Analysis of Local Image Structure using Intersections of Conics

We propose an algorithm for the analysis of local image structure that is able to distinguish between a number of different structures like corners, crossings, y-junctions, t-junctions, lines and line segments. Furthermore, parameters of the detected structures can be evaluated, as, for example, the opening angle of corners. The main idea of the algorithm is to fit the intersection of two conics to the local image structure. The results of the algorithm when applied to synthetic and real data will be presented

Dense Image Point Matching through Propagation of Local Constraints

We present a conceptually simple algorithm for dense image point matching between two multi-modal (e.g. color) images. The algorithm is based on the assumption that correct image point matches satisfy locally a particular statistical distribution. Through an iterative evaluation of a local probability measure, global constraints are taken into account and the most likely set of image point matches is found. An advantage of this approach is that no information about the camera geometries, as for example the epipoles, has to be known. Therefore, the algorithm may be used for stereo matching and optic flow

Aspects of Geometric Algebra in Euclidean, Projective and Conformal Space

This report is meant to be a script of a tutorial on Clifford (or Geometric) algebra. It is therefore not complete in the description of the algebra and neither completely rigorous. The reader is also not likely to be able to perform arbitrary calculations with Clifford algebra after reading this script. The goal of this text is to give the reader a feeling for what Clifford algebra is about and how it may be used. It is attempted to convey the basic ideas behind the use of Clifford algebra in the description of geometry in Euclidean, projective and conformal space

The Twist Representation of Shape

We give a contribution to the representation problem of free-form curves and surfaces. Our proposal is an operational or kinematic approach based on the Lie group SE(3). While in Euclidean space the modelling of shape as orbit of a point under the action of SE(3) is limited, we are embedding our problem into the conformal geometric algebra R_4,1 of the Euclidean space R^3. This embedding results in a number of advantages which makes the proposed method a universal and flexible one with respect to applications. Especially advantagous is the equivalence of the proposed shape model to that of the Fourier representations

Pose Estimation 3D Free-form Contours

In this report we discuss the 2D-3D pose estimation problem of 3D free-form contours. In our scenario we observe objects of any 3D shape in an image of a calibrated camera. Pose estimation means to estimate the relative position and orientation (containing a rotation $R$ and translation $T$) of the 3D object to the reference camera system. The fusion of modeling free-form contours within the pose estimation problem is achieved by using the conformal geometric algebra. The conformal geometric algebra is a geometric algebra which models entities as stereographic projected entities in an homogeneous model. This leads to a linear description of kinematics on the one hand and projective geometry on the other hand. To model free-form contours in the conformal framework we use twists to model cycloidal curves as twist-depending functions and interpret $n$-times nested cycloidal curves as functions generated by 3D Fourier descriptors. This means, we use the twist concept to apply a spectral domain representation of 3D contours within the pose estimation problem. We will show that twist representations of objects can numerically efficient and easily be applied to the pose estimation problem. The pose problem itself is formalized as implicit problem and we gain constraint equations, which have to be fulfilled with respect to the unknown rigid body motion. Several experiments visualize the robustness and real-time performance of our algorithms

Neoclassical Theory of Elementary Charges with Spin of 1/2

We advance here our neoclassical theory of elementary charges by integrating into it the concept of spin of 1/2. The developed spinorial version of our theory has many important features identical to those of the Dirac theory such as the gyromagnetic ratio, expressions for currents including the spin current, and antimatter states. In our theory the concepts of charge and anticharge relate naturally to their "spin" in its rest frame in two opposite directions. An important difference with the Dirac theory is that both the charge and anticharge energies are positive whereas their frequencies have opposite signs

FIMic: design for ultimate 3D-integral microscopy of in-vivo biological samples

In this work, Fourier integral microscope (FIMic), an ultimate design of 3D-integral microscopy, is presented. By placing a multiplexing microlens array at the aperture stop of the microscope objective of the host microscope, FIMic shows extended depth of field and enhanced lateral resolution in comparison with regular integral microscopy. As FIMic directly produces a set of orthographic views of the 3D-micrometer-sized sample, it is suitable for real-time imaging. Following regular integral-imaging reconstruction algorithms, a 2.75-fold enhanced depth of field and √2-time better spatial resolution in comparison with conventional integral microscopy is reported. Our claims are supported by theoretical analysis and experimental images of a resolution test target, cotton fibers, and in-vivo 3D-imaging of biological specimens

Refocusing distance of a standard plenoptic camera

Recent developments in computational photography enabled variation of the optical focus of a plenoptic camera after image exposure, also known as refocusing. Existing ray models in the field simplify the camera’s complexity for the purpose of image and depth map enhancement, but fail to satisfyingly predict the distance to which a photograph is refocused. By treating a pair of light rays as a system of linear functions, it will be shown in this paper that its solution yields an intersection indicating the distance to a refocused object plane. Experimental work is conducted with different lenses and focus settings while comparing distance estimates with a stack of refocused photographs for which a blur metric has been devised. Quantitative assessments over a 24 m distance range suggest that predictions deviate by less than 0.35 % in comparison to an optical design software. The proposed refocusing estimator assists in predicting object distances just as in the prototyping stage of plenoptic cameras and will be an essential feature in applications demanding high precision in synthetic focus or where depth map recovery is done by analyzing a stack of refocused photographs

Higher spin quaternion waves in the Klein-Gordon theory

Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order perturbation theory and the result of the Dirac theory is reproduced except for an overall factor of sixteen. The discrepancy is not resolved as the study points into another direction. The vertex structures involved in the scattering calculations indicate the relevance of a modified Klein-Gordon equation, which takes into account the number of polarization states of the considered quantum field. In this equation the d'Alembertian is acting on quaternion-like plane waves, which can be generalized to representations of arbitrary spin. The method provides the same relation between mass and spin that has been found previously by Majorana, Gelfand, and Yaglom in infinite spin theories

Visualising text co-occurrence networks

We present a tool for automatically generating a visual summary of unstructured text data retrieved from documents, web sites or social media feeds. Unlike tools such as word clouds, we are able to visualise structures and topic relationships occurring in a document. These relationships are determined by a unique approach to co-occurrence analysis. The algorithm applies a decaying function to the distance between word pairs found in the original text such that words regularly occurring close to each other score highly, but even words occurring some distance apart will make a small contribution to the overall co-occurrence score. This is in contrast to other algorithms which simply count adjacent words or use a sliding window of fixed size. We show, with examples, how the network generated can be presented in tree or graph format. The tree format allows for the user to interact with the visualisation and expand or contract the data to a preferred level of detail. The tool is available as a web application and can be viewed using any modern web browse