Image reduction using fuzzy quantifiers

In this work we propose an image reduction algorith based on local reduction operators. We analyze the construction of weak local reduction operators by means of aggregation functions and we analyze the effect of several aggregation functions in image reduction with original and noisy images.

Image reduction with local reduction operators

In this work we propose an image reduction algorithm based on weak local reduction operators. We use several averaging functions to build these operators and we analyze their properties. We present experimental results where we apply the algorithm and weak local reduction operators in procedures of reduction, and later, reconstruction of images. We analyze these results over natural images and noisy images.

Some averaging functions in image reduction

In this work we propose a definition of weak local reduction operators and an algorithm that uses such operators to reduce images. We show how to construct local reduction operators by means of different aggregation functions. We also present several experimental results obtained using these aggregation functions-based reduction operators.

Image reduction using means on discrete product lattices

We investigate the problem of averaging values on lattices, and in particular on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme, need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties, and we discuss which of them coincide with the Cartesian product of the standard mean and median. We apply these functions in image processing. We present three algorithms for color image reduction based on minimizing penalty functions on discrete product lattices.

One image reduction algorithm for RGB color images

We investigate the problem of combining or aggregating several color values given in coding scheme RGB. For this reason, we study the problem of averaging values on lattices, and in particular on discrete product lattices. We study the arithemtic mean and the median on product lattices. We apply these aggregation functions in image reduction and we present a new algorithm based on the minimization of penalty functions on discrete product lattices.

Color image reduction by minimizing penalty functions

In image processing, particularly in image reduction, averaging aggregation functions play an important role. In this work we study the aggregation of color values (RGB) and we present an image reduction algorithm for RGB color images. For this purpose, we define and study aggregation functions and penalty functions in product lattices. We show how the arithmetic mean and the median can be obtained by minimizing specific penalty functions. Moreover, we study other penalty functions and we show that, in general, aggregation functions on product lattices do not coincide with the cartesian product of the corresponding aggregation functions. Finally, we make an experimental study where we test our reduction algorithm and we analyze the stability of the penalty functions in images affected by noise.

Image reduction operators based on non-monotonic averaging functions

Image reduction is a crucial task in image processing, underpinning many practical applications. This work proposes novel image reduction operators based on non-monotonic averaging aggregation functions. The technique of penalty function minimisation is used to derive a novel mode-like estimator capable of identifying the most appropriate pixel value for representing a subset of the original image. Performance of this aggregation function and several traditional robust estimators of location are objectively assessed by applying image reduction within a facial recognition task. The FERET evaluation protocol is applied to confirm that these non-monotonic functions are able to sustain task performance compared to recognition using nonreduced images, as well as significantly improve performance on query images corrupted by noise. These results extend the state of the art in image reduction based on aggregation functions and provide a basis for efficiency and accuracy improvements in practical computer vision applications.

Image reduction operators as aggregation functions: Fuzzy transform and undersampling

After studying several reduction algorithms that can be found in the literature, we notice that there is not an axiomatic definition of this concept. In this work we propose the definition of weak reduction operators and we propose the properties of the original image that reduced images must keep. From this definition, we study whether two methods of image reduction, undersampling and fuzzy transform, satisfy the conditions of weak reduction operators.

Fuzzy measures of pixel cluster compactness

Pixel-scale fine details are often lost during image processing tasks such as image reduction and filtering. Block or region based algorithms typically rely on averaging functions to implement the required operation and traditional function choices struggle to preserve small, spatially cohesive clusters of pixels which may be corrupted by noise. This article proposes the construction of fuzzy measures of cluster compactness to account for the spatial organisation of pixels. We present two construction methods (minimum spannning trees and fuzzy measure decomposition) to generate measures with specific properties: monotonicity with respect to cluster size; invariance with respect to translation, reflection and rotation; and, discrimination between pixel sets of fixed cardinality with different spatial arrangements. We apply these measures within a non-monotonic mode-like averaging function used for image reduction and we show that this new function preserves pixel-scale structures better than existing monotonie averages.

Characterizing compactness of geometrical clusters using fuzzy measures

Certain tasks in image processing require the preservation of fine image details, while applying a broad operation to the image, such as image reduction, filtering, or smoothing. In such cases, the objects of interest are typically represented by small, spatially cohesive clusters of pixels which are to be preserved or removed, depending on the requirements. When images are corrupted by the noise or contain intensity variations generated by imaging sensors, identification of these clusters within the intensity space is problematic as they are corrupted by outliers. This paper presents a novel approach to accounting for spatial organization of the pixels and to measuring the compactness of pixel clusters based on the construction of fuzzy measures with specific properties: monotonicity with respect to the cluster size; invariance with respect to translation, reflection, and rotation; and discrimination between pixel sets of fixed cardinality with different spatial arrangements. We present construction methods based on Sugeno-type fuzzy measures, minimum spanning trees, and fuzzy measure decomposition. We demonstrate their application to generating fuzzy measures on real and artificial images.

Speckle reduction in optical coherence tomography imaging by affine-motion image registration

Signal-degrading speckle is one factor that can reduce the quality of optical coherence tomography images. We demonstrate the use of a hierarchical model-based motion estimation processing scheme based on an affine-motion model to reduce speckle in optical coherence tomography imaging, by image registration and the averaging of multiple B-scans. The proposed technique is evaluated against other methods available in the literature. The results from a set of retinal images show the benefit of the proposed technique, which provides an improvement in signal-to-noise ratio of the square root of the number of averaged images, leading to clearer visual information in the averaged image. The benefits of the proposed technique are also explored in the case of ocular anterior segment imaging.

Efficient dimensionality reduction and one-class classification for content-based image retrieval

The thesis investigates various machine learning approaches to reducing data dimensionality, and studies the impact of asymmetric data on learning in image retrieval. Efficient algorithms are proposed to reduce the data dimensionality. Integration strategies for one-class classification are designed to address asymmetric data issue and improve retrieval effectiveness.