Revisiting Complex Moments For 2D Shape Representation and Image Normalization

When comparing 2D shapes, a key issue is their normalization. Translation and scale are easily taken care of by removing the mean and normalizing the energy. However, defining and computing the orientation of a 2D shape is not so simple. In fact, although for elongated shapes the principal axis can be used to define one of two possible orientations, there is no such tool for general shapes. As we show in the paper, previous approaches fail to compute the orientation of even noiseless observations of simple shapes. We address this problem. In the paper, we show how to uniquely define the orientation of an arbitrary 2D shape, in terms of what we call its Principal Moments. We show that a small subset of these moments suffice to represent the underlying 2D shape and propose a new method to efficiently compute the shape orientation: Principal Moment Analysis. Finally, we discuss how this method can further be applied to normalize grey-level images. Besides the theoretical proof of correctness, we describe experiments demonstrating robustness to noise and illustrating the method with real images.Comment: 69 pages, 20 figure

Edge and Line Feature Extraction Based on Covariance Models

age segmentation based on contour extraction usually involves three stages of image operations: feature extraction, edge detection and edge linking. This paper is devoted to the first stage: a method to design feature extractors used to detect edges from noisy and/or blurred images. The method relies on a model that describes the existence of image discontinuities (e.g. edges) in terms of covariance functions. The feature extractor transforms the input image into a “log-likelihood ratio” image. Such an image is a good starting point of the edge detection stage since it represents a balanced trade-off between signal-to-noise ratio and the ability to resolve detailed structures. For 1-D signals, the performance of the edge detector based on this feature extractor is quantitatively assessed by the so called “average risk measure”. The results are compared with the performances of 1-D edge detectors known from literature. Generalizations to 2-D operators are given. Applications on real world images are presented showing the capability of the covariance model to build edge and line feature extractors. Finally it is shown that the covariance model can be coupled to a MRF-model of edge configurations so as to arrive at a maximum a posteriori estimate of the edges or lines in the image

Applying machine learning methods for characterization of hexagonal prisms from their 2D scattering patterns – an investigation using modelled scattering data

This document is the Accepted Manuscript version of the following article: Emmanuel Oluwatobi Salawu, Evelyn Hesse, Chris Stopford, Neil Davey, and Yi Sun, 'Applying machine learning methods for characterization of hexagonal prisms from their 2D scattering patterns – an investigation using modelled scattering data', Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 201, pp. 115-127, first published online 5 July 2017. Under embargo. Embargo end date: 5 July 2019. The Version of Record is available online at doi: https://doi.org/10.1016/j.jqsrt.2017.07.001. © 2017 Elsevier Ltd. All rights reserved.Better understanding and characterization of cloud particles, whose properties and distributions affect climate and weather, are essential for the understanding of present climate and climate change. Since imaging cloud probes have limitations of optical resolution, especially for small particles (with diameter < 25 μm), instruments like the Small Ice Detector (SID) probes, which capture high-resolution spatial light scattering patterns from individual particles down to 1 μm in size, have been developed. In this work, we have proposed a method using Machine Learning techniques to estimate simulated particles’ orientation-averaged projected sizes (PAD) and aspect ratio from their 2D scattering patterns. The two-dimensional light scattering patterns (2DLSP) of hexagonal prisms are computed using the Ray Tracing with Diffraction on Facets (RTDF) model. The 2DLSP cover the same angular range as the SID probes. We generated 2DLSP for 162 hexagonal prisms at 133 orientations for each. In a first step, the 2DLSP were transformed into rotation-invariant Zernike moments (ZMs), which are particularly suitable for analyses of pattern symmetry. Then we used ZMs, summed intensities, and root mean square contrast as inputs to the advanced Machine Learning methods. We created one random forests classifier for predicting prism orientation, 133 orientation-specific (OS) support vector classification models for predicting the prism aspect-ratios, 133 OS support vector regression models for estimating prism sizes, and another 133 OS Support Vector Regression (SVR) models for estimating the size PADs. We have achieved a high accuracy of 0.99 in predicting prism aspect ratios, and a low value of normalized mean square error of 0.004 for estimating the particle’s size and size PADs.Peer reviewe

Computing global shape measures

Global shape measures are a convenient way to describe regions. They are generally simple and efficient to extract, and provide an easy means for high level tasks such as classification as well as helping direct low-level computer vision processes such as segmentation. In this chapter a large selection of global shape measures (some from the standard literature as well as other newer methods) are described and demonstrated

LEARNING VISUAL FEATURES FOR GRASP SELECTION AND CONTROL

J. J. Gibson suggested that objects in our environment can be represented by an agent in terms of the types of actions that the agent may perform on or with that object. This affordance representation allows the agent to make the connection between the perception of key properties of an object and these actions. In this dissertation, I explore the automatic construction of visual representations that are associated with components of objects that afford certain types of grasping actions. I propose that the type of grasp used on a class of objects should form the basis of these visual representations. The visual categories are driven by grasp types. A grasp type is defined as a cluster of grasp samples in the 6D hand position and orientation space relative to the object. Specifically, for each grasp type, a set of view-dependent visualoperators can be learned that match the appearance of the part of the object that is to be grasped. By focusing on object parts, as opposed to entire objects, the resulting visual operators can generalize across different object types that exhibit some similarities in 3D shape. In this dissertation, the training/testing data set is composed of a large set of example grasps made by a human teacher, and includes a set of fifty unique objects. Each grasp example consists of a stereo image pair of the object alone, a stereo image pair of the object being grasped, and information about the 3D pose of the hand relative to the object. The grasp regions in a training/testing image that correspond to locations at which certain grasp types could be applied to the object are automatically estimated. First, I show that classes of objects can beformed on the basis of how the individual objects are grasped. Second, I show that visual models based on Pair of Adjacent Segments (PAS) features can capture view-dependent similarities in object part appearance for different objects of the same class. Third, I show that these visual operators can suggest grasp types and hand locationsand orientations for novel objects in novel scenarios. Given a novel image of a novel object, the proposed algorithm matches the learned shape models to this image. A match of the shape model in a novel image is interpreted as that the corresponding component of the image affords a particular grasp action. Experimental results show that the proposed algorithm is capable of identifying the occurrence of learned grasp options in images containing novel objects

Predicting Landslides Using Locally Aligned Convolutional Neural Networks

Landslides, movement of soil and rock under the influence of gravity, are common phenomena that cause significant human and economic losses every year. Experts use heterogeneous features such as slope, elevation, land cover, lithology, rock age, and rock family to predict landslides. To work with such features, we adapted convolutional neural networks to consider relative spatial information for the prediction task. Traditional filters in these networks either have a fixed orientation or are rotationally invariant. Intuitively, the filters should orient uphill, but there is not enough data to learn the concept of uphill; instead, it can be provided as prior knowledge. We propose a model called Locally Aligned Convolutional Neural Network, LACNN, that follows the ground surface at multiple scales to predict possible landslide occurrence for a single point. To validate our method, we created a standardized dataset of georeferenced images consisting of the heterogeneous features as inputs, and compared our method to several baselines, including linear regression, a neural network, and a convolutional network, using log-likelihood error and Receiver Operating Characteristic curves on the test set. Our model achieves 2-7% improvement in terms of accuracy and 2-15% boost in terms of log likelihood compared to the other proposed baselines.Comment: Published in IJCAI 202

Regular Pattern Detection and Analysis Using Shapelets

The presence of regular patterns in natural and technological phenomena is pervasive, often being present in both time and space. To increase our understanding of many phenomena where patterns are present, measurable quantities or metrics are typically defined and used for quantitative analysis. In many fields of study, methods for robustly computing these metrics do not exist, impeding further progress in these areas. Self-assembled materials is one area where significant advances in microscopy techniques have enabled the generation of detailed imaging of self-assembled domains. Unfortunately, image analysis methods to quantify self-assembly patterns in this imaging data either do not exist or are severely limited in their applicability. With the ability to acquire this data but not quantify it, scientists and engineers face significant challenges in determining relationships between structure and properties of these materials. In this work, a generalized method for the quantitative analysis of pattern images is developed which addresses many of the existing challenges, specifically for the field of self-assembled materials. The presented method is based upon a family of localized functions called shapelets and is fundamentally different from existing approaches. The method is composed of sets of shapelets reformulated to be "steerable" filters and a guided machine learning algorithm. We demonstrate using realistic surface self-assembly data that this approach is able to quantitatively distinguish between uniform (defect-free) and non-uniform (strained, defects) regions within the imaged self-assembled domains. In addition to being a fundamental departure from existing pattern analysis methods, we show that the presented method provides a generalized (pattern agnostic) analysis method with significantly enhanced resolution (pixel-level) compared to existing techniques (pattern feature-level)