A new area-based convexity measure with distance weighted area integration for planar shapes

In this paper we propose a new area-based convexity measure. We assume that convexity evaluation of an arbitrary planar shape is related to the total influence of dents of the shape, and discover that those attributes of the dents, such as the position, area, and depth with respect to the Geometric Center of Convex Hull (GCCH) of the shape, determine the dent influence. We consider that the convex hull of the shape consists of infinitely small patches, to each of which we assign a weight showing the patch influence. We can simply integrate all the patch weights in any regions within the convex hull to calculate their total influence. We define this operation as the Distance Weighted Area Integration, if the weight is associated with the Euclidean distance from the patch to the GCCH. Our new measure is a distance weighted generalization of the most commonly used convexity measure, making this conventional measure fully replaceable for the first time. Experiments demonstrate advantages of the new convexity measure against the existing ones

Measuring linearity of curves in 2D and 3D

In this paper we define a new linearity measure for open curve segments in 2D and 3D . The measure considers the distance of the curve end points to the curve centroid. It is simple to compute and has the basic properties that should be satisfied by any linearity measure. The new measure ranges over the interval (0,1], and produces the value 1 if and only if the measured curve is a perfect straight line segment. Also, the new linearity measure is invariant with respect to translations, rotations and scaling transformations. The new measure is theoretically well founded and, because of this, its behaviour can be well understood and predicted to some extent. This is always beneficial because it indicates the suitability of the new measure to the desired application. Several experiments are provided to illustrate the behaviour and to demonstrate the efficiency and applicability of the new linearity measure

Measuring squareness and orientation of shapes

In this paper we propose a measure which defines the degree to which a shape differs from a square. The new measure is easy to compute and being area based, is robust—e.g., with respect to noise or narrow intrusions. Also, it satisfies the following desirable properties: •it ranges over (0,1] and gives the measured squareness equal to 1 if and only if the measured shape is a square; •it is invariant with respect to translations, rotations and scaling. In addition, we propose a generalisation of the new measure so that shape squareness can be computed while controlling the impact of the relative position of points inside the shape. Such a generalisation enables a tuning of the behaviour of the squareness measure and makes it applicable to a range of applications. A second generalisation produces a measure, parameterised by δ, that ranges in the interval (0,1] and equals 1 if and only if the measured shape is a rhombus whose diagonals are in the proportion 1:δ. The new measures (the initial measure and the generalised ones) are naturally defined and theoretically well founded—consequently, their behaviour can be well understood. As a by-product of the approach we obtain a new method for the orienting of shapes, which is demonstrated to be superior with respect to the standard method in several situations. The usefulness of the methods described in the manuscript is illustrated on three large shape databases: diatoms (ADIAC), MPEG-7 CE-1, and trademarks

Measuring linearity of curves in 2D and 3D

In this paper we define a new linearity measure for open curve segments in 2D and 3D . The measure considers the distance of the curve end points to the curve centroid. It is simple to compute and has the basic properties that should be satisfied by any linearity measure. The new measure ranges over the interval (0,1], and produces the value 1 if and only if the measured curve is a perfect straight line segment. Also, the new linearity measure is invariant with respect to translations, rotations and scaling transformations. The new measure is theoretically well founded and, because of this, its behaviour can be well understood and predicted to some extent. This is always beneficial because it indicates the suitability of the new measure to the desired application. Several experiments are provided to illustrate the behaviour and to demonstrate the efficiency and applicability of the new linearity measure

Identification of Change in a Dynamic Dot Pattern and its use in the Maintenance of Footprints

Examples of spatio-temporal data that can be represented as sets of points (called dot patterns) are pervasive in many applications, for example when tracking herds of migrating animals, ships in busy shipping channels and crowds of people in everyday life. The use of this type of data extends beyond the standard remit of Geographic Information Science (GISc), as classification and optimisation problems can often be visualised in the same manner. A common task within these fields is the assignment of a region (called a footprint) that is representative of the underlying pattern. The ways in which this footprint can be generated has been the subject of much research with many algorithms having been produced. Much of this research has focused on the dot patterns and footprints as static entities, however for many of the applications the data is prone to change. This thesis proposes that the footprint need not necessarily be updated each time the dot pattern changes; that the footprint can remain an appropriate representation of the pattern if the amount of change is slight. To ascertain the appropriate times at which to update the footprint, and when to leave it as it is, this thesis introduces the concept of change identifiers as simple measures of change between two dot patterns. Underlying the change identifiers is an in-depth examination of the data inherent in the dot pattern and the creation of descriptors that represent this data. The experimentation performed by this thesis shows that change identifiers are able to distinguish between different types of change across dot patterns from different sources. In doing so the change identifiers reduce the number of updates of the footprint while maintaining a measurably good representation of the dot pattern

Using an anisotropic diffusion scale-space for the detection and delineation of shacks in informal settlement imagery

PhD, Faculty of Engineering and the Built Environment, University of the Witwatersrand, 2010Informal settlements are a growing world-wide phenomenon. Up-to-date spatial information mapping settlements is essential for a variety of end-user applications from planning settlement upgrading to monitoring expansion and infill. One method of gathering this information is through the analysis of nadir-view aerial imagery and the automated or semi-automated extraction of individual shacks. The problem of shack detection and delineation in, particularly South African, informal settlements is a unique and difficult one. This is primarily due to the inhomogeneous appearance of shack roofs, which are constructed from a variety of disparate materials, and the density of shacks. Previous research has focused mostly on the use of height data in conjunction with optical images to perform automated or semi-automated shack extraction. In this thesis, a novel approach to automating shack extraction is presented and prototyped, in which the appearance of shack roofs is homogenised, facilitating their detection. The main features of this strategy are: construction of an anisotropic scale-space from a single source image and detection of hypotheses at multiple scales; simplification of hypotheses' boundaries through discrete curve evolution and regularisation of boundaries in accordance with an assumed shack model - a 4-6 sided, compact, rectilinear shape; selection of hypotheses competing across scales using fuzzy rules; grouping of hypotheses based on their support for one another, and localisation and re-regularisation of boundaries through the incorporation of image edges. The prototype's performance is evaluated in terms of standard metrics and is analysed for four different images, having three different sets of imaging conditions, and containing well over a hundred shacks. Detection rates in terms of building counts vary from 83% to 100% and, in terms of roof area coverage, from 55% to 84%. These results, each derived from a single source image, compare favourably with those of existing shack detection systems, especially automated ones which make use of richer source data. Integrating this scale-space approach with height data offers the promise of even better results

A two-component rectilinearity measure

Recently several approaches for measuring the rectilinearity of shapes have been published [P.L. Rosin, J. Žunić, Measuring rectilinearity, Computer Vision and Image Understanding, 99(2) (2005) 175–188; J. Žunić, P.L. Rosin, Rectilinearity measurements for polygons, IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(9) (2003) 1193–1200]. This paper generalises the and measures defined by Žunić and Rosin [J. Žunić, P.L. Rosin, Rectilinearity measurements for polygons, IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(9) (2003) 1193–1200] to detect rectilinearity in two new situations: (1) the polygon has been skewed and (2) the shape contains two rectilinear components oriented differently to each other