Diferencia entre revisiones de «Matrices de confusión y otros valores estadísticos»
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where R1 and R2 are the number of pixels within the segmented regions to be compared. | where R1 and R2 are the number of pixels within the segmented regions to be compared. | ||
This sensitive measure varies in the range [0,1]... | This sensitive measure varies in the range [0,1]... | ||
(for medical images) | (for medical images) | ||
where values greater than 0.6 for smaller structures and 0.8 for larger structures are considered good by some authors (Avants et al., 2007). | where values greater than 0.6 for smaller structures and 0.8 for larger structures are considered good by some authors (Avants et al., 2007). | ||
Apart from being highly dependent upon the application, isn't it also dependent upon image resolution? As the higher my resolution is, then better should the segmentation algorithm work. | Apart from being highly dependent upon the application, isn't it also dependent upon image resolution? As the higher my resolution is, then better should the segmentation algorithm work. | ||
Revisión del 17:39 17 feb 2009
Introducción
Hemos realizado esta página para resumir y concretar algunos coeficientes estadísticos que siempre aparecen en muchos de nuestros experimentos. Estos coeficientes nos ayudan a medir la calidad de nuestros resultados al compararlos con la verdad del terreno.
El trabajo en el que se basa esta página es sobre evaluación de algunos resultados de segmentación de imágenes de resonancia magnética, entonces oiréis hablar sobre vóxeles, aunque estos coeficientes son aplicables a otras materias.
Definiciones
In statistics, the terms Type I error (also, α error, or false positive) and type II error (β error, or a false negative) are used to describe possible errors made in a statistical decision process. In 1928, Jerzy Neyman (1894-1981) and Egon Pearson (1895-1980), both eminent statisticians, discussed the problems associated with "deciding whether or not a particular sample may be judged as likely to have been randomly drawn from a certain population" (1928/1967, p.1): and identified "two sources of error", namely:
(α) the error of rejecting a "correct" null hypothesis, and (β) the error of not rejecting a "false" null hypothesis
La matriz de contingencia donde las filas corresponden a la verdad del terreno y las columnas a los resultados:
TP FP
FN TN
En muchas referencias las columnas corresponden a la verdad del terreno y las filas a los resultados, entonces la matriz de contingencia es la traspuesta de la descrita arriba.
Por otro lado, nombraremos como N el número total de vóxeles de cada imagen.
N = número total de vóxeles de la imagen
Valores estadísticos
En principio tenemos que: TP + FP + FN + TN = N
Misclassification Ratio or Mean error: MCR = (FP + FN) / N
Jaccard Similarity: Jaccard = TP / (TP + FN + FP)
Dice's Coefficient: DC = (2*TP) / (2*TP + FN + FP)
Dice is similar to Jaccard but gives twice the weight to agreements.
It is also known as "overlap ratio" when used for segmentation validation and computed as: S(R1,R2) = (2*(R1 - R2)) / (R1 + R2). where R1 and R2 are the number of pixels within the segmented regions to be compared. This sensitive measure varies in the range [0,1]...
(for medical images)
where values greater than 0.6 for smaller structures and 0.8 for larger structures are considered good by some authors (Avants et al., 2007).
Apart from being highly dependent upon the application, isn't it also dependent upon image resolution? As the higher my resolution is, then better should the segmentation algorithm work.
True Positive Fraction or Sensitivity: TPF = TP / (TP + FN) = sensitivity
Esta puede ser multiplicada por 100 para expresarlo como un porcentaje.
True Negative Fraction or Specificity: TNF = TN / (FP + TN) = specificity
Esta puede ser multiplicada por 100 para expresarlo como un porcentaje.
False Positive Fraction: FPF = FP / (FP + TN) = 1 - specificity
Esta puede ser multiplicada por 100 para expresarlo como un porcentaje.
Segmentation Accuracy : SA = ((TP + TN) / N) (x 100)
Accurate Segmentation Ratio :
The ASR is only meaningful when we are dealing with multiple class problems: Gray Matter, White Matter and CSF. Then we will have specific contigency matrices, one for each class of the problem. So, in our problem we have three contingency matrices, one for each brain tissue class:
TP_c, FP_c, TN_c, FN_c, N_c where c = GM, WM or CSF
Then, ASR = (sum_c TP_c) / (sum_c (TP_c + FP_c ))
where sum_c means the sum over all different classes.
The ASR provides the overall evaluation based on the entire image volume, while TPF and FPF are used to measure the performance of different algorithm for a specific tissue.
Nota
The difference between ratio and fraction in the literature seems to be that the ratio is a value between 0 and 1, while the fraction seems to be a percentage (ratio x 100).
Otras referencias
http://en.wikipedia.org/wiki/Sensitivity_and_specificity
http://en.wikipedia.org/wiki/True_positive
http://en.wikipedia.org/wiki/Receiver_operating_characteristic
http://www.medcalc.be/manual/roc.php
http://www.fraudwiki.org/index.php/Measuring_Performance
http://people.revoledu.com/kardi/tutorial/Similarity/Jaccard.html
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1283110
Autores
Resumen hecho por Alexandre Savio de una comunicación por correo electrónico con Manuel Graña, Maite García-Sebastián, Jean-Luc Lor y Charlotte Rosak
Cualquier añadido, correción o comentario será bienvenido.
