Figure 4
From: Quality measures for fully automatic CT histogram-based fat estimation on a corpse sample
(a) Scatterplot for the variables FM separability τα* and logarithm of weighted least squares sum ln Sα of the Monte Carlo images YA,r and YB,r with r = 1, … , 20 (where A: z = 0.3 and B: z = 0.5). The data-points are labelled with the number of their grey-scale value histograms true standard deviations S+ = SF+ = SM+. The dashed rectangle on the left side marks the τα* − ln Sα—area of the diagram in Fig. 2d. (b) In the middle: Scatterplot for the variables FM separability τα* and logarithm of weighted least squares sum ln Sα of the Monte Carlo images YA,r with r = 1, … , 20. The data-dots are labelled with the value of their grey-scale value histograms true standard deviations S+ = SF+ = SM+. Encircling the central scatterplot five empirical and estimated grey-scale value histograms X (thin, drawn), X(Θ) (fat, drawn), XF(Θ) (fat, dashed), XM(Θ) (fat, dotted) are presented, each is connected to its corresponding data-dot in the central scatterplot by a fat drawn pointer-line. (c) 3-D scatterplot of the variables FM separability estimator τα*, the logarithm of the weighted least squares distance ln Sα and relative error REz of the z-estimator for the image-series YA,r and YB,r with r = 1, … , R. Black bubbles : A: z = 0.3 void bubbles: B: z = 0.5. Images YA,r and YB,r were excluded if S ≤ 5 or S ≥ 100 as well as if REZ ≥ 0.2. The weighting exponent was set to α = 1. (d) Computed diagrams of the z-estimator’s standard deviation S(z*) as a function of the standard deviations S = SF = SM of the partial fat and muscle distributions in the scenario YA and YB with EF = −80 HU, EM = 50 HU, z = 0 and ranges 20 HU ≤ S ≤ 90 HU (A: left) and 20 HU ≤ S ≤ 130 HU (B: right). Note the different ranges on the ordinate. The graphs were generated with a true fat ratio value z+ = 0.3. However the choice of the true fat ratio value z+ had virtually no influence on the result when it was changed from z+ = 0.3 to z+ = 0.5. The weight exponent was chosen α = 0 which means z* is an LS-estimator rather than an WLS estimator as it is in the case α = 1.
