Stochastic Modeling of Trees in Forest Environments

Our article deals with the detection and model generation of complex objects with curvilinear parts, like trees, with stochastic relaxation. The proposed algorithm can rely on any initial estimation of object parts as a probability map (like those generated by Gaussian mixture models or neural networks) and can model the relation of randomly sampled parts resulting in a structural representation of whole objects. Semantic segmentation by convolutional neural networks or the pose estimation with deep learning of object parts can predict the possible areas or positions of interest, but in many cases, a higher representation of structures is needed for further (e.g., shape or connectivity) analysis. The model validation of such data is straightforward for objects with known structure (like the human body or other rigid things) but tough for such complex objects like trees in forest environments. In our approach, the possible configurations of structures are generated by a marked point process while the optimal state is achieved by a solver based on reversible jump Markov chain Monte Carlo dynamics. The model generator relaxation method itself is unsupervised, no training is required, and our analyses show it has satisfactory stability, regarding detection accuracy, against changing its parameters. Besides giving the theoretical background and algorithmic steps, we present numerical evaluations on three datasets: synthetic trees, another of natural images with different species of trees in various forest environments, and the third is of road maps. The analyzed examples show that our approach, contrary to previous thin line detectors, can handle thin and thick objects.