KDT-SPSO: A multimodal particle swarm optimisation algorithm based on k-d trees for palm tree detection

Palm tree detection, as any other problem of object localisation in an image, can be formulated mathematically as a multimodal optimisation problem that seeks for the best set of positions and scales that maximise the classification score. In recent decades, many bio-inspired multimodal optimisation algorithms using different niching techniques have been proven effective and robust in solving optimisation problems. In many niching-based algorithms, e.g., species-based particle swarm optimisation (SPSO), repetitive distance evaluations to search for nearest neighbours are unavoidable to find multiple optima in the search space, which are computationally expensive. In this paper, we propose an improved SPSO named KDT-SPSO to speed up the nearest neighbour search using a special tree-based structure, called k-d tree. KDT-SPSO reduces the computation complexity by only visiting the subtrees that most likely contain the neighbours. We statistically tested KDT-SPSO on a number of benchmark functions and the results showed that it was up to 48% faster than the original SPSO. After proving its effectiveness, we optimised the parameters of KDT-SPSO for palm tree detection and introduced a restart mechanism to speed up its convergence and to improve the recall rate. The local binary pattern (LBP) feature extractor and modified support vector machine (SVM) classifier with radial basis function (RBF) kernel were used to compute the fitness value of palm trees. The optimised KDT-SPSO was able to achieve on average 91.80% palm tree detection accuracy and 5 times faster than the traditional sliding window approach.