A bilateral schema for interval-valued image differentiation
Title: A bilateral schema for interval-valued image differentiation
Conference: IEEE International Conference on Fuzzy Systems 2016 (FUZZ’IEEE 2016), Vancouver (BC, Canada).
Abstract: Differentiation of interval-valued functions is an intricate problem, since it cannot be defined as a direct generalization of differentiation of scalar ones. Literature on interval arithmetic contains proposals and definitions for differentiation, but their semantic is unclear for the cases in which intervals represent the ambiguity due to hesitancy or lack of knowledge. In this work we analyze the needs, tools and goals for interval-valued differentiation, focusing on the case of interval-valued images. This leads to the formulation of a differentiation schema inspired by bilateral filters, which allows for the accommodation of most of the methods for scalar image differentiation, but also takes support from interval-valued arithmetic. This schema can produce area-, segment- and vector-valued gradients, according to the needs of the image processing task it is applied to. Our developments are put to the test in the context of edge detection.
Keywords: Interval-valued images; Bilateral filters; Image differentiation; Uncertainty; Digital images; Visualization; Measurement errors; Image edge detection
Cite as: C. Lopez-Molina, C. Marco-Detchart, L. D. Miguel, H. Bustince, J. Fernandez and B. D. Baets, “A bilateral schema for interval-valued image differentiation”, IEEE International Conf. on Fuzzy Systems (FUZZ-IEEE), 2016, pp. 516-523.
Due to technical and economic reasons, digital sampling has become the most common way to measure and store continuous facts, e.g. visual or acoustic information. The discretization processes faced by the original information necessarily lead to missing (or losing) a portion of it, simply because the range of possible measured values is limited to a predefined set. In the case of digital imagery, the loss of information inherent to the image model (e.g. the limitation in the number of tones) is combined with quality losses alien to it (e.g. lens noise or broken cells in a sensor). This fact holds for any possible coding or compression schema used in the representation of the digital image. Hence, automatic processing tools must deal with some uncerainty in the visual data.
Code (in the KITT): The following pieces of code are of interest for the study and/or use of the developments in this work:
- Function makeIntervalar.m to create IV-Images (package generalImageProcessing);
- Function IVFiltering.m for gradient extraction on IV images using first order differentiation filters (package generalImageProcessing);
- Function IVBilateralFiltering.m for gradient extraction on IV images using bilateral filters (not available yet).
- The paper at IEEExplore
Related works (in the KITT):
- Edge Detection on Interval-Valued Images (link, not available);
- Gradient extraction operators for discrete interval-valued data (link, not available).