A Solution for Multi-Alignment by Transformation Synchronisation

The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered usually iterative methods are used. In practice the iterative methods perform well if the relative transformations between any pair of objects are free of noise. However, if only noisy relative transformations are available (e.g. due to missing data or wrong correspondences) the iterative methods may fail. Based on the observation that the underlying noise-free transformations can be retrieved from the null space of a matrix that can directly be obtained from pairwise alignments, this paper presents a novel method for the synchronisation of pairwise transformations such that they are transitively consistent. Simulations demonstrate that for noisy transformations, a large proportion of missing data and even for wrong correspondence assignments the method delivers encouraging results.Comment: Accepted for CVPR 2015 (please cite CVPR version

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

Ball-Scale Based Hierarchical Multi-Object Recognition in 3D Medical Images

This paper investigates, using prior shape models and the concept of ball scale (b-scale), ways of automatically recognizing objects in 3D images without performing elaborate searches or optimization. That is, the goal is to place the model in a single shot close to the right pose (position, orientation, and scale) in a given image so that the model boundaries fall in the close vicinity of object boundaries in the image. This is achieved via the following set of key ideas: (a) A semi-automatic way of constructing a multi-object shape model assembly. (b) A novel strategy of encoding, via b-scale, the pose relationship between objects in the training images and their intensity patterns captured in b-scale images. (c) A hierarchical mechanism of positioning the model, in a one-shot way, in a given image from a knowledge of the learnt pose relationship and the b-scale image of the given image to be segmented. The evaluation results on a set of 20 routine clinical abdominal female and male CT data sets indicate the following: (1) Incorporating a large number of objects improves the recognition accuracy dramatically. (2) The recognition algorithm can be thought as a hierarchical framework such that quick replacement of the model assembly is defined as coarse recognition and delineation itself is known as finest recognition. (3) Scale yields useful information about the relationship between the model assembly and any given image such that the recognition results in a placement of the model close to the actual pose without doing any elaborate searches or optimization. (4) Effective object recognition can make delineation most accurate.Comment: This paper was published and presented in SPIE Medical Imaging 201

Digital design of medical replicas via desktop systems: shape evaluation of colon parts

In this paper, we aim at providing results concerning the application of desktop systems for rapid prototyping of medical replicas that involve complex shapes, as, for example, folds of a colon. Medical replicas may assist preoperative planning or tutoring in surgery to better understand the interaction among pathology and organs. Major goals of the paper concern with guiding the digital design workflow of the replicas and understanding their final performance, according to the requirements asked by the medics (shape accuracy, capability of seeing both inner and outer details, and support and possible interfacing with other organs). In particular, after the analysis of these requirements, we apply digital design for colon replicas, adopting two desktop systems. ,e experimental results confirm that the proposed preprocessing strategy is able to conduct to the manufacturing of colon replicas divided in self-supporting segments, minimizing the supports during printing. ,is allows also to reach an acceptable level of final quality, according to the request of having a 3D presurgery overview of the problems. ,ese replicas are compared through reverse engineering acquisitions made by a structured-light system, to assess the achieved shape and dimensional accuracy. Final results demonstrate that low-cost desktop systems, coupled with proper strategy of preprocessing, may have shape deviation in the range of ±1 mm, good for physical manipulations during medical diagnosis and explanation

Galaxy density profiles and shapes -- I. simulation pipeline for lensing by realistic galaxy models

Studies of strong gravitational lensing in current and upcoming wide and deep photometric surveys, and of stellar kinematics from (integral-field) spectroscopy at increasing redshifts, promise to provide valuable constraints on galaxy density profiles and shapes. However, both methods are affected by various selection and modelling biases, whch we aim to investigate in a consistent way. In this first paper in a series we develop a flexible but efficient pipeline to simulate lensing by realistic galaxy models. These galaxy models have separate stellar and dark matter components, each with a range of density profiles and shapes representative of early-type, central galaxies without significant contributions from other nearby galaxies. We use Fourier methods to calculate the lensing properties of galaxies with arbitrary surface density distributions, and Monte Carlo methods to compute lensing statistics such as point-source lensing cross-sections. Incorporating a variety of magnification bias modes lets us examine different survey limitations in image resolution and flux. We rigorously test the numerical methods for systematic errors and sensitivity to basic assumptions. We also determine the minimum number of viewing angles that must be sampled in order to recover accurate orientation-averaged lensing quantities. We find that for a range of non-isothermal stellar and dark matter density profiles typical of elliptical galaxies, the combined density profile and corresponding lensing properties are surprisingly close to isothermal around the Einstein radius. The converse implication is that constraints from strong lensing and/or stellar kinematics, which are indeed consistent with isothermal models near the Einstein radius, cannot trivially be extrapolated to smaller and larger radii.Comment: 31 pages, 15 figures; paper II at arXiv:0808.2497; accepted for publication in MNRAS; PDF file with full resolution figures at http://www.sns.ias.edu/~glenn/paper1.pd

A flexible geometric model for leaf shape descriptions with high accuracy

Accurate assessment of canopy structure is crucial in studying plant-environment interactions. The advancement of functional-structural plant models (FSPM), which incorporate the 3D structure of individual plants, increases the need for a method for accurate mathematical descriptions of leaf shape. A model was developed as an improvement of an existing leaf shape algorithm to describe a large variety of leaf shapes. Modelling accuracy was evaluated using a spatial segmentation method and shape differences were assessed using principal component analysis (PCA) on the optimised parameters. Furthermore, a method is presented to calculate the mean shape of a dataset, intended for obtaining a representative shape for modelling purposes. The presented model is able to accurately capture a large range of single, entire leaf shapes. PCA illustrated the interpretability of the parameter values and allowed evaluation of shape differences. The model parameters allow straightforward digital reconstruction of leaf shapes for modelling purposes such as FSPMs