Representing Whole Slide Cancer Image Features with Hilbert Curves

Regions of Interest (ROI) contain morphological features in pathology whole slide images (WSI) are delimited with polygons[1]. These polygons are often represented in either a textual notation (with the array of edges) or in a binary mask form. Textual notations have an advantage of human readability and portability, whereas, binary mask representations are more useful as the input and output of feature-extraction pipelines that employ deep learning methodologies. For any given whole slide image, more than a million cellular features can be segmented generating a corresponding number of polygons. The corpus of these segmentations for all processed whole slide images creates various challenges for filtering specific areas of data for use in interactive real-time and multi-scale displays and analysis. Simple range queries of image locations do not scale and, instead, spatial indexing schemes are required. In this paper we propose using Hilbert Curves simultaneously for spatial indexing and as a polygonal ROI representation. This is achieved by using a series of Hilbert Curves[2] creating an efficient and inherently spatially-indexed machine-usable form. The distinctive property of Hilbert curves that enables both mask and polygon delimitation of ROIs is that the elements of the vector extracted ro describe morphological features maintain their relative positions for different scales of the same image.