Weighted Quasi-Interpolant Spline Approximations of Planar Curvilinear Profiles in Digital Images

Abstract

The approximation of curvilinear profiles is very popular for processing digital images and leads to numerous applications such as image segmentation, compression and recognition. In this paper, we develop a novel semi-automatic method based on quasi-interpolation. The method consists of three steps: a preprocessing step exploiting an edge detection algorithm; a splitting procedure to break the just-obtained set of edge points into smaller subsets; and a final step involving the use of a local curve approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), chosen for its robustness to data perturbation. The proposed method builds a sequence of polynomial spline curves, connected C0 in correspondence of cusps, G1 otherwise. To curb underfitting and overfitting, the computation of local approximations exploits the supervised learning paradigm. The effectiveness of the method is shown with simulation on real images from various application domains.

On spline quasi-interpolation through dimensions

“…In particular, [62,79] deal with the construction and study of new quasi-interpolating operators, in [12,48,59] generalized spline quasi-interpolants are proposed, in [1,20,[49][50][51]53] new integration formulas based on spline quasi-interpolants are constructed, in [15,54,61,63,64,80,81,84] and [4,11] quasi-interpolants are used for the numerical approximation of the solution of differential and integral equations, respectively. Furthermore, in [7,16,17,23,52,65,66] quasi-interpolants are used in different areas of science and engineering: imaging, Computer Aided Geometric Design, industry, etc. Finally, in [19], we find some other interesting references to papers on the above topics.…”

An Automatic Extraction Method of Rebar Processing Information Based on Digital Image

“…In order to realize the accurate extraction of steel bar processing information, an important step is to perform image segmentation. Image segmentation refers to the process of dividing an image into multiple segments and extracting regions of interest based on similarity criteria such as color, brightness or texture [27,28]. Image segmentation can help computers better understand images and extract the corresponding information or objects.…”