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Knot placement for curve approximation is a well known and yet open problem in geometric modeling. Selecting knot values that yield good approximations is a challenging task, based largely on heuristics and user experience. More advanced approaches range from parametric averaging to genetic algorithms.
In this paper, we propose to use Support Vector Machines (SVMs) to determine suitable knot vectors for B-spline curve approximation. The SVMs are trained to identify locations in a sequential point cloud where knot placement will improve the approximation error. After the training phase, the SVM can assign, to each point set location, a so-called score. This score is based on geometric and differential geometric features of points. It measures the quality of each location to be used as knots in the subsequent approximation. From these scores, the final knot vector can be constructed exploring the topography of the score-vector without the need for iteration or optimization in the approximation process. Knot vectors computed with our approach outperform state of the art methods and yield tighter approximations.
FishNet
(2016)
Mapping of tree seedlings is useful for tasks ranging from monitoring natural succession and regeneration to effective silvicultural management. Development of methods that are both accurate and cost-effective is especially important considering the dramatic increase in tree planting that is required globally to mitigate the impacts of climate change. The combination of high-resolution imagery from unmanned aerial vehicles and object detection by convolutional neural networks (CNNs) is one promising approach. However, unbiased assessments of these models and methods to integrate them into geospatial workflows are lacking. In this study, we present a method for rapid, large-scale mapping of young conifer seedlings using CNNs applied to RGB orthomosaic imagery. Importantly, we provide an unbiased assessment of model performance by using two well-characterised trial sites together containing over 30,000 seedlings to assemble datasets with a high level of completeness. Our results showed CNN-based models trained on two sites detected seedlings with sensitivities of 99.5% and 98.8%. False positives due to tall weeds at one site and naturally regenerating seedlings of the same species led to slightly lower precision of 98.5% and 96.7%. A model trained on examples from both sites had 99.4% sensitivity and precision of 97%, showing applicability across sites. Additional testing showed that the CNN model was able to detect 68.7% of obscured seedlings missed during the initial annotation of the imagery but present in the field data. Finally, we demonstrate the potential to use a form of weakly supervised training and a tile-based processing chain to enhance the accuracy and efficiency of CNNs applied to large, high-resolution orthomosaics.