Aaron Mavrinac

Hector: Alright, explain your game to me, Mr. Hare. Hare: First, I will stand somewhere along the race track, but I won’t tell you where, and this wall hides me from view. Now, do you see this large contraption here? Hector: Indeed. There is a -meter long net suspended from a high cable that extends [...]

In my AIM 2010 paper, I describe how to obtain a projective transformation from the image plane to the laser plane in a line laser 3D range imaging system. With the laser oriented vertically (i.e. perpendicular to the transport direction of the object being scanned), this allows for mapping of image coordinates directly to 3D [...]

Adolphus finally quit messing around and started using a quaternion representation for rotations internally! The quaternion class itself is simple, and conversion to and from rotation matrix and axis-angle representations is fairly straightforward. The magic happens in converting from Euler angles — all twelve valid conventions! By solving the conversion to quaternion for all twelve [...]

I humbly entreat any analytical intellects of greater constitution than my own (of which, to be sure, there is no dearth) to enlighten me in matters mathematical. First of all, if I have a 5-dimensional space which consists of a 3-dimensional Euclidean space plus direction (defined by inclination and azimuth) — that is, the set [...]

In my M.A.Sc. work on stereo camera network calibration, I made use of a series of graphs to describe the relationships between nodes. Existing work had already produced the vision graph and what I will call the transition graph (after Farrell and Davis‘ transition model). In both graphs, each vertex represents a node (camera or [...]

There have been a number of approaches to build topological models of multi-camera networks. The idea is to represent, in some useful and relatively simple mathematical way, the relationship — usually meaning the overlap — between the fields of view of the cameras. To date, it seems as though all such methods fall into two [...]

I like Gabor Herman‘s definition of discrete Euclidean space. He defines, for any positive real number and any positive integer : This chops N-space up into a square (cubic, etc.) Bravais lattice, with primitive vectors of magnitude . Each point in the discrete space is then associated with a primitive cell (or Voronoi neighbourhood, in [...]

You have a right-handed Cartesian coordinate basis of a three-dimensional Euclidean space, with axes , , and . You’re given some spatial-directional vectors of the form , where and are, respectively, the inclination angle (from the positive -axis zenith) and the azimuth angle (measured right-handed from the positive -axis) of an associated direction, which is [...]

How does one define the strength of a path in a fuzzy graph? Mathew and Sunitha state that “the degree of membership of a weakest [edge] is defined as [a path's] strength” without any apparent justification. Saha and Udupa mention that several measures, including sum, product, and minimum, all seem plausible, but also ultimately choose [...]

My research area at school is distributed smart cameras, a field which is primarily rooted in computer vision. Despite having access to a range of expensive proprietary software libraries by virtue of having purchased the equipment, most of my computer vision work uses a stack of free software running on Gentoo Linux. For interfacing to [...]