Mathematical Methods for IoT-Based Annotating Object Datasets with Bounding Boxes

Object datasets used in the construction of object detectors are typically annotated with horizontal or oriented bounding rectangles for IoT-based. The optimality of an annotation is obtained by fulfilling two conditions: (i) the rectangle covers the whole object and (ii) the area of the rectangle is minimal. Building a large-scale object dataset requires annotators with equal manual dexterity to carry out this tedious work. When an object is horizontal for IoT-based, it is easy for the annotator to reach the optimal bounding box within a reasonable time. However, if the object is oriented, the annotator needs additional time to decide whether the object will be annotated with a horizontal rectangle or an oriented rectangle for IoT-based. Moreover, in both cases, the final decision is not based on any objective argument, and the annotation is generally not optimal. In this study, we propose a new method of annotation by rectangles for IoT-based, called robust semi-automatic annotation, which combines speed and robustness. Our method has two phases. The first phase consists in inviting the annotator to click on the most relevant points located on the contour of the object. The outputs of the first phase are used by an algorithm to determine a rectangle enclosing these points. To carry out the second phase, we develop an algorithm called RANGE-MBR, which determines, from the selected points on the contour of the object, a rectangle enclosing these points in a linear time. The rectangle returned by RANGE-MBR always satisfies optimality condition (i). We prove that the optimality condition (ii) is always satisfied for objects with isotropic shapes. For objects with anisotropic shapes, we study the optimality condition (ii) by simulations. We show that the rectangle returned by RANGE-MBR is quasi-optimal for the condition (ii) and that its performance increases with dilated objects, which is the case for most of the objects appearing on images collected by aerial photography.