Gradient estimation for hexagonal grids and its application to classification of instrumentally registered tactile images
Introduction. The majority of known finite difference schemes are designed for rectangular grids as rectangular grids are natural for many applications. However, these schemes are inapplicable to the analysis of images registered by Medical Tactile Endosurgical Complex (MTEC) — a novel device for intraoperative examination of tactile properties of tissues, as sensors of MTEC are located in nodes of a hexagonal grid. Objectives. The aim of the research was to develop a finite difference scheme for gradient estimation designed for hexagonal grids, study theoretical properties of this scheme, and examine classification of MTEC-registered tactile images that included gradient estimation in its feature space. Materials and Methods. Classification was tested using a library of artificial samples which contained six sample classes. Registration of tactile images was performed by 20 mm MTEC mechanoreceptors under five different angles which varied from 0 ◦ to 14 ◦ ; 450 tactile images were registered in total. Classification algorithm utilized k-nearest neighbors classifier applied to a set of features associated with the most informative frame of a tactile image. Multiple stratified 5-fold cross-validation with 10 repeats was used for parameter optimization and measuring classifier accuracy. Result. A finite difference scheme for gradient estimation on a hexagonal grid was constructed as a solution of a minimization problem directly related to the definition of differentiability. Error estimate for this scheme was obtained under C 2 assumption both for the case of error-free measurements of function values and for the case of measurements with errors. Classification of instrumentally registered tactile images that used gradient estimation space had mean accuracy above 90% for all classes of samples except one. Conclusion. The designed finite difference scheme for gradient estimation on a hexagonal grid extends a list of mathematical methods applicable to an automated analysis of tactile images registered by MTEC. In particular, usage of feature space that includes gradient estimates increases the accuracy of multi-class classification of MTEC-registered tactile images.