Evaluation of Directed Secant Methods in 2D

FELIX SEBASTIAN LEO THOMSEN; JUAN ÁLVARO FERNÁNDEZ MUÑOZ; CLAUDIO DELRIEUX

Bahía Blanca

Congreso; XVIII Reunión de Trabajo en Procesamiento de la Información y Control; 2019

Universidad Nacional del Sur, Bahía Blanca, Argentina

The secant method is one of the first methods to compute anisotropy from textured 2D images or 3D volumes. While computer science developed more accurate methods to compute anisotropy, the secant method keeps being applied in the analysis of bone micro-structure. Over the last decades, different improvements of the method have been suggested, in particular smoothing of the input signal, applying a three pixels wide secant line and computation in gray scale. We evaluate those modifications and suggest additionally the usage of a two pixels wide secant and bi-cubic interpolation instead of the commonly applied single pixel secant and nearest neighbor interpolations. We provide pseudo-code of the tested 2D algorithms and compare them on measures of precision and accuracy of shape and size based on the root-mean square error, and median and inter-quantile range of repeated experiments to compute the mean intercept density and degree of anisotropy. Both, precision and accuracy could be improved. Our results showed large improvements when incorporating smoothing, two pixels secants and bi-cubic interpolation, achieving on 2D slices of CT scans of human bone a reduction of up to 91% for accuracy errors of the size and 57% for errors of the shape. Our methods are similarly applicable in 3D, either in binary or gray scale. We strongly suggest the consideration of our suggested modifications for applications that require the secant method, in particular for the micro-structural analysis of human bone with CT.