AMinkowski plane is Euclidean iff the two tangent segments from any exterior point to the unit circle have the same length. MSC 2000: 52A10, 46B20, 46C99, 51M04

We introduce the idea of using a perception-based medial point description [9] of a natural form (2D static or in movement) as a framework for a part-based shape representation which can then be efficiently used in biological species identification and matching tasks. The first step is one of fuzzy medialness measurements of 2D segmented objects from intensity images which emphasises main shape...

Digital aerial photography acquired with unmanned aerial vehicles (UAVs) has great value for resource management due to flexibility and relatively low cost for image acquisition. The very high resolution imagery (5 cm) allows for mapping bare soil and vegetation types, structure and patterns in great detail. While image acquisition is relatively straightforward, the creation of orthorectified, ...

The high-precision building exterior facade corner point (BEFCP) is an essential element in topographic and cadastral surveys. However, current extraction methods rely on the interactions of humans with 3D real-scene models produced by unmanned aerial vehicle (UAV) oblique photogrammetry, which have a high workload, low efficiency, poor precision, cannot satisfy requirements automation. dense c...

For many years we have had digital photogrammetric systems available that can perform automatic interior and relative orientation of aerial photographs. Developments in absolute and exterior orientation are not so robust because the problem is significantly more difficult. The reason for the increase in difficulty is that there is no easy way to create the master image or target patch which rep...

Let V be a four-dimensional real vector space with a fixed orientation. Then the wedge product can be viewed, up to a positive factor, as a canonical quadratic form of signature (3, 3) on the six-dimensional space ΛV . This gives a homomorphism from the identity component of the general linear group GL(V ) to the conformal group of the indefinite form, which is a local isomorphism. The signific...

The Hodge dual operator ∗ is one of the 3 basic operations on differential forms. (The other 2 are wedge product ∧ and exterior differentiation d.) However most treatments consider only positive-definite inner products, and there are at least 2 standard ways of generalizing this to inner products of arbitrary signature. We outline here a construction of the Hodge dual operator which works for a...

Algorithms are presented for the determination of whether a given point in is interior to, exterior to or on an arbitrary polygonal boundary and for the determination of whether a point in is interior to, exterior to or on a simple polyhedral boundary. The algorithms are based on the principle of using binary coded coordinate systems and parity counting of the number of intersections of the pol...

We present implicit surface reconstruction algorithms for point clouds. We view the implicit surface reconstruction as a three dimensional binary image segmentation problem that segments the entire space R3 or the computational domain into an interior region and an exterior region while the boundary between these two regions fits the data points properly. The key points with using an image segm...