Curve irregularity index for quantification of roughness in non-fractal curves

Fractal geometry is widely used to study the roughness of irregular curves and this has a number of biomedical and geological applications. However, many natural and biological objects are semi-fractal,multi-fractal or non-fractal objects, where the fractal dimension (FD) measure does not work. This paper proposes an irregularity index (Ic) to quantify curve irregularity by measuring the change in the roughness of the segments of the curve with change in window sizes. The proposed index has been validated using synthetically generated curves having different degrees of roughness and the results showed linear relationship of the index with the roughness level (R2=0.99). Statistical significance using ANOVA was tested to determine the difference in the value of the index for curves having different irregularity for both Ic and FD and it was found that only Ic values showed significant difference among the different groups of curves with varying irregularity (p-value<0.001).