How to reliably estimate the tortuosity of an animal's path:

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.

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“…5 As expected, there is substantial confusion between certain classes (e.g. "0" and "8"; "2", "6" and "9"; "4" and "7").…”

supporting

confidence: 60%

“…This is a natural and simple definition which is also called the straightness index (or simply straightness) [5].…”

Section: Introductionmentioning

confidence: 99%

Measuring linearity of curves in 2D and 3D

Rosin

Pantović

Žunić

2016

Pattern Recognition

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“…HMMs can be simple (few states), but have large error around them, or complicated to the extreme case of one state per observation and zero error. As a model selection exercise, we trained a series of candidate HMMs with an increasing number of putative states (2)(3)(4)(5)(6)(7)(8)(9)(10). The iterative addition of states (each explaining fewer observations with less error) increased log-likelihood monotonically, favouring over-fitting of complex (many state) models.…”

Section: Model Trainingmentioning

confidence: 99%

“…Many tracking studies use recorded locations to examine movement and habitat use only in broad terms [3][4][5][6], leaving key questions about where and when animals engage in specific behaviours unanswered. However, behaviour may be inferred by characterizing patterns of movement based solely on the geometry or complexity of an animal's path using techniques such as tortuosity [8,9], positional entropy [10,11] or first-passage time [12]. In addition, modelling approaches such as Gaussian mixtures have been used to classify animal tracking data into discrete modes of movement [2,13], while state-space models including hidden Markov models (HMMs) [10,[14][15][16][17][18][19] have been used to identify different modes of movement and the dynamics of switching between them.…”

Section: Introductionmentioning

confidence: 99%

Behavioural mapping of a pelagic seabird: combining multiple sensors and a hidden Markov model reveals the distribution of at-sea behaviour

Dean

Freeman

Kirk

et al. 2013

J. R. Soc. Interface.

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The use of miniature data loggers is rapidly increasing our understanding of the movements and habitat preferences of pelagic seabirds. However, objectively interpreting behavioural information from the large volumes of highly detailed data collected by such devices can be challenging. We combined three biologging technologies-global positioning system (GPS), saltwater immersion and time-depth recorders-to build a detailed picture of the at-sea behaviour of the Manx shearwater (Puffinus puffinus) during the breeding season. We used a hidden Markov model to explore discrete states within the combined GPS and immersion data, and found that behaviour could be organized into three principal activities representing (i) sustained direct flight, (ii) sitting on the sea surface, and (iii) foraging, comprising tortuous flight interspersed with periods of immersion. The additional logger data verified that the foraging activity corresponded well to the occurrence of diving. Applying this approach to a large tracking dataset revealed that birds from two different colonies foraged in local waters that were exclusive, but overlapped in one key area: the Irish Sea Front (ISF). We show that the allocation of time to each activity differed between colonies, with birds breeding furthest from the ISF spending the greatest proportion of time engaged in direct flight and the smallest proportion of time engaged in foraging activity. This type of analysis has considerable potential for application in future biologging studies and in other taxa.

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“…Finally, they underwent six further individual releases (S2) to determine to what extent they would maintain the performance level of flock navigation. We also calculated the straightness index D/L for each track, in which D is the beeline distance from the starting point to the goal, and L is the path actually followed by the animal (Batschelet 1981;Benhamou 2004). This is a scale independent measure and, given the high recording frequency of one positional fix per second, a reliable estimator of the efficiency of the orientation process already used also by other authors (i.e.…”

Section: Subjects and General Proceduresmentioning

confidence: 99%

Flock flying improves pigeons' homing: GPS track analysis of individual flyers versus small groups

et al. 2008

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The effects of aggregation in navigating animals have generated growing interest in field and theoretical studies. The few studies on the effects of group flying on the performance of homing pigeons (Columba livia) have led to controversial conclusions, chiefly because of the lack of appropriate technology to follow pigeons during their entire homeward flight. Therefore, we used GPS data-loggers in six highly pre-trained pigeons from a familiar release site first by releasing them six times individually, then six times as a group from the same site, and finally, again six times individually. Flight data showed that the homing performance of the birds flying as a flock was significantly better than that of the birds released individually. When flying in a flock, pigeons showed no resting episodes, shorter homing times, higher speed, and almost no circling around the start zone in comparison to individual flights. Moreover, flock-flying pigeons took a nearly direct, "beeline" route to the loft, whereas individually flying birds preferred to follow roads and other longitudinal landmarks leading towards the loft, even when it caused a detour. Our results show that group cohesion facilitates a shift towards more efficient homing strategies: individuals prefer navigating by familiar landmarks, while flocks show a compass orientation.

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How to reliably estimate the tortuosity of an animal's path:

Cited by 444 publications

References 37 publications

Measuring linearity of curves in 2D and 3D

Measuring linearity of curves in 2D and 3D

Behavioural mapping of a pelagic seabird: combining multiple sensors and a hidden Markov model reveals the distribution of at-sea behaviour

Flock flying improves pigeons' homing: GPS track analysis of individual flyers versus small groups

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