{"content":[{"text":"584","bbox":{"left":0.136293,"top":0.063968,"width":0.02979000000000001,"height":0.018027}},{"text":"Artificial Intelligence Applications and Innovations","bbox":{"left":0.439696,"top":0.065347,"width":0.42200100000000007,"height":0.0165}},{"text":"^ (x,j/,*) , . = | I j X I if motion is detected at point (x, y) at time t .^. \n h{x,y,t) = {^ . (1) \n ' \" otherwise \n Note that moving points given by h correspond to the projection of moving \n objects on the sensor plane. When using a camera for example, the detected \n points result from processing frames that correspond to perspective projection \n at the camera projection plane and using the foreground extraction technique \n presented in [2] at a specific time (frame) is given in Figure 1(b).","bbox":{"left":0.135477,"top":0.094459,"width":0.726907,"height":0.132282}},{"text":"(a) (b) \n Fig. 1. A video scene and the corresponding binaxy mask for the moving points. The \n original image comes from the EC funded CAVIAR project [1].","bbox":{"left":0.136294,"top":0.397882,"width":0.726641,"height":0.061651999999999985}},{"text":"The subset 5 C R^ of the moving points forms a topological space such that \n the function I^ defined above is the characteristic function of S, Moreover, every \n cross-section ^(^o) C R^ of 5 at time to also defines a topological space, and \n the corresponding characteristic function is Ib{x,y,to), An example is given in \n Figure 2, as obtained from a video sequence. \n Any subset T of S that is connected and its cross-section T PI S{to) at to \n is also connected for any to is called a tube. A single connected component of \n S is called a composite tube, in the sense that it is formed by union of tubes. \n Note that for composite tubes and tubes, connectivity refers to x — y — t space, \n while for their intersections at a specific time t, it refers to the x — y space. \n Moreover, the above definitions allow tubes to have common elements. There \n are four main events that can be observed on tubes forming a composite tube: \n 1. Start, A tube starts at time to if for every point (a;, y,t) 6 T, t > to. If tubes \n are maximal sets, i.e., they are the maximal sets that axe connected and \n their cross-section T H S{to) forms a connected component in S{to), then \n their start points are the start points of the corresponding composite tube. \n 2. Stop, A tube stops at time to if for every point {x, y,t) eT,t <to. As with \n start points, if tubes are maximal sets, then their stop points are the stop \n points of the corresponding composite tube. \n 3. Merge, Two tubes Ti and T2 merge at point to if their cross sections TinS(t) \n and T2 n S{t) are not connected for t <to and are connected at to.","bbox":{"left":0.135477,"top":0.491756,"width":0.738851,"height":0.35967}}],"images_bbox":[],"images_bbox_not_text_overlap":[]}