Linearity testing using local polynomial approximation

Linearity Testing Using Local Polynomial Approximation

Polynomial Approximation, Local Polynomial Convexity, and Degenerate Cr Singularities

We begin with the following question: given a closed disc D ⋐ C and a complex-valued function F ∈ C(D), is the uniform algebra on D generated by z and F equal to C(D) ? When F ∈ C 1 (D), this question is complicated by the presence of points in the surface S := graph D (F) that have complex tangents. Such points are called CR singularities. Let p ∈ S be a CR singularity at which the order of co...

Polynomial Approximation, Local Polynomial Convexity, and Degenerate Cr Singularities

We begin with the following question: given a closed disc D b C and a complexvalued function F ∈ C(D), is the uniform algebra on D generated by z and F equal to C(D) ? When F ∈ C1(D), this question is complicated by the presence of points in the surface S := graphD(F ) that have complex tangents. Such points are called CR singularities. Let p ∈ S be a CR singularity at which the order of contac...

On adaptive local polynomial approximation with varying bandwidth

The local polynomial approximation (LPA) of noisy data is considered with the new adaptive procedure for varying bandwidth selection. The algorithm is simple to implement and nearly optimal within In N factor in the point-wise risk for estimating the function and its derivatives. The adaptive varying bandwidth enables the algorithm to be spatial adaptive over a wide range of the classes of func...

Local Polynomial Approximation for Unsupervised Segmentation of Endoscopic Images

In this paper we present a novel technique for unsupervised texture segmentation of wireless capsule endoscopic images of the human gastrointestinal tract. Our approach integrates local polynomial approximation algorithm with the well-founded methods of color texture analysis and clustering (k-means) leading to a robust segmentation procedure which produces fine-grained segments well matched to...