Discrete pulse transform of images and applications

The LULU operators Ln and Un operate on neighbourhoods of size n. The Discrete Pulse Transform (DPT) of images is obtained via recursive peeling of so-called local maximum and minimum sets with the LULU operators as n increases from 1 to the maximum number of elements in the array. The DPT provides a new nonlinear decomposition of a multidimensional array. This thesis investigates the theoretical and practical soundness of the decomposition for image analysis. Properties for the theoretical justification of the DPT are provided as consistency of the decomposition (a pseudo-linear property), and its setting as a nonlinear scale-space, namely the LULU scalespace. A formal axiomatic theory for scale-space operators and scale-spaces is also presented. The practical soundness of the DPT is investigated in image sharpening, best approximation of an image, noise removal in signals and images, feature point detection with ideas to extending work to object tracking in videos, and image segmentation. LULU theory on multidimensional arrays and the DPT is now at a point where concrete signal, image and video analysis algorithms can be developed for a wide variety of applications.Thesis (PhD)--University of Pretoria, 2013.Mathematics and Applied Mathematicsunrestricte

Nonlinear Filters and Characterization of the Discrete Pulse Transform of Images

The Discrete Pulse Transform (DPT) for images and videos has been developed over the past few years and provides a theoretically sound setting for a nonlinear decomposition of an image or video. In [1] the theoretical basis of the DPT was presented. In this paper we now present a sound  characterization of this useful nonlinear hierarchical decomposition by referring to its ability as a separator, the consistency of the decomposition, as well as the smoothing ability of the decomposition

SHAPE FROM FOCUS USING LULU OPERATORS AND DISCRETE PULSE TRANSFORM IN THE PRESENCE OF NOISE

A study of three dimension (3D) shape recovery is an interesting and challenging area of research. Recovering the depth information of an object from normal two dimensional (2D) images has been studied for a long time with different techniques. One technique for 3D shape recovery is known as Shape from Focus (SFF). SFF is a method that depends on different focused values in reconstructing the shape, surface, and depth of an object. The different focus values are captured by taking different images for the same object by varying the focus length or varying the distance between object and camera. This single view imaging makes the data gathering simpler in SFF compared to other shape recovery techniques. Calculating the shape of the object using different images with different focused values can be done by applying sharpness detection methods to maximize and detect the focused values. However, noise destroys many information in an image and the result of noise corruption can change the focus values in the images. This thesis presents a new 3D shape recovery technique based on focus values in the presence of noise. The proposed technique is based on LULU operators and Discrete Pulse Transform (DPT). LULU operators are nonlinear rank selector operators that hold consistent separation, total variation and shape preservation properties. The proposed techniques show better and more accurate performance in comparison with the existing SFF techniques in noisy environment

Demonstrating the use of a class of min-max smoothers for D-region event detection in narrowband VLF phase

This paper describes the use of a class of non‐linear smoothers for the identification of interesting phenomena in narrowband very low frequency (VLF) transmission phase caused by perturbation events in the D‐region of the ionosphere. The LULU smoothers, named for their smoothing of upward (L) and downward (U) peaks in a signal, usually used for image processing tasks, are described and examples are shown where these operators are used to automatically isolate and identify features in the phase of narrow band transmissions received at high and high‐middle latitudes (Antarctica and Marion Island, respectively). Identification of solar flare events, electromagnetic ion cyclotron wave precipitation and substorm injection events are demonstrated, showing the potential for this technique to be used for space weather monitoring

SHAPE FROM FOCUS USING LULU OPERATORS AND DISCRETE PULSE TRANSFORM IN THE PRESENCE OF NOISE

A study of three dimension (3D) shape recovery is an interesting and challenging area of research. Recovering the depth information of an object from normal two dimensional (2D) images has been studied for a long time with different techniques. One technique for 3D shape recovery is known as Shape from Focus (SFF). SFF is a method that depends on different focused values in reconstructing the shape, surface, and depth of an object. The different focus values are captured by taking different images for the same object by varying the focus length or varying the distance between object and camera. This single view imaging makes the data gathering simpler in SFF compared to other shape recovery techniques. Calculating the shape of the object using different images with different focused values can be done by applying sharpness detection methods to maximize and detect the focused values. However, noise destroys many information in an image and the result of noise corruption can change the focus values in the images. This thesis presents a new 3D shape recovery technique based on focus values in the presence of noise. The proposed technique is based on LULU operators and Discrete Pulse Transform (DPT). LULU operators are nonlinear rank selector operators that hold consistent separation, total variation and shape preservation properties. The proposed techniques show better and more accurate performance in comparison with the existing SFF techniques in noisy environment

Multiscale image representation in deep learning

Deep learning is a very popular field of research which can input a variety of data types [1, 16, 30]. It is a subfield of machine learning consisting of mostly neural networks. A challenge which is very commonly met in the training of neural networks, especially when working with images is the vast amount of data required. Because of this various data augmentation techniques have been proposed to create more data at low cost while keeping the labelling of the data accurate [65]. When a model is trained on images these augmentations include rotating, flipping and cropping the images [21]. An added advantage of data augmentation is that it makes the model more robust to rotation and transformation of an object in an image [65]. In this mini-dissertation we investigate the use of the Discrete Pulse Transform [54, 2] decomposition algorithm and its Discrete Pulse Vectors (DPV) [17] as data augmentation for image classification in deep learning. The DPVs is used to extract features from the image. A convolutional neural network is trained on the original and augmented images and a comparison made to a convolutional neural network only trained on the unaugmented images. The purpose of the models implemented is to correctly classify an image as either a cat or dog. The training and testing accuracy of the two approaches are similar. The loss of the model using the proposed data augmentation is improved. When making use of probabilities predicted by the model and determining a custom cut off to classify an image into one of the two classes, the model trained on using the proposed augmentation outperforms the model trained without the proposed data augmentation.Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2020.The financial assistance of the National Research Foundation (NRF) towards this research is hereby acknowledged. Opinions expressed and conclusions arrived at, are those of the author and are not necessarily to be attributed to the NRF.StatisticsMSc (Advanced Data Analytics)Unrestricte

LULU operators on multidimensional arrays and applications

The LULU operators, Ln and Un, are smoothers, that is they smooth data received as a signal. They are nonlinear and this nonlinearity makes them more robust but also more complicated to study since the projection theorem does not hold. Their smoothing action is aimed at removing the impulsive noise present in any received signal. A signal can be of one or two dimensions, or of any higher dimension. In one dimension a signal is represented as a sequence and in two dimensions as an image. Higher dimensions include video feed and other more complex data streams. Carl Rohwer developed the LULU smoothers for sequences over the last three decades and the need for an extension to higher dimensions became more and more obvious as the applications of these smoothers were investigated. Perhaps the most important application is that of the Discrete Pulse Transform which is obtained via recursive application of the smoothers. In this dissertation the extension to dimensions higher than one is presented. All the essential properties developed for the one dimensional smoothers are replicated in this work. In addition, the Discrete Pulse Transform is used to illustrate some simple applications to image smoothing and feature detection. CopyrightDissertation (MSc)--University of Pretoria, 2010.Mathematics and Applied Mathematicsunrestricte