

Pearson’s

Answer 25

rp=sum(I1(x,y)-avr(I1)I2(x,y)avr(I2)/sqt sum(I1(x,y)-avr(I1))* sum(I2(x,y)*avr(I2))
rp=1 perfectly related
rp=0 perfectly unrelated
rp=-1 perfectly inversely related
It is the measure for which the cloud of dots looks like a line

Question 26

Manders’

Answer 26

rm=Sum(I1(x,y)I2(x,y))/sqrt(sum(I1^2))sum(I2^2))
Better for asymmetric images
Manders tells us about The colocaliazation

Question 27

Limitations

Answer 27

• Constrained to the level dictated by the microscop PSF
• Intermediate color shows only if probes have similar intensities
• Subjective
• Infeasible for large numbers of images
• Sumbersome in 3D
• Colocalization does not imply physical interactions and more experiments need to be done

Question 28

Guidelines

Answer 28

• Optimize microscope settings -> use confocal microscopy and sample at Nyquist rate
• Optimize probe selection -> minize bleed throug
• Optimize signal information -> reduce noise & exclude irrelevant pixels

Question 29

Sources of error Image analysis

Answer 29

• Imperfections in the biological sample preparation
• Imperfections in the image acquistion process
• Imperfections in the image processing methods

Question 30

Precision

Answer 30

Positive predictive value:

P = TP/(TP+FP)

Question 31

Recall

Answer 31

Sensitivity: Fraction of true object that is correctly segmented
R=TP/(TP+FN)

Question 32

Total bending energy

Answer 32

B=integral over c(k^2)ds

Total absolute curvature: K=integral over c(k)ds

Question 33

Fourier analysis

Answer 33

Estimate object contour roughness:
Er=sum(Zn^2)/sum(Zn^2)
First is fraction of high frequency components
Second is sum over all frequency fourier components.