Abstract:
Computing a time-to-contact (TTC) of a vehicle with an object. The object includes a light source. The system mountable in the vehicle includes a camera and a processor configured to capture images of the object. The processor is operable to track a spot between the images to produce a tracked spot. The spot includes an image of the light source. The processor is operable to compute time-to-contact (TTC) responsive to changes in brightness of the tracked spot.

Description:
BACKGROUND 
       [0001]    1. Technical Field 
         [0002]    The present invention relates to driver assistance systems and in particular to collision warning systems 
         [0003]    2. Description of Related Art 
         [0004]    During the last few years camera based driver assistance systems (DAS) have been entering the market; including lane departure warning (LDW), Automatic High-beam Control (AHC), pedestrian recognition, and forward collision warning (FCW). 
         [0005]    A core technology behind conventional forward collision warning (FCW) camera based driver assistance systems and headway distance monitoring is vehicle detection in the image frames. Assume that reliable detection of vehicles in a single image a typical forward collision warning (FCW) system requires that a vehicle image be 13 pixels wide, then for a car of width 1.6 m, a typical camera gives initial detection at 115 m and multi-frame approval at 100 m. A narrower horizontal field of view (FOV) for the camera gives a greater detection range however; the narrower horizontal field of view (FOV) will reduce the ability to detect passing and cutting-in vehicles. A horizontal field of view (FOV) of around 40 degrees was found by Mobileye (to be almost optimal (in road tests conducted with a camera) given the image sensor resolution and dimensions. A key component of a conventional forward collision warning (FCW) algorithm is the estimation of distance from a camera and the estimation of time-to-contact/collision (TTC) from the scale change. as disclosed for example in U.S. Pat. No. 7,113,867. 
       BRIEF SUMMARY 
       [0006]    Various methods are provided herein for computing a time-to-contact (TTC) of a vehicle with an object. The object includes a light source. The method is performable by a camera connectible to a processor. Multiple images of the object are captured. A spot, including an image of the light source is tracked between the images and a tracked spot is produced. Time-to-contact is computed responsive to change in brightness of the tracked spot. The time-to-contact may be computed from energy of the spot in the image. The energy may be computed by summing pixel values from a multiple pixels of the spot. The time-to-contact may be computed from change in the energy over time. A function of the energy may be fit to a function of the time-to-contact. The reciprocal of the square root of the energy may be fit to a linear function of the time-to-contact. It may be determined whether the vehicle and the object are on a collision course responsive to image motion of the tracked spot. 
         [0007]    Various systems are provided herein for computing a time-to-contact (TTC) of a vehicle with an object. The object includes a light source. The system mountable in the vehicle includes a camera and a processor configured to capture the camera a plurality of images of the object. The processor is operable to track a spot between the images to produce a tracked spot. The spot includes an image of the light source. The processor is operable to compute time-to-contact (TTC) responsive to changes in brightness of the tracked spot. The time-to-contact may be computed from energy of the spot in the image. The energy may be computed by summing pixel values from multiple pixels of the spot. The time-to-contact may be computed from change in the energy over time. A function of the energy may be fit to a function of the time-to-contact. The camera may be a camera from a stereo pair of cameras. The time-to-contact may computed from a sensor input to the processor from a combination of the camera with a radar system. The time-to-contact may be computed from a sensor input provided to the processor from a combination of the camera with a lidar system. 
         [0008]    The foregoing and/or other aspects will become apparent from the following detailed description when considered in conjunction with the accompanying drawing figures. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]    The invention is herein described, by way of example only, with reference to the accompanying drawings, wherein: 
           [0010]      FIGS. 1 and 2  illustrate a system including a camera or image sensor mounted in a vehicle, according to an aspect of the present invention. 
           [0011]      FIG. 3  shows a flowchart of a method, according to features of the present invention. 
           [0012]      FIG. 4  shows schematically an image frame, according to a feature of the present invention. 
           [0013]      FIG. 5  illustrates a flow diagram of a method, according to a feature of the present invention. 
           [0014]      FIG. 6   a  shows a representative image frame of a leading vehicle at night 
           [0015]      FIG. 6   b  shows a plot of energy (e) as a function of frame number, where time-to-contact (TTC) is computed for a spot from a taillight of a lead vehicle, according to an aspect of the present invention. 
           [0016]      FIGS. 6   c  and  6   d  show plots of inverse of the square root of energy (e) as a function of frame number, where time-to-contact (TTC) is computed for a spot on the lead vehicle. 
           [0017]      FIG. 7  shows a plot of the distribution of time of a Take Over Request (TOR) signal, showing distribution and cumulative curves respectively, according to a feature of the present invention. 
           [0018]      FIG. 8   a  shows an example of a lead vehicle at the right edge of the image with only one taillight. 
           [0019]      FIG. 8   b  shows a plot of energy (e) as a function of frame number, where time-to-contact (TTC) is computed for the spot from the taillight of the lead vehicle of  FIG. 8   a.    
           [0020]      FIGS. 8   c  and  8   d  show the inverse of the square root of energy (e), as a function of frame number, where time-to-contact (TTC) is computed for the spot from the taillight of lead vehicle. 
           [0021]      FIG. 9  shows stationary light spots on a curved tunnel wall. 
           [0022]      FIG. 10   a  shows a plot of energy (e) as a function of frame number, with the effects of the light sources of the tunnel overhead lights, according to a feature of the present invention. 
           [0023]      FIGS. 10   b  and  10   c  show respectively the inverse of the square root of energy (e) as a function of frame number, where time-to-contact (TTC) is computed with the effects of the AC light sources of the tunnel overhead lights and with the effects removed, both according to a feature of the present invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0024]    Reference will now be made in detail to features of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the like elements throughout. The features are described below to explain the present invention by referring to the figures. 
         [0025]    Before explaining features of the invention in detail, it is to be understood that the invention is not limited in its application to the details of design and the arrangement of the components set forth in the following description or illustrated in the drawings. The invention is capable of other features or of being practiced or carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein is for the purpose of description and should not be regarded as limiting. 
         [0026]    By way of introduction, features of the present invention are directed to an accurate computation of time-to-contact (TTC) with an object. The accurate computation of time-to-contact (TTC) may be used to provide a warning to a driver of a vehicle to prevent a collision with the object. The object may be a light source such as a taillight of a lead vehicle or a headlight of an oncoming vehicle, for example. The accurate computation may be derived from the changes in brightness of a tracked spot of the light source in an image or multiple images acquired in a forward view of the vehicle. The accurate computation may be used among other applications, for forward collision warning (FCW) and/or collision mitigation by braking (CMbB). 
         [0027]    Reference is now made to  FIGS. 1 and 2  which illustrate a system  16  including a camera or image sensor  12  mounted in a vehicle  18 , according to an aspect of the present invention. Image sensor  12 , imaging a field of view in the forward direction provides image frames  15  in real time and image frames  15  are captured by processor  14 . Processor  14  may be used to process image frames  15  simultaneously and/or in parallel to serve a number of driver assistance systems/applications including: forward collision warning, automatic headlight control, traffic sign recognition etc. The driver assistance systems may be implemented using specific hardware circuitry with on board software and/ or software control algorithms in memory or storage  13 . Image sensor  12  may be monochrome or black-white, i.e. without color separation or image sensor  12  may be color sensitive. By way of example in  FIG. 2 , image frames  15  are used to serve and forward collision warning  22  using spot brightness and/or collision mitigation by braking  20  based on spot brightness, according to different aspects of the present invention. 
         [0028]    Although embodiments of the present invention are presented in the context of driver assistance applications, embodiments of the present invention may be equally applicable in other real time vision processing applications such as machine vision. 
         [0029]    Reference is now made to  FIG. 3  which shows a flowchart of a method  301 , according to features of the present invention. Method  301  computes a time-to-contact (TTC) of a vehicle  18  with an object. The object may be a taillight of a lead vehicle, a headlight of an oncoming vehicle or other light source. Reference is also made to  FIG. 4  which shows schematically features of an image frame  15 , by way of example according to an aspect of the present invention. In the example of  FIG. 4 , image frame  15  includes a lead vehicle  40  with a spot  42  from one of the taillights of vehicle  40   
         [0030]    If t′ is the expected contact time with the object, e.g. lead vehicle  40 , and time t is current time, then time-to-contact (TTC) between vehicle  18  and the object is the time interval between current time t and the expected contact time t′ and may be given by equation 1. 
         [0000]        TTC=t′−t   (1)
 
         [0031]    Distance Z to the object is given by equation 2 
         [0000]        Z=V   rel   *TTC   (2)
 
         [0000]    where V rel  is the relative speed between vehicle  18  and lead vehicle  40 , assuming constant relative speed. 
         [0032]    The measured energy (e) of a taillight of in image sensor  12  may be given in equation 3, where K is some constant. 
         [0000]    
       
         
           
             
               
                 
                   
                     e 
                     * 
                     K 
                   
                   = 
                   
                     1 
                     
                       Z 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0033]    Combining equations 1-3 above gives: 
         [0000]    
       
         
           
             
               
                 
                   
                     t 
                     = 
                     
                       
                         1 
                         
                           
                             e 
                           
                           * 
                           A 
                         
                       
                       + 
                       
                         t 
                         ′ 
                       
                     
                   
                   ; 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0000]    for some constant A. Time-to-contact TTC may be estimated according to the square root of spot energy e (or brightness). 
         [0034]    Referring now to  FIG. 3 , image frames  15  are captured (step  303 ) by image sensor  12  at known time intervals with a certain exposure. Spot  42  is tracked (step  305 ) across multiple image frames  15 . In step  307 , a time-to-contact between host vehicle  18  and lead vehicle  40  may be computed for the tracked spot  42  between pairs of image frames  15 , according to features of the present invention as described below. In step  309 , it may be determined if lead vehicle  40  and/or the light source is on a collision course with host vehicle  18 . 
         [0035]    With reference to the equations above and  FIG. 4 , time-to-contact (TTC) step  307  may be calculated in the following manner:
       1. A small rectangular neighborhood  44  around spot  42  may be selected for instance using the shortest exposure for image sensor  12 .   2. A threshold value may be estimated to separate spot  42  from its background bounded by rectangular neighborhood  44 . The threshold value is a gray-scale value darker than spot  42  and brighter than the background of spot  42 . The histogram of rectangular neighborhood  44  has a bimodal distribution. The threshold gray-scale value may be selected between the two modes of the histogram.   3. The values for all the pixels above the separating threshold may be summed.   4. Optional: Spot  42  may be checked for connectedness so that two close spots  42  are not combined.       
 
         [0040]    In practice, a dynamic threshold for computing the energy of spot  42  performs better than a fixed threshold such as the fixed threshold used to first detect spot  42 . 
         [0041]    If pixels in spot  42  are saturated, the saturated pixels do not contribute correctly to an energy estimation of spot  42 . Saturated pixels may be avoided in a number of ways such as by use of:
       1. Newer high dynamic range (HDR) cameras which do not get saturated from taillights.   2. Additional shorter exposures with older (linear) sensors, may be used.   3. In a predictive spot model, the non-saturated pixels at the edge of the spot  42  can be used to predict the true spot intensity in the center of spot  42 . The true spot intensity in the center of spot  42  function may be learned from multiple examples using for instance machine learning techniques such as support vector machines (SVMs).       
 
       Calculation of Constant A and Time-to-Contact TTC 
       [0045]    As an example for calculating the constant A and time-to-contact TTC, the most recent 16 frames  15  may be used. For image frames  15 , there are couples of energy e i , t i  where the index i varies between −15 and 0. All possible pairs of frames  15  may be chosen for the 16 frames. However, it was found that pairs with consecutive image frames  15  may be discarded since it was found that consecutive image frames  15  in practice may not give accurate results. For each i, j pair of selected image frames  15 , the following two equations may be solved, where T i , T j  are time measurements and e i  and e j  are energy measurements for frames i and j respectively. Constant A and time offset t are estimated: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     i 
                   
                   = 
                   
                     
                       
                         1 
                         A 
                       
                       * 
                       
                         e 
                         i 
                         
                           
                             - 
                             1 
                           
                           / 
                           2 
                         
                       
                     
                     + 
                     t 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     T 
                     j 
                   
                   = 
                   
                     
                       
                         1 
                         A 
                       
                       * 
                       
                         e 
                         j 
                         
                           
                             - 
                             1 
                           
                           / 
                           2 
                         
                       
                     
                     + 
                     t 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0046]    The above two equations (5) (6) are linear equations with an unknown slope A and offset t. 
         [0047]    T i  and T j  are the corresponding times of the measurements where the time of image frame  15  (i=−15) is set to be zero. 
         [0048]    Constant A may be extracted is by solving equations 5 and 6: 
         [0000]    
       
         
           
             
               
                 
                   A 
                   = 
                   
                     
                       
                         e 
                         i 
                         
                           
                             - 
                             1 
                           
                           / 
                           2 
                         
                       
                       - 
                       
                         e 
                         j 
                         
                           
                             - 
                             1 
                           
                           / 
                           2 
                         
                       
                     
                     dt 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where dt is the difference between the time-to-contact TTC i  for frame i and the time-to-contact TTC j  for frame j. 
         [0049]    When the history for spot  42  is less than sixteen image frames  15 , fewer than sixteen frames may be used such as eight frames. However, calculating time-to-contact (TTC) with a history less than eight frames may not achieve sufficiently accurate results. 
         [0050]    Multiple measurements may be combined together. Multiple measurements may be combined as weighted least squares where each measurement provides one equation to a large number of linear equations in the same variables slope A and offset time t. The equation for each measurement may be weighted according to when in time the measurements of time T and energy e are taken. It is advantageous to use robust estimation techniques. Iteratively re-weighted least squares may be used. The value of slope A may be computed as the most frequent in a distribution as follows: 
       Compute Constant A as Most Frequent in a Distribution 
       [0051]    A histogram of the solutions for slopes A may be calculated using up to 50 bins from a minimum slope A min  to a maximum slope A max . The slopes A received from image frames  15  which are further apart in time, may receive a higher weight and contribute more to the histogram, for instance in the following manner:
       Slopes from consecutive image frames  15  are discarded because the energy fluctuations usually add noise.   Slopes from energies which are between two and seven image frames  15  apart are added once to the histogram.   Slopes from energies which are between eight and eleven image frames  15  apart are added twice to the histogram.   Slopes from energies which are twelve to fifteen image frames  15  apart are added three times to the histogram.       
 
         [0056]    The bin with the maximal number is identified. For slope A with the maximal number, the mean offset or intercept t is calculated over the 16 data points. In the simplest form, the following equation may be solved for intercept t as a least squares. 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     i 
                   
                   = 
                   
                     
                       
                         1 
                         A 
                       
                       * 
                       
                         e 
                         i 
                         
                           
                             - 
                             1 
                           
                           / 
                           2 
                         
                       
                     
                     + 
                     t 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0057]    The spread of intercept t values may then computed. A tighter spread means intercept t is calculated to a higher confidence. 
         [0058]    The calculation of the mean offset t may be made more robust, by rejecting equations from image frames  15  which did not appear in any of the inlier pairs used to estimate A. It would also be possible to use the L1 norm or other known robust methods to improve the calculation of the mean offset t. 
         [0059]    Offset t is computed in the time frame of frame i=−15. The subtraction T 15 −T i  adjusts the offset to the current i th  image frame  15 . 
       Multi-Frame Model 
       [0060]    In the single frame (SF) model as described above, each image frame  15  and fifteen prior image frames  15  are used to compute slope A and intercept t as described above. A time-to-contact (TTC) warning could be triggered by a single frame (SF) model showing time-to-contact TTC below a threshold. However, a spot  42  is typically tracked for significantly more than 16 image frames  15  before the time-to-contact (TTC) becomes critical. Each image frame  15  typically gives a new single frame (SF) model. A multi-frame model (MF) accumulates information from the single frame models over time:
       The multi-frame (MF) model may be a weighted sum of the current multi-frame (MF) and the new single frame (SF), with the models&#39; confidences as weights (0&lt;confidence&lt;1)   The single frame (SF) confidence C SF  is lower when the standard deviation STD(A) of the histogram of A is high, and when the time-to-contact TTC range received by the different offsets is too wide or STD(t i ) is large.       
 
         [0000]    
       
         
           
             
               
                 
                   
                     C 
                     SF 
                   
                   = 
                   
                     1 
                     
                       
                         α 
                          
                         
                             
                         
                          
                         
                           STD 
                            
                           
                             ( 
                             A 
                             ) 
                           
                         
                       
                       + 
                       
                         β 
                          
                         
                             
                         
                          
                         
                           STD 
                            
                           
                             ( 
                             
                               t 
                               i 
                             
                             ) 
                           
                         
                       
                       + 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where α, β are respective weights.
       The multi-frame (MF) confidence C MF  is a combination of the current multi-frame (MF) confidence C MF  and the new single frame (SF) confidence C SF .       
 
         [0000]        C   MF =0.9* C   MF +0.1 *C   SF − γ   |δTTC|   (10)
       multi-frame (MF) confidence C MF  is lowered when the MF time-to-contact (TTC) sharply changes, shown as term δTTC with weight γ.   multi-frame (MF) confidence decays when there is no new single frame (SF) data.       
 
         309  Detecting Collision Course: Friend or Foe 
       [0066]    An example is now shown for detecting collision course, step  309  of  FIG. 3 . Reference is now again made to  FIG. 4  and to  FIG. 5  which shows a flow chart of a method  501 , according to a feature of the present invention. A collision course with a leading vehicle  40  may be detected. Motion of spot  42  is tracked (step  503 ) in image space in the horizontal axis x and the vertical axis y. Times t x  and t y  are then defined (step  505 ) as to how long will it take spot  42  to exit rectangle  44  in each axis x and y respectively. In decision  507 , spot  42  is on a collision course (step  509 ) with lead vehicle  40  if:
       (i) the motion in y-axis is big enough, and   (ii) time t y  during which spot  42  leaves rectangle  44  vertically is less than time t x  during which spot  42  leaves rectangle  44  horizontally.       
 
         [0069]    Otherwise, spot  42  is not on a collision course with lead vehicle  40  and tracking of spot  42  continues with step  503 . 
         [0070]    Method  501  checks whether spot  42  is predicted to leave in the y direction through the bottom of image rectangle  44 , indicating a collision; rather than spot  42  leaving the side of rectangle  44  in the x direction indicating no collision. The choice of the image dimensions for the rectangle  44  is rather arbitrary. The algorithm above can be fine-tuned by adjusting rectangle  44 , assuming the target taillight of lead vehicle  40  is about the same height as the host vehicle  18  headlamp. Rectangle  44  may be adjusted as follows:
       1. Draw a line in image space that is the projection of a line in three dimensional (3d) real space that joins host vehicle  18  headlamps. Note that the projected line in image space may not fall inside image frames  15 .   2. Extend the real space line to the full width of host vehicle  18  plus any required safety margin. The projection of the extended real space line to image space is the bottom of the rectangle.   3. Extend vertical lines from the ends of the horizontal image line to above the image of spot  42 .       
 
         [0074]    Steps 1-3 above may be used define the rectangle  44  in image space. Two rectangles may be defined based on the minimum and maximum expected heights of the target taillights. 
       Results 
       [0075]    Collision course algorithm  501  was applied to night time pre-crash test-track scenes using spot  42  based time-to-contact (TTC) method  301 , according to an embodiment of the present invention with other methods of vehicle detection and collision warning disabled. 
         [0076]    There were  106  relevant test cases.  FIG. 6   a  is a representative image frame  15  for one example of a test case of a leading vehicle  40 . Left spot  42  was computed which is an image of the left taillight of leading vehicle  40 . 
         [0077]    For the  106  cases, a time-to-contact (TTC) signal was generated on 81 cases (77%). where all 25 misses of threat assessment had only blinking hazard lights on but with taillights of leading vehicle  40  were off. 
         [0078]      FIG. 6   b  shows a graph of energy (e), as a function of frame number, where time-to-contact (TTC) is computed for left spot  42  on lead vehicle  40  as shown in  FIG. 6   a .  FIGS. 6   c  and  6   d  show graphs of the inverse of the square root of energy (e), as a function of frame number, where time-to-contact (TTC) is computed for the left spot  42  on lead vehicle  40 . 
         [0079]      FIG. 7  shows the distribution of time of a Take Over Request (TOR) signal for use in a collision mitigation by braking (CMbB) system. Normalized distribution  72  and cumulative  74  are shown. The time-to-contact (TTC) average: 2.37 seconds. 
       Real World Examples 
       [0080]      FIG. 8   a  shows an example of a lead vehicle  40  at the right edge of the image frame with only one taillight  42 . Methods  301  and  501 , according to feature of the present invention, were run on over 20 thousand prerecorded night clips which represent about 350 hours of driving. There were many examples where the target or lead vehicle  40  vehicle had only one taillight and some where the standard vehicle detection failed to detect the target vehicle and the spot based time-to-contact (TTC). Methods  301  and  501  worked well. In addition, 60 motorcycles were correctly detected using methods  301  and  501 . 
         [0081]      FIG. 8   b  shows a graph of energy (e) as a function of frame number, where time-to-contact (TTC) is computed for the left spot  42  on lead vehicle  40 .  FIGS. 8   c  and  8   d  show a graph of the inverse of the square root of energy (e) as a function of frame number where time-to-contact (TTC) is computed for a single taillight spot  42  on lead vehicle  40  as shown in  FIG. 8   a.    
         [0082]    There were 35 false time-to-contact (TTC) warnings giving a Mean Time Between Failure (MTBF) of 10 hours. Of these, 13 were stationary light spots on a curved tunnel wall as shown in  FIG. 9 . The stationary light spots are reflection of the tunnel overhead lights. Eight were small spots/reflector on a leading vehicle, but outside its bounding rectangle. Two were reflections on the road and two on reflectors on poles on the side of the road. Other failures were due to significant host vehicle  18  yaw and vehicles at the image boundary. 
         [0083]    As shown in  FIGS. 10   a  and  10   b,  the AC light sources of the tunnel overhead lights can be filtered out by noticing the known fluctuations in energy due to the AC power source. 
         [0084]      FIG. 10   a  shows energy (e) with the effects of the AC light sources of the tunnel overhead lights.  FIGS. 10   b  and  10   c  show the inverse of the square root of energy (e) where time-to-contact (TTC) is computed with and without the effects of the AC light sources of the tunnel overhead lights respectively. 
       Combination with Other Driver Assistance Systems 
     Combination with Stereo 
       [0085]    Consider a classic two camera stereo system with a focal length of f=950 pixels and a baseline b=0.2 m. Approaching a single light target with a closing speed of 60 km/h. A time-to-contact (TTC) of 2.5 seconds would be at a distance Z=41 meters. At that distance the stereo disparity d, would be: 
         [0000]    
       
         
           
             
               
                 
                   d 
                   = 
                   
                     
                       fb 
                       Z 
                     
                     = 
                     
                       
                         
                           950 
                           * 
                           0.2 
                         
                         41 
                       
                       = 
                       
                         4.6 
                          
                         
                             
                         
                          
                         pixels 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0086]    In order to compute the time-to-contact (TTC) from a classic stereo system, the disparity may be calculated at multiple time steps. The change in disparity over time gives an estimate of the time-to-contact (TTC). Alternatively, disparity may be converted to distance and reason in metric space. In any case, the change in disparity over 0.25 secs will be about 1/10 of the value d computed above or about 0.46 pixels. Given the slight differences between cameras it may be often difficult to determine stereo disparity on a spot with the required accuracy. 
         [0087]    A solution is to apply the time-to-contact (TTC) from method  301  to each spot where the disparity indicates a distance below v×T, where v is the host vehicle  18  velocity and T is some time threshold such as T=2.5 sec. 
         [0088]    The time-to-contact (TTC) method  301  can be applied to one camera  12 , to both cameras  12  individually or to both cameras  12  together, summing up the energy from the corresponding spot  42  in the left and right images. 
       Combination with Radar 
       [0089]    The radar system gives accurate range and range rate information using a Doppler shift. Computing time-to-contact (TTC) from radar range and range rate of change is straightforward. However, the angular resolution of the radar may be poor and thus the lateral distance accuracy is weak. It may be advantageous to combine radar information with camera  12  information. A key task is matching radar targets and vision targets. Matching may be performed using various known techniques based on angle or based on angle plus range. 
         [0090]    Time-to-contact (TTC) from spots  42  information enables matching using angle and time-to-contact (TTC). Both radar and vision system  16  provide a list of targets with angle and time-to-contact (TTC) value.
       1. For each radar target find all vision targets that are within a given angular range.   2. Find the vision target that maximizes:       
 
         [0000]    
       
         
           
             M 
             = 
             
               
                 α 
                  
                 
                     
                 
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                   e 
                   
                     
                       - 
                       
                         
                           ( 
                           
                             
                               θ 
                               r 
                             
                             - 
                             
                               θ 
                               v 
                             
                           
                           ) 
                         
                         2 
                       
                     
                     
                       σ 
                       θ 
                     
                   
                 
               
               + 
               
                 β 
                  
                 
                     
                 
                  
                 
                   e 
                   
                     
                       - 
                       
                         
                           ( 
                           
                             
                               TTC 
                               r 
                             
                             - 
                             
                               TTC 
                               v 
                             
                           
                           ) 
                         
                         2 
                       
                     
                     
                       σ 
                       TTC 
                     
                   
                 
               
             
           
         
       
     
         [0000]    where: σ is the angle of the target found by radar, θ v  is the angle of the target found by vision, TTC r  is the time-to-contact from radar, TTC v  is the time-to-contact from spots. 
         [0093]    σ 0 , σ TTC  are standard deviations of the difference in angle and time-to-contact as calculated respectively using radar and vision. α and β are weight constants. 
         [0094]    After matching, the more accurate vision angle can be combined with the accurate radar range and time-to-contact (TTC) to provide improved collision course detection and forward collision warning (FCW)  22  using brightness of spots or to provide collision mitigation by braking (CMbB)  21 . 
       Combination with Lidar 
       [0095]    The Lidar system typically provides better angular resolution than radar and provides an accurate range but does not provide range rate directly. Range rate may be provided by differentiating distance to target Z. The same algorithm can be used as for radar for matching using angle but with different weight constants. Following the matching, the time-to-contact (TTC) values from Lidar and vision can be combined. 
         [0096]    The term “inlier” as used herein is in the context of the estimation of parameters of a mathematical model from a set of observed data. Data whose distribution can be explained by some set of the mathematical model parameters are known as “inliers” as opposed to “outliers” which are data which does not fit the mathematical model parameters. 
         [0097]    The term “energy” as used herein for an imaged spot of a light source in real space is proportional to the sum of the grey scale or color intensity values of the picture elements (pixels) of the imaged spot. The term “pixel value” refers to the grey scale and/or color intensity value of the picture element. 
         [0098]    The indefinite articles “a”, “an” is used herein, such as “a light source”, “a spot” have the meaning of “one or more” that is “one or more light sources” or “one or more spots”. 
         [0099]    Although selected features of the present invention have been shown and described, it is to be understood the present invention is not limited to the described features. Instead, it is to be appreciated that changes may be made to these features and combinations between the various embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and the equivalents thereof.