Lecture 5 Flashcards
Methods to quantify segmentation performances
- ROC analysis
- F-measure
- JSC
- DSC
Sensitivity
True positive rate:
TPR=TP/(TP+FN)
Specificity
True negative rate:
TNR = TN/(TN+FP)
ROC analysis
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
Precision vs accuracy
High accuracy implies that the mean of repeated estimates has low bias
High precision implies that the variance of repeated estimates is low.
True postive, true negative, false positive and false negative
- 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
F-measure
F= 2(RP)/(R+P)
JSC
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)
DSC
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)
Basic measures to quantify binary object properties
- 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
Perimeter
Boundary chain code analysis to estimate object parameter
Major & minor axes
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
Advanced measures to quantify binary object shape
- Eccentricity
- Circularity
- Convex hull
- Convex defiency
- Curvature measures
Eccentricity
How much a conic section varies from being circular. Circle has eccentricity zero.
E=major axis length/minor axis length= sqrt(lambda1/lambda2)
Circularity
C=4piA/P^2
with P=2pir as the circle perimeter
C=1 for circles
Convex hull
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
Convex deficiency
Set difference betwee the convex hull and the object
Curvature measures
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.
Measures to quantify image intensities and structures
- Histogram based properties
- Gradient tensor analysis
- Orientation
- Anistropy
Histogram based properties
from the normalized histogram you can figure out the mean, mode, median, moments, variance, skewness, kurtosis, engergy and entropy
Gradient tensor analysis
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]
Orientation
&=(1/2)arctan(2Ix*Iy/(Ix^2-Iy^2)
Anisotropy
Alpha=(lambda1-lambda2)/(lambda1+lambda2)
Quantitative colocalization measures
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
Pearson’s
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
Manders’
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
Limitations
- 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
Guidelines
- 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
Sources of error Image analysis
- Imperfections in the biological sample preparation
- Imperfections in the image acquistion process
- Imperfections in the image processing methods
Precision
Positive predictive value:
P = TP/(TP+FP)
Recall
Sensitivity: Fraction of true object that is correctly segmented
R=TP/(TP+FN)
Total bending energy
B=integral over c(k^2)ds
Total absolute curvature: K=integral over c(k)ds
Fourier analysis
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.
