Tracking Multiple Circular Objects In Video Using Helmholtz Principle Snehasis Mukherjee and Dipti Prasad Mukherjee Electronics and Communication Sciences Unit Indian Statistical Institute Kolkata, India {snehasis_r, dipti}@isical.ac.in Abstract— A novel algorithm is introduced to track multiple circular objects present in a video using Helmholtz perception principle. First, segmentation of circular objects in the video frame is performed using the perception principle and then same perception principle is applied to track the circular objects. For each circular object present in video, we have taken an assessment of the meaningfulness of the shift of its center of gravity and meaningfulness of the deviation of the direction of movement of the object due to inter-frame displacement. We have shown that a logical threshold in the meaningfulness value tracks circular objects in a video effectively and efficiently. I. INTRODUCTION Recently Gestalt hypotheses are being used for solving several problems of computer vision [1]. In most cases Gestalt theory is used to find meaningful image segment or geometric shape in an image after extracting the image level lines, which are the edges of iso-intensity surfaces present in an image [1,2,3,4]. The term meaningful here refers to the objects present in an image which exhibit some specific features (such as linearity, circularity, rectangularity, etc.) of our interest. Gestalt hypotheses has also been used for detecting circular level lines [3] using the concept of number of false alarms (NFA), where the term false refers to a non-meaningful event. The NFA is the expected number of occurrences of an event, where an event is defined as the occurrences of the features of some pattern in an image. Our contribution in particular is to extend the concept of NFA for tracking multiple circular objects in a video. Here we have estimated meaningful displacements of the circular objects present in any two consecutive frames using the Helmholtz perception principle. Helmholtz principle for images states that every large deviation from randomness in an image should be perceptible, provided, the large deviation corresponds to an a priori fixed list of geometric structures (such as, straight line, circle, rectangle, etc.) [1]. In this paper we have extended this idea to the context of video as, large deviations in any feature (such as displacement of the center of gravity of an object in two consecutive frames) modulo a perceptible limit is meaningful in case of a successful tracking. Well-known approach like Hough Transform is available to detect objects of specific shape in an image frame [5]. The current approach provides equally good result with fewer computations and user selectable parameters. At the same time tracking multiple objects simultaneously in a video is a widely researched topic [6]. However, the proposed approach is less computational intensive compared to competing tracking methods. In this paper we have first detected a set of image level lines [7] from two consecutive frames. Out of these level lines we have picked up a further reduced set of level lines those exhibit regularity in terms of circularity [3]. Then, given a potential circular object in one frame, we calculate the displacement of its centre of gravity (CG) with respect to all the detected circular targets in the next frame. For n number of detected targets in the next frame, n different displacements are calculated. We have estimated a measurement of regularity of these distances. This regularity measure of these distances may be expressed numerically in terms of meaningfulness of an event, the event being the regularity of an object in a frame to be similar to an object in the next frame. At the same time meaningfulness of the potential tracking path consistency is exploited. In the next section, we first define the term NFA and meaningfulness of an event and then use them to detect the level lines with a specific geometric shape like circular shaped objects. In Section 3, we present our technique to track the circular objects present in a video. In Section 4, we present the result of our work on videos of moving blood cells followed by conclusions in Section 5. II. BACKGROUND We define the number of false alarms (NFA) as the expected number of occurrences of an event, where an event is defined as the occurrences of the features of some pattern such as, smoothness, circularity, rectangularity, etc. in images or inter-frame displacement of an object in video. For an exhaustive trial, if the NFA is sufficiently small, then the event is meaningful, i.e., the event cannot occur out of a uniform random process [1]. Then we need a threshold to indicate the value  below which, we consider the NFA as