Contour detection with bicubic spline surfaces

Abstract

Contour detection has a rich history in multiple fields such as geography, engineering, and earth science. The predominant approach is based on piecewise planar tessellation and now being challenged concerning the extraction of contour objects for non-linear elevation functions, particularly with respect to bicubic spline functions. A storage-efficient method was developed in previous research, but the detection of the complete set of contour objects is yet to be realized. Although intractable, theoretical underpinnings pertinent to curvature resulted in an approach to realize the complete detection of objects. Given a digital elevation model dataset, in this study, a bicubic spline surface function was first determined. Thereafter, candidate initial points on the edges across the region of interest were identified, and the recursive disaggregation of rectangles was repeated if the non-existence of a solution could not be assured. A developed tracking method was then applied. During advancement, other initial points on the same contour curve were identified and eliminated to circumvent duplicate detection. The completeness of the outlets provides analytical tools for elevation and other geographical assessments. Demonstrative experiments included the development of a three-dimensional contour-based network and slope assessments. The latter application transforms the slope analysis type from raster-based to vector-based. Highlights Detection of a complete set of contour objects amenable to bicubic spline surfaces. Small closure inside a single patch is detectable if size exceeds the standard. Curvature & tolerances central to step length adjustment and tangent angle determination. Redundant initial points are identified and eliminated during the tracking process. Various potential applications in addition to geographical elevations.

Keywords

• contour detection
• bicubic spline surface
• curvature
• tolerance
• patch disaggregation