Abstract:
An image based obstacle detection method. A camera mounted on a vehicle provides a set of image frames while the vehicle is in motion. The image frames define an image plane having a vertical aspect and a horizontal aspect. The relevancy of an object is determined by (i) selecting first and second feature points from the object that are spaced apart vertically in a first image frame; (ii) tracking the positions of the first and second feature points over at least a second image frame; and (iii) deciding the object to be relevant if the first and second feature points move dissimilar distances in physical space, within a tolerance, and deciding the object to be irrelevant otherwise. The motion of relevant objects is then estimated to determine if any relevant object is likely to become an obstacle to the vehicle.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a 371 U.S. national phase application of PCT Application No. PCT/CA2012/000057 filed Jan. 20, 2012 which claims priority to U.S. Provisional Patent Application No. 61/478,717, filed Apr. 25, 2011. 
    
    
     FIELD OF INVENTION 
     The invention relates to the field of image processing, and more particularly to a method and system for discerning three-dimensional objects using relative motion between the camera and the objects, and an object detection system based on same. 
     BACKGROUND OF INVENTION 
     Many vehicles now incorporate one or more obstacle detection system which use cameras to provide a field of view of the roadway and surrounding environment. The obstacle detection systems process the video stream or sequence of image frames provided by the camera in an attempt to ascertain the existence of an obstacle in the path of vehicle. Obstacle detection algorithms do this by attempting identify a variety of objects localized in one or more predefined regions of interest in the captured field of view, determine whether or not such objects are real, and estimate their path relative to the vehicle to determine whether or not such objects will indeed become obstacles. 
     The conventional approach to solving such a problem is to develop a series of classifiers and detectors to detect a group of predefined objects. The classifiers work in a cascade or in a parallel fashion to detect image content such as pedestrians, vehicles and geometrically shaped objects such as balls and poles. Such systems may require significant computational resources provided by expensive signal processors. In addition, in such a system, all the objects that need to be detected have to be defined in the development stage and require extensive training for the classifiers. Such a process is expensive and time consuming and might not be generic enough with respect to all possible different objects that might be encountered in the real world. 
     SUMMARY OF INVENTION 
     In order to overcome some of the above mentioned shortcomings, the invention proposes a more generic approach which does not depend upon the design of specific classifiers. Instead, the invention uses the relative motion between the vehicle and the surrounding environment to identify whether or not detected objects are relevant. This approach uses a single image sensor and can be employed for detecting generic objects. 
     Generally speaking, the invention utilizes the principle that spaced apart physical points that in reality have a vertical dimension will move at different rates when projected to the image plane provided by the vehicular camera, whereas spaced apart physical points that in reality lie only horizontally along the ground plane will move at the same rate when projected to the image plane. Using this principle the invention is able to rapidly distinguish between three dimensional objects that could be relevant to the obstacle detection analysis and irrelevant two dimensional objects that, for example, may be pavement markings or artifacts such as shadows. 
     The foregoing principle will be better understood with reference to  FIGS. 1 and 2 . Referring to  FIG. 1 , the vehicular camera establishes an image plane  20 . The camera has a focal point f through which all light rays pass. Axis  21  is a normal projection to the image plane  20 . Axis  22  represents the real vertical plane, and axis  24  represents the ground plane (a horizontal plane corresponding to the roadway). An object lies in the camera field of view. The object has a first point seen by image pixel  26 , corresponding to ray  28 , and a second point, seen by image pixel  27 , corresponding to ray  29 . This object may be either a vertical object  30  or a horizontal object  40  (lying along the ground plane  22 ) because the vertical object  30  has a first point P 1  lying along the ray  28  and the horizontal object  40  also has a first point G 1  lying along the ray  28 , and likewise the vertical object  30  has a second point P 2  lying along the ray  29  and the horizontal object  40  also has a second point G 2  lying along the ray  29 . The camera sees only two vertically spaced points at pixels  26  and  27 , so without further information it is not possible for the camera to discern if the rays  28 ,  29  impinging on pixel  26 ,  27  come from points lying on the ground or from a vertical object. 
     However, referring additionally to  FIG. 2 , if there is relative motion between the object and the image plane additional information can be garnered to be able to differentiate between a vertically oriented object and a horizontally oriented object. Consider again the horizontally oriented object  40  which lies on the ground plane. It has two opposing edge points that lie at initial positions G 1 , G 2 . (To the camera, these two points could also correspond to points P 1  and H of vertical object  30 .) If the horizontal object  40  moves relative to the camera by a real distance d, then the edge points will move to positions G 1 ′, G 2 ′. With the height and angular orientation of the camera known, it is possible to calculate the distance moved in the ground plane by the end points, i.e., the distance between G 1  to G 1 ′ and between G 2  to G 2 . As the object is presumed to be of constant length for at least a short period of time, the distance between G 1  and G 1 ′ will be d and the distance between G 2  to G 2 ′ will also be d. 
     Now consider the vertical object  30 . It has two opposing edge points that lie at initial positions P 1 , P 2 . The point P 1 , lying along ray  28 , projects onto the ground plane at point G 1  as previously discussed. Point P 2  in this example lies along the ground plane (but it need not). Let the vertical object  30  move relative to the camera by a real distance d. The top edge point moves from position P 1  to position P 1 ′, and the bottom edge point moves from position P 2  to P 2 ′. Now calculate the distance moved in the ground plane by these end points. P 1  projects onto the ground plane at point G 1 . Point P 1 ′ projects onto the ground plane at point X. So, a distance calculation in the ground plane between points P 1  and P 1 ′ effectively yields a result computing the distance between G 1  and X, resulting in a much larger distance d++. On the other hand, P 2  and P 2 ′ are located on the ground plane so the distance between them will be computed as d. The change d++ in the ground plane between P 1  and P 1 ′ differs considerably from the change d between P 2  and P 2 ′, thus enabling a vertical object to be distinguished from an object lying substantially along the ground plane. 
     The principle holds for distinguishing between an object lying substantially along any selected real horizontal plane and an object lying generally transverse to the selected horizontal plane. Likewise, the principle applies even when the vertical object does not touch the selected real horizontal plane because vertically spaced apart points will move at different rates when projected onto the selected horizontal plane. 
     In the preferred obstacle detection system described in greater detail below, a vehicular camera is utilized to capture a video stream or sequence of image frames. The image frames are processed by an image processor which executes an obstacle detection algorithm. The preferred system then processes the images to extract edges therein. (An example of a road image  10  and its edge image  12  can be seen in  FIGS. 3 and 4  respectively.) 
     The preferred system processes the edge images to identify potential objects preferably within a region of interest (ROI) in the image frame. Objects (obstacles or not) are identified by their boundaries or contours. If an object moves across successive image frames, the edges of such an object will also move and so edge based features are used to identify the location of the objects and are also used to track the objects across frames. However, owing to environmental effects and low contrast, it is possible that the edges of an object are not always isolated from other objects or the general background. In order to make the object localization more reliable, the preferred system examines different features such as color and texture cues, in conjunction with the edges, in order to detect and isolate objects from one another. 
     The isolated objects could be actual three dimensional objects or they could be two dimensional objects on the ground such as shadows or pavement markings. Using a single monocular image sensor, it can be quite difficult to differentiate one type of object from another. However, if there is relative motion between these objects and the camera, then using the principles outlined above the preferred system can estimate which of the detected objects are above a certain specified height threshold and which detected objects are not (such as markings on the ground). Accordingly, the preferred system examines the motion of at least two different feature points in the edge image of each object across image frames. If there is relative motion between the camera and the object, for the same physical distances traveled, points lying at different physical heights will have different rates of change in the image plane (termed “differential-gradient effect”). Thus, if the selected feature points in the edge image of an isolated object do not have different rates of change, within a tolerance, the preferred system deems that object to be an irrelevant two dimensional object. Similarly, if the selected feature points in the edge image of an isolated object do have different rates of change, within a tolerance, the preferred system deems that object to be relevant and estimates the relative path of that object to determine whether or not it will become an obstacle to the vehicle. 
     Thus, one aspect of the invention provides a method of obstacle detection. In this method, a vehicle is provisioned with a camera having an external field of view and a set of image frames provided by the camera are acquired whilst the vehicle is in motion. The image frames define an image plane having a vertical aspect and a horizontal aspect. The relevancy of an object is determined by (i) selecting first and second feature points from the object that are spaced apart vertically in a first image frame; (ii) tracking the positions of the first and second feature points over at least a second image frame; and (iii) deciding the object to be relevant if the first and second feature points move dissimilar distances in physical space, within a tolerance, and deciding the object to be irrelevant otherwise. The motion of relevant objects is then estimated to determine if any relevant object is likely to become an obstacle to the vehicle. 
     In practice, an edge detection is preferably carried out on the set of images frames and one or more objects are isolated based on their edge contours. The most desirable feature points for tracking across frames are the topmost and bottommost pixel points of any given isolated object as these can be used to estimate the relative physical displacement of the object. For this estimated displacement of the object, by comparing the estimated pixel movement of the topmost detected point of the object with the actual pixel movement of the same point, the object can be determined to be a relevant object. 
     In addition, in practice, a given pixel is preferably position is de-warped to account for lens distortion prior to determining a physical location corresponding to the given pixel position. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and other aspects of the invention will be better understood with respect to the attached drawings, wherein: 
         FIG. 1  is a schematic diagram illustrating how vertical and horizontal objects in the real world are viewed by a vehicular camera; 
         FIG. 2  is a schematic diagram illustrating how the movement of vertical and horizontal objects in the real world are viewed differently by a vehicular camera; 
         FIG. 3  is a system block diagram of an object detection algorithm according to a preferred embodiment; 
         FIG. 4  is a flowchart of a software module employed by the object detection algorithm; 
         FIG. 5  is a graph illustrating derivatives of a exemplary single dimension function; 
         FIG. 6  is an image frame provided vehicular camera which sees a vertical object and a horizontal object; 
         FIG. 7  is a edge image of  FIG. 6 ; 
         FIG. 8  is composite image showing the image of  FIG. 6  with associated edge detection contours; 
         FIGS. 9A and 9B  are schematic diagrams illustrating the function of a block detection algorithm; 
         FIGS. 10A and 10B  are successive image frames provided by a vehicular camera which has moved relative to a object seen by the camera; 
         FIG. 11A-11C  are schematic diagrams illustrating the operation of an object height detection filter employed by the object detection algorithm; and 
         FIG. 12  is a flowchart of a software module employed by the object detection algorithm. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     For reference purposes, the following mathematical nomenclature is used in this description. A vector or a matrix is represented in bold face, while a scalar entity is represented in a regular face. The lower case is used to denote the dimensions and pixel locations in two dimensional image space. Thus, the collection of all the pixels in an image can be denoted as f and a pixel at column x and row y in the image f can be represented as f(x, y). The coordinates of a point in the three-dimensional world are represented using the upper case. A point on the ground can be represented in its vector form as X, or also as [X w , Y w , Z w ]. 
       FIG. 3  shows a system block diagram of a preferred obstacle detection system  100 . The inputs to system  100  include the image frames  102  from the vehicular camera (not explicitly shown) and vehicle CAN (controller area network) data  104  such as the instantaneous speed of the vehicle and its steering angle. In an overall system, knowledge of the vehicle speed allows for the optimization of the tracking of feature points and assessing the priority of the detected obstacles and the steering angle can be used for estimating and predicting the relative trajectory of the detected obstacles. In addition, the system  100  also has or receives information  105  about the camera. This includes intrinsic camera parameters such as its principal or central point, focal length, and lens map and extrinsic parameters such as the position of the camera. The lens map refers to the characteristic description of the particular lens being used in the system which describes the behavior of the lens and allows for the generation of the output angle of the light given any input incidence angle. In the preferred embodiment the system  100  is operated in conjunction with a dynamic calibration system that is capable of dynamically ascertaining the translation position and rotational angles of the camera in the field so that any deviations in the position of the camera from a nominal position/angle over time are accounted for. The preferred calibration system is described in Applicant&#39;s PCT Application No. PCT/CA2012/000056, titled “Method and System for Dynamically Calibrating Vehicular Cameras” and filed contemporaneously herewith, and published Nov. 1, 2012 as International Publication No. WO 2012/145818, the contents of which are incorporated by reference herein in their entirety. 
     The system  100  outputs one or more detected objects  106  (if any). The detected objects  106  are output as an array of data structures indicating: object centroid; object bounding box (position and breadth); and an estimated distance from the vehicle. 
     A differential, gradient-based, segmentation module  110  receives the input information  102 - 105 . At an initial stage  112  the module  110  uses the input image frames to hypothesize or postulate the existence of an object by detecting and isolating objects from the background, within a predefined region of interest (ROI). At a subsequent stage  114  the module  110  filters the postulated objects to discern those which have dimensions above a defined height threshold. This is an important practical consideration because most real life objects that pose any threat to the vehicle (or to a pedestrian) have a significant vertical component. This module thus generates initial object hypotheses at output  116  which can be further refined and processed for final output. 
     The segmentation module  110  is based on a differential gradient based pseudo-stereo effect, which has the following features:
         Points lying on the same vertical axis at different planar heights (in reality) move at different pixel rates in the captured video. This allows for separation of hypothesized objects which lie on the ground plane (or other selected horizontal plane) versus those which are three dimensional in nature and pose a threat to the vehicle.   Owing to the above principle, this approach allows the detection of even those objects which are stationary around the vehicle if the vehicle itself is moving. This allows for detection of stationary pedestrians or poles or other objects which the vehicle might be driving towards.   Only relative motion is required between the objects and vehicle.       

     Referring additionally to  FIG. 4 , the segmentation module  110  includes the following functional blocks, discussed in turn below: edge feature extraction  110 A; feature selection and tracking  110 B; physical distance estimation of detected points  110 C; and obstacle detection  110 D. 
     The edge detection block  110 A uses the contours of objects as a means to segment them from the background image. An object can be assumed to be bound by its contour or its edge, which can be extracted using the gradient operator. 
     The edge points of an image can be detected by finding the zero crossings of the second derivative of the image intensity. The idea is illustrated for a one dimensional signal f(1) in  FIG. 5 . However, calculating the 2 nd  derivative is very sensitive to noise. This noise should be filtered out before edge detection. To achieve this, edge detection block  110 A uses the “Laplacian of Gaussian (LoG)” method as known in the art per se. This method combines Gaussian filtering with the Laplacian for edge detection. 
     There are three main steps in Laplacian of Gaussian edge detection: filtering, enhancement, and detection. 
     Gaussian filtering is used for smoothing and the second derivative of which is used for the enhancement step. The detection criterion is the presence of a zero crossing in the second derivative with a corresponding large peak in the first derivative. 
     In this approach, noise is first reduced by convoluting the image with a Gaussian filter which removes isolated noise points and small structures. Those pixels, that have locally maximum gradient in the zero crossing of the second derivative, are considered as edges by the edge detector. To avoid detection of insignificant edges, only the zero crossings whose corresponding first derivative is above some threshold, are selected as edge point. The edge direction is obtained using the direction in which zero crossing occurs. 
     The output of the LoG operator; h(x,y); is obtained by the convolution operation: 
     
       
         
           
             
               
                 
                   
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       FIG. 7  shows an example of an edge image  140  obtained by using the LoG operator on an input image  138  shown in  FIG. 6 . 
     Once the objects have been isolated using their contours, each object or group of objects can be identified by its edge. The feature selection and tracking block  110 B assumes that the bottom of the each objects lies on the ground while the top of the object is either on the ground or not, depending if the object is flat or has a three-dimensional shape. Most preferably the top and bottom of each contour are selected as the points of interest in the image frame which need to be investigated to determine if the object is above a certain threshold of height or not. These topmost and bottommost points of each edge contour are then tracked from the current frame to the next frame to find their corresponding location in the next frame. For example,  FIG. 8  shows the top and bottom feature points of interest O 1t  and O 1b  which are tracked across frames. (Note that the feature points O 1t  or O 1b  may each comprise multiple pixels.) 
     In addition, for more robustness, instead of just selecting the topmost and bottommost points, the feature selection and tracking block  110 B preferably also selects and processes a set of additional feature points along the contour. 
     Once the feature points that define the top and bottom of each object are isolated, they, as well as any other selected feature points, can be tracked across frames using a block matching algorithm. (Note that there is no need to track the entire image or object contour, only the selected feature points need to be tracked across frames.) 
     Any given feature point will likely subsist for least a few following image frames and with the typical frame rate of 30 fps the given feature point will move relatively slowly across image frames. The block matching algorithm establishes a macro block around the feature point and looks for a best match. For example,  FIG. 9A  shows as an example a feature point  152  selected by the feature selection and tracking block  110 B that consists of a 3×3 pixel array in image frame  150 . The pixel array  152  has a middle position at pixel position j,k. In the following or otherwise subsequent image frame  160  shown in  FIG. 9B , the feature selection and tracking block  110 B establishes a macro-block  162  centered on the position of the selected feature point  152 . The size of the macro-block  162  is based on the estimated degree of movement of the feature point/area to be tracked, and in this example encompasses a 10×10 array centered at pixel position j,k. A search window  164  is defined. The feature selection and tracking block  110 B slides the search window  164  in a raster fashion one pixel at a time to find a contiguous array of pixels in the macro-block  162  whose values are the closest match to the values of the selected feature point  152 . The closest match is preferably defined based on a minimum absolute error criterion. To make the search process optimal, a hierarchical search may be performed if the search window  164  is larger than a default size. In this manner, the position of the selected feature point  152  may be tracked to a new location, for example to pixel position p,q as indicated in  FIG. 9 . 
     The distance estimation block  110 C calculates the physical distances to the selected feature points in the ground plane. 
     A point in the image, x i , can be defined as
 
 x   i   =[x   p   y   p 1] T  
 
     It is desired to compute the real world coordinates of this point on the ground plane, given the camera position and geometry. Before estimating the distance, a selected pixel location is de-warped using the distortion function of the lens, which is one of the intrinsic parameters provided in input  105 . In a de-warped image, every image point can be expressed as a 3D Plucker line matrix, which correlates to one of the rays running through the camera focal point and impinging upon the image plane (see  FIG. 1 ). As the projected real world is assumed to be flat or planar, the intersection point of the Plucker line matrix and the ground plane is needed. The Homography matrix, H (a 3×4 matrix), describes the projection from the image point to the world coordinate inside the plane and so the intersection point with the plane, which is defined as
 
 X   i   =H·x   i  
 
     where X i [X 1  Y 1  Z 1  N 1 ] T    
     The real world coordinates of the image point on the ground plane can be estimated with respect to the origin using X i  as: [X w =X 1 /N 1 ; Y w =Y 1 /N i ; Z w =Z 1 /N 1 ]. To compute the real world distance of the various points using the above equation, the intrinsic and the extrinsic parameters of the camera being used are necessary. Given these parameters, the Homography matrix, H, can be estimated as the inverse of the projection matrix, P, which is defined as: 
     
       
         
           
             
                 
             
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     In the above equations, f and p are the focal length of the lens and the pixel size of the sensor, respectively. axisX and axisY are the column and row coordinates of the optical center on the image plane. α, β, and γ represent the angles of rotation around X, Y, and Z axes, respectively, and t 1 , t 2 , and t 3  are the translations along X, Y, and Z axes, respectively. 
     The object detection block  110 D filters the segmented objects based on the estimated real height of the objects. Those objects that are estimated to have a real height greater than a selected threshold are considered to be relevant objects worth tracking, whereas those objects that are estimated to have a real height less than a selected threshold are considered to be irrelevant objects not worth tracking. 
     For height threshold verification, the object detection block  110 D assumes that there is some relative motion between the object and the camera, i.e., either the camera moves or the object itself moves with respect to the camera. For example,  FIGS. 10A and 10B  illustrate two images frames  170 ,  172  in which the camera has moved and thus shows the relative displacement of the object in the image. Since the objects are solid connected entities, it is fair to assume that the real-world distance traversed by the bottommost point on the object, O 1b  ( FIG. 10A ) would be the same as that of the topmost point of the object, O 1t . The object detection block  110 D use this as the basis for detecting if the topmost point of the object is above a certain height threshold, T, or not. 
     The steps involved in this detection are as follows: 
     (1) Estimate the initial distance of the object from the reference camera using the pixel location of the bottommost point, O 1b , and use it with the Homography matrix to estimate the real-world coordinate, D 1 , in the ground plane. See, for example,  FIG. 11A . 
     (2) Track the motion of the bottommost point the object from pixel location O 1b  to pixel location O 2b  and using the Homography equation estimate the real-world coordinate D 2  of the bottommost point on the ground plane, and the distance ΔD the bottommost point has moved. See, for example,  FIG. 11B . 
     (3) Use the Homography equation to estimate a real world coordinate of the topmost point of the object corresponding to its location O 1t  in the first frame. Assume that the top of the object is at a height T, which will correspond to a point D T  at this height. See  FIG. 11A . 
     (4) Since the top and the bottom points of the physical object move by the same distance in the real world, then presuming that the topmost point of the object it is at height T, the new real world location of the top-most point, D* T , is D T +ΔD. See  FIG. 11B . 
     (5) Using the inverse of the Homography equation, compute the pixel coordinate O* 2T  of the top-most point after accounting for its real world displacement if it was at a height T. See  FIG. 11B . 
     (6) Compare the pixel displacement of the estimated pixel location of the top most point with respect to the initial location, ∥O 2t *−O 1t ∥, with that of actual pixel location of the tracked topmost point of the object with respect to the initial location ∥O 2t −O 1t . If ∥O 2t *−O 1f ∥&lt;∥O 2t −O 1t ∥, then the topmost point of the object is above the height threshold and if ∥O 2t *−O 1t ∥&gt;∥O 2t −O 1t ∥, then the topmost point of the object is below the height threshold. See, for example,  FIG. 10B  where the object is higher than the threshold height T and so O* 2t  is closer to O 1t  than O 2t . 
     The foregoing steps utilized the image plane. It should also be appreciated that the analysis can just as well be carried out in real physical space. In this methodology, as exemplified in  FIG. 11C , the rays in the first and second image frames corresponding to the topmost point of the object are projected onto the selected horizontal physical plane corresponding to height T to generate real points G 1  and G 2 . The object is deemed to be a valid object, i.e., having a height greater than T, if ∥G 2 −G 1 ∥&gt;ΔD. 
     It will also be understood that in the case of T=0 the selected horizontal physical plane corresponds to the ground plane. 
     Referring back to  FIG. 3 , the output of the segmentation module  110 —postulated objects—is fed in to a hypothesis evaluation stage  118 . This stage evaluates the postulated objects and multiple hypotheses which could belong to the same object are combined to form a single hypothesis or postulated object. 
     Stage  122 —temporal hypotheses assignment—tracks postulated objects over time. The postulated objects from stage  118  are further evaluated using the predicted hypotheses from the previous image frame. The corresponding hypotheses are assigned to the current frame where a match is found. However, if no match is found between the predicted hypothesis and the current estimated hypothesis, then a new hypothesis is instantiated. 
     In addition, if a hypothesis existed in the previous frame but is not currently detected, then this hypothesis is not immediately rejected, but is held in memory for a specified number of frames to verify that the postulated object is no longer present. In case where the postulated object is actually present, the detection may be missed intermittently, and therefore this temporal processing leads to a significant reduction in the false negatives. 
     Stage  126  is a distance and trajectory estimation block. Before the physical distance of the pixel locations can be estimated at step  128 , the fish-eye distortion of the lens needs to be corrected. See  FIG. 12 . For this correction, the lens distortion is modeled as a fifth order polynomial and using this polynomial, each point in the captured image which needs further processing is de-warped. 
     The de-warped points used for estimating the distance of postulated objects are preferably the bottommost points of the objects which are assumed to lie on the ground plane. These points can be used to estimate the distance of the objects from the camera and this distance can then be translated to the vehicle coordinates. This allows the further processing of relevant postulated objects based on their relative distance to the vehicle. 
     The distance estimation of the same postulated object across multiple frames is subject to small variations owing to real world, non-ideal conditions. Thus, these estimated distances are filtered using a Kalman filter which can smooth out instantaneous variations. The same filter can also be used to predict the location of the object in the next frame and thus help predict the trajectory of the object, which is computed at step  132  ( FIG. 3 ). 
     Owing to the nature of the problem, a modified Kalman filter is preferably used, which has the following order of steps:
         Update Step: Update the filter parameters and estimate the filtered distance of the object detected in the current frame, ({circumflex over (X)},Ŷ), using the input real world distance (X,Y). (See  FIG. 12 .)   Prediction Step: Predict the distance of the object in the next frame.       

     Stage  136  provides a hypothesis prediction. Based on the predicted physical location of the object, the location of each hypothesis in the next frame is estimated by projecting the distances back to the image plane. These projected pixel locations can then be used for the temporal assignation of the hypotheses in the next frame. 
     The system output is provided at stage  106 . Based on the trajectory estimation of each object, if the detected object is in the path of the vehicle, or poses a threat to the vehicle, then the object is output using its centroid as well as its bounding region or contour. This output may be displayed visually on a display screen or the like mounted in the vehicle and may be accompanied by audible warnings such as an alarm or voice, or by tactile feedback such as a buzz in the steering wheel. In addition, in the event the system detects an imminent crash by virtue of an obstacle being immediately in the path of the vehicle various pre-emptive actions may be taken such as automated braking or tensioning of set belts. 
     Those skilled in the art will appreciate that a variety of modifications may be made to the embodiments described herein without departing from the spirit of the invention.