Convergence analysis and validation of low cost distance metrics for computational cost reduction of the Iterative Closest Point algorithm

The Iterative Closest Point algorithm (ICP) is commonly used in engineering applications to solve the rigid registration problem of partially overlapped point sets which are pre-aligned with a coarse estimate of their relative positions. This iterative algorithm is applied in many areas such as the medicine for volumetric reconstruction of tomography data, in robotics to reconstruct surfaces or scenes using range sensor information, in industrial systems for quality control of manufactured objects or even in biology to study the structure and folding of proteins. One of the algorithm’s main problems is its high computational complexity (quadratic in the number of points with the non-optimized original variant) in a context where high density point sets, acquired by high resolution scanners, are processed. Many variants have been proposed in the literature whose goal is the performance improvement either by reducing the number of points or the required iterations or even enhancing the complexity of the most expensive phase: the closest neighbor search. In spite of decreasing its complexity, some of the variants tend to have a negative impact on the final registration precision or the convergence domain thus limiting the possible application scenarios. The goal of this work is the improvement of the algorithm’s computational cost so that a wider range of computationally demanding problems from among the ones described before can be addressed. For that purpose, an experimental and mathematical convergence analysis and validation of point-to-point distance metrics has been performed taking into account those distances with lower computational cost than the Euclidean one, which is used as the de facto standard for the algorithm’s implementations in the literature. In that analysis, the functioning of the algorithm in diverse topological spaces, characterized by different metrics, has been studied to check the convergence, efficacy and cost of the method in order to determine the one which offers the best results. Given that the distance calculation represents a significant part of the whole set of computations performed by the algorithm, it is expected that any reduction of that operation affects significantly and positively the overall performance of the method. As a result, a performance improvement has been achieved by the application of those reduced cost metrics whose quality in terms of convergence and error has been analyzed and validated experimentally as comparable with respect to the Euclidean distance using a heterogeneous set of objects, scenarios and initial situations.

Detection and mapping of burnt areas from time series of MODIS-derived NDVI data in a Mediterranean region

Moderate resolution remote sensing data, as provided by MODIS, can be used to detect and map active or past wildfires from daily records of suitable combinations of reflectance bands. The objective of the present work was to develop and test simple algorithms and variations for automatic or semiautomatic detection of burnt areas from time series data of MODIS biweekly vegetation indices for a Mediterranean region. MODIS-derived NDVI 250m time series data for the Valencia region, East Spain, were subjected to a two-step process for the detection of candidate burnt areas, and the results compared with available fire event records from the Valencia Regional Government. For each pixel and date in the data series, a model was fitted to both the previous and posterior time series data. Combining drops between two consecutive points and 1-year average drops, we used discrepancies or jumps between the pre and post models to identify seed pixels, and then delimitated fire scars for each potential wildfire using an extension algorithm from the seed pixels. The resulting maps of the detected burnt areas showed a very good agreement with the perimeters registered in the database of fire records used as reference. Overall accuracies and indices of agreement were very high, and omission and commission errors were similar or lower than in previous studies that used automatic or semiautomatic fire scar detection based on remote sensing. This supports the effectiveness of the method for detecting and mapping burnt areas in the Mediterranean region.