Abstract
Recent work on virtual reality navigation in humans has suggested that navigational success is inversely correlated with the fractal dimension (FD) of artificial scenes. Here we investigate the generality of this claim by analysing the relationship between the fractal dimension of natural insect navigation environments and a quantitative measure of the navigational information content of natural scenes. We show that the fractal dimension of natural scenes is in general inversely proportional to the information they provide to navigating agents on heading direction as measured by the rotational image difference function (rotIDF). The rotIDF determines the precision and accuracy with which the orientation of a reference image can be recovered or maintained and the range over which a gradient descent in image differences will find the minimum of the rotIDF, that is the reference orientation. However, scenes with similar fractal dimension can differ significantly in the depth of the rotIDF, because FD does not discriminate between the orientations of edges, while the rotIDF is mainly affected by edge orientation parallel to the axis of rotation. We present a new equation for the rotIDF relating navigational information to quantifiable image properties such as contrast to show (1) that for any given scene the maximum value of the rotIDF (its depth) is proportional to pixel variance and (2) that FD is inversely proportional to pixel variance. This contrast dependence, together with scene differences in orientation statistics, explains why there is no strict relationship between FD and navigational information. Our experimental data and their numerical analysis corroborate these results.
Highlights
Navigation is a vital ability for humans and animals and it relies on spatial representations of their environments
We conclude that neighbouring places in the natural world do differ in their fractal dimension, but that changes in illumination caused by the movement of the sun, shadows, winddriven vegetation and clouds can cause large changes in FD
We have further shown that the geometric complexity of natural scenes and the navigational information they provide are related through image pixel variance and image contrast
Summary
Navigation is a vital ability for humans and animals and it relies on spatial representations of their environments. One of the most influential concepts originating in insect navigation research is the snapshot hypothesis, which was derived from classical experiments on bees [1] and ants [2]. According to this hypothesis, insects store panoramic snapshots when looking back at goal locations such as the nest or a food source and are able to return to such goals by deriving navigational instructions from a comparison between current views with. It has subsequently been shown that panoramic image differences develop smoothly with distance from a reference location (translational image differences: transIDF) in natural environments and in addition provide robust local visual compass information (rotational image differences: rotIDF) [3,4,5,6,7]
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