InShaDe: Invariant Shape Descriptors for visual analysis of histology 2D cellular and nuclear shapes

We present a shape processing framework for visual exploration of cellular nuclear envelopes extracted from histology images. The framework is based on a novel shape descriptor of closed contours relying on a geodesically uniform resampling of discrete curves to allow for discrete differential-geometry-based computation of unsigned curvature at vertices and edges. Our descriptor is, by design, invariant under translation, rotation and parameterization. Moreover, it additionally offers the option for uniform-scale-invariance. The optional scale-invariance is achieved by scaling features to z-scores, while invariance under parameterization shifts is achieved by using elliptic Fourier analysis (EFA) on the resulting curvature vectors. These invariant shape descriptors provide an embedding into a fixed-dimensional feature space that can be utilized for various applications: (i) as input features for deep and shallow learning techniques; (ii) as input for dimension reduction schemes for providing a visual reference for clustering collection of shapes. The capabilities of the proposed framework are demonstrated in the context of visual analysis and unsupervised classification of histology images.