Bounded Multivariate Surfaces On Monovariate Internal Functions

TL;DR

This paper introduces a hybrid model that decomposes images into bounded multivariate surfaces using monovariate internal functions and Chebyshev inequalities, enabling efficient image segmentation and reduced data representation.

Contribution

It presents a novel hybrid approach combining monovariate internal functions with Chebyshev bounds for image segmentation, addressing leakage and sample size issues.

Findings

Effective segmentation on Berkeley benchmark

Reduced image representation with bounded surfaces

Insights into Chebyshev parameters and pixel interactions

Abstract

Combining the properties of monovariate internal functions as proposed in Kolmogorov superimposition theorem, in tandem with the bounds wielded by the multivariate formulation of Chebyshev inequality, a hybrid model is presented, that decomposes images into homogeneous probabilistically bounded multivariate surfaces. Given an image, the model shows a novel way of working on reduced image representation while processing and capturing the interaction among the multidimensional information that describes the content of the same. Further, it tackles the practical issues of preventing leakage by bounding the growth of surface and reducing the problem sample size. The model if used, also sheds light on how the Chebyshev parameter relates to the number of pixels and the dimensionality of the feature space that associates with a pixel. Initial segmentation results on the Berkeley image segmentation benchmark indicate the effectiveness of the proposed decomposition algorithm.