[Paper Review] On Image Filtering, Noise and Morphological Size Intensity Diagrams

Vitorino Ramos, Fernando Muge|ArXiv.org|Dec 17, 2004

Neural Networks and Applications11 references3 citations

TL;DR

This paper proposes a novel method for adaptive noise removal in images using morphological size-intensity diagrams (M-SID) derived from two morphological filtering transformations (FT1, FT2). By analyzing quantitative measures on these diagrams, the approach determines optimal filtering parameters and stop criteria for alternating sequential filters (ASF), improving noise suppression while preserving image structure.

ABSTRACT

In the absence of a pure noise-free image it is hard to define what noise is, in any original noisy image, and as a consequence also where it is, and in what amount. In fact, the definition of noise depends largely on our own aim in the whole image analysis process, and (perhaps more important) in our self-perception of noise. For instance, when we perceive noise as disconnected and small it is normal to use MM-ASF filters to treat it. There is two evidences of this. First, in many instances there is no ideal and pure noise-free image to compare our filtering process (nothing but our self-perception of its pure image); second, and related with this first point, MM transformations that we chose are only based on our self - and perhaps - fuzzy notion. The present proposal combines the results of two MM filtering transformations (FT1, FT2) and makes use of some measures and quantitative relations on their Size/Intensity Diagrams to find the most appropriate noise removal process. Results can also be used for finding the most appropriate stop criteria, and the right sequence of MM operators combination on Alternating Sequential Filters (ASF), if these measures are applied, for instance, on a Genetic Algorithm's target function.

Motivation & Objective

• To address the ambiguity in defining noise due to lack of pure noise-free reference images.
• To overcome the subjective and fuzzy nature of noise perception in image analysis.
• To develop a quantitative method for selecting optimal morphological filtering parameters based on image-specific characteristics.
• To provide a systematic approach for determining stop criteria in alternating sequential filtering (ASF).
• To enable automated optimization of morphological operator sequences using measurable features from size-intensity diagrams.

Proposed method

• Apply two distinct morphological filtering transformations (FT1, FT2) to the input noisy image.
• Construct size-intensity diagrams (M-SID) from the outputs of FT1 and FT2 to represent structural features across intensity and size scales.
• Extract quantitative measures (e.g., area, peak intensity, distribution shape) from the M-SID of both filtered outputs.
• Use comparative analysis of these measures to evaluate and rank filtering performance.
• Integrate the M-SID analysis into a target function for metaheuristic optimization (e.g., Genetic Algorithm) to guide operator sequence selection in ASF.
• Define stop criteria for ASF based on convergence trends observed in the M-SID measures.

Experimental results

Research questions

• RQ1 How can noise be objectively quantified in the absence of a ground-truth noise-free image?
• RQ2 What measurable image features in morphological size-intensity diagrams can guide optimal filtering parameter selection?
• RQ3 Can size-intensity diagram analysis improve the selection of stop criteria in alternating sequential filtering?
• RQ4 How can M-SID-based measures be used to optimize the sequence of morphological operators in ASF?
• RQ5 To what extent does the proposed method reduce subjectivity in noise perception and filtering decisions?

Key findings

• The proposed method enables objective, data-driven selection of morphological filtering parameters based on measurable features in size-intensity diagrams.
• Quantitative analysis of M-SID from two filtering stages (FT1, FT2) provides a reliable basis for evaluating noise removal effectiveness.
• The method supports the determination of optimal stop criteria for alternating sequential filters by detecting convergence trends in diagram features.
• The integration of M-SID measures into a target function allows for automated optimization of morphological operator sequences.
• The approach reduces reliance on subjective perception of noise, offering a more consistent and repeatable filtering process.
• The method was validated in a real-world pattern recognition context, demonstrating improved filtering outcomes in the absence of ground-truth noise-free images.