Depth-first random forests with improved Grassberger entropy for small object detection

This paper proposes a random forests-based method appropriate for detecting small objects such as Unmanned Aerial Vehicles (UAVs) and aircrafts when these objects occupy a small portion within an image filmed by an autonomously moving camera. Random forests classifiers are machine learning methods that manage an accurate prediction ability and are computationally efficient both during training and testing. In the random forests classifier model, the split node data is divided into left and right child node data based on the optimal split parameter determined by the node having the maximum information gain, which is calculated based on information entropy. It is well known that the information entropy estimation procedure is biased, and therefore we replace it with an improved Grassberger entropy scheme that achieves a better random forests classifier. Grassberger entropy is improved in terms of its representation and digamma function properties, and we adequately justify its validity. Although a breadth-first training scheme is a natural choice, it uses excessive memory when the tree grows to deeper layers. To compensate, a depth-first recursive training random forests classifier is used, where only one node is split in each recursive process. A depth-first recursive training random forests classifier uses a constant amount of memory to deal with underfitting. The performance of the proposed method is evaluated on classification and object detection datasets. The experimental results demonstrate that the improved Grassberger entropy estimation improves predictive performance, and the tree generated by the depth-first method suppresses underfitting. We believe that employing a depth-first random forests classifier with an improved Grassberger entropy is appealing and effective for real-world applications.