Patent Publication Number: US-7221776-B2

Title: Video stabilizer

Description:
COPYRIGHT NOTICE 
     A portion of the disclosure of this patent document contains material that is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent files or records, but otherwise reserves all copyright rights whatsoever. 
     BACKGROUND 
     1. Field of the Invention 
     The invention is generally related to digital image processing, and, in particular, is related to video stabilization. 
     2. Description of Related Art. 
     Video cameras are becoming more popular today as they become more widely available at lower prices. A video camera records sequential images within “frames.” A frame is a representation of an image at an instant of time. Each frame in a video segment (i.e., a sequence of frames) represents the image at a different instant in time. When several frames are recorded, at sequential instances in time, and are shown to the human eye in quick succession, the human eye is able to discern motion in the video segment. 
     Video (i.e., moving pictures) normally consist of a lot of motion, including object motion, such as a bird flying, and camera motion, such as camera panning, zooming, and tilting. The human eye may feel uncomfortable if the motion in the video is too fast, especially if the motion is changing very quickly in its direction or speed. 
     Other than natural motion of an object (e.g., one that is moving away from a stable or non-moving video camera), the video camera may record unwanted motion. The term “unwanted” usually refers to camera motion frequently resulting from hand jittering or from the camera person walking or otherwise moving. Other unwanted motion may result if, for example, wind shakes a mounted camera or a vehicle carrying a camera traverses rough terrain. Unwanted motion is very common in home videos. 
     Unwanted motion is also said to include “high frequency” components. The term “high frequency” refers to the motion changing very quickly in direction (e.g., left to right) or in speed (e.g., getting very fast or slowing down) in a unit of time (e.g., one second). 
     Video stabilization refers to a process for compensating for “unwanted” motion in a video segment. Video stabilization has been discussed in the literature for a number of years. The problem of “shaking shot” is common in home video. When a hand held camera is unsteady, video frames may be blurred or displaced, making viewing of the video difficult. Some high-end hand held video cameras support hardware video stabilization devices, notably “liquid lens” and electronic solutions. Some video cameras with such electronic solutions include the Sony® DCR-TRV900 video camera available from Sony Electronics, Inc. and the-Canon® ZR20 video camera available from Canon, U.S.A. Inc. 
     Such devices incorporating electronic solutions are expensive and are typically unavailable to the casual photographer. Moreover, these electronic solutions handle small amounts of movement. The electronic solutions are unable to distinguish between scanning and a lot of shaking, so they are unable to eliminate shaking. Overall, the electronic solutions try to slow down all motion in the video, without distinguishing between wanted and unwanted motion. 
     Additionally, video stabilization has been a topic in academic research. In some cases, the motion between each pair of consecutive frames or between each frame and a chosen origin frame is estimated. Based on the motion estimation, some inter-frame transformation parameters are computed for transforming (sometimes referred to as warping) each frame with respect to the origin frame. This technique, however, does not work when the camera is moving normally (e.g., panning, zooming, or tilting). Instead, the technique works only with a static camera. 
     Another conventional solution for unwanted motion is to map the estimated motion to some camera motion model (e.g., panning, zooming, tilting, etc.). Based on the camera model, each frame is transformed (i.e., its pixels are adjusted). There are several difficulties in these techniques. For example, motion estimation in video is time consuming and inaccurate when there are many outliers (i.e., data points that do not fall in the range of other data points). Another difficulty is that it is not uncommon to have several camera motions simultaneously, and, therefore, application of a single camera motion model leads to inaccurate results. 
     SUMMARY 
     A video segment is processed to remove unwanted motion, resulting in a stabilized video segment. 
     According to one embodiment of the invention, a method for stabilizing motion in a sequence of frames is provided. One or more features in a first frame in the sequence of frames are identified. Tracked positions are calculated for one or more features in each other frame in the sequence of frames based on the features in the first frame. Ideal positions are calculated for the features in each other frame in the sequence of frames based on the tracked positions. Transformation information is identified based on the tracked positions and the ideal positions. Each other frame in the sequence of frames is transformed by adjusting pixels based on the transformation information. 
     According to another embodiment of the invention, a method for stabilizing a sequence of frames is provided. A first position of a point of interest in a first frame is calculated. Estimated positions of points of interest are identified in a second frame and a third frame that correspond to the point of interest in the first frame. Tracked positions of points of interest are identified in the second frame and the third frame based on the estimated positions of the point of interest. The tracked positions comprise a second position for the point of interest in the second frame and a third position for the point of interest in the third frame. The first position, the second position, and the third position are plotted on an X,Y coordinate graph. The first position is connected to the third position on the X,Y coordinate graph. The ideal positions of the point of interest in the first frame, second frame, and third frame lie on the connection. 
     According to a further embodiment of the invention, a system comprises a computer including a processor and a memory, a sequence of frames stored in the memory, and a program stored in the memory of the computer. The program is executed by the processor of the computer to identify one or more features in a first frame in the sequence of frames and to calculate tracked positions for one or more features in each other frame in the sequence of frames based on the features in the first frame. Execution of the program calculates ideal positions for the features in each other frame in the sequence of frames based on the tracked positions and identifies transformation information based on the tracked positions and the calculated positions. Furthermore, execution of the program transforms each other frame in the sequence of frames by adjusting pixels in each other frame based on the transformation information. 
     According to yet another embodiment of the invention, a system comprises a camera, a sequence of frames captured by the camera, a computer with a processor and a memory. The sequence of frames is stored in the memory of the computer. The system includes means for performing local tracking to obtain tracked positions for a feature in multiple frames of the sequence of frames and means for calculating ideal positions for the feature in each of the multiple frames. The system also includes means for identifying transformation information based on the tracked positions and the ideal positions for each feature in the one or more features. Additionally, the system includes means for transforming each other frame by adjusting pixels in each other frame based on the transformation information. 
     According to a further embodiment of the invention, a computer readable storage medium encoded with software instructions. Execution of the instructions performs the following: one or more features in a first frame in the sequence of frames are identified; tracked positions are calculated for one or more features in each other frame in the sequence of frames based on the features in the first frame; ideal positions are calculated for the features in each other frame in the sequence of frames based on the tracked positions; transformation information is identified based on the tracked positions and the calculated positions; and, each other frame in the sequence of frames is transformed by adjusting pixels in each other frame based on the transformation information. 
     The invention is better understood upon consideration of the detailed description below, and the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram that illustrates components that may be used in one embodiment of the invention; 
         FIG. 2  is a flow diagram that illustrates processing of a video segment in one embodiment of the invention; 
         FIGS. 3A ,  3 B, and  3 C illustrate frames in a video segment in one embodiment of the invention; 
         FIGS. 4A and 4B  are flow diagrams that illustrate video stabilization processing in one embodiment of the invention; 
         FIG. 5  illustrates motion of points of interest of an image when motion is slow versus when motion is fast in one embodiment of the invention; 
         FIG. 6  illiterates lines in a frame in one embodiment of the invention; 
         FIGS. 7A ,  7 B, and  7 C illustrate tracking in one embodiment of the invention; 
         FIGS. 8A and 8B  illustrate sample graphs showing motion trajectories in embodiments of the invention. 
     
    
    
     Use of the same reference symbols in different figures indicates similar or identical items. 
     DETAILED DESCRIPTION 
     In accordance with an embodiment of the invention, a computer programmed with software (referred to herein as “video stabilization system”) processes a video segment to remove unwanted motion, resulting in a stabilized video segment. The video stabilization system tracks one or more features through multiple frames, identifies ideal positions for the features, and then generates transformation information (e.g., rotation, scaling, shearing, and/or translation) to transform all pixels in each frame to ideal positions based on the ideal positions of the features. 
     In particular, the video stabilization system of the invention tracks some features all the way through some video segment, rather than estimating camera motion between two frames. In one embodiment, a “feature” may be, for example, a point, line, region, edge, etc. For example, a feature may be a point of interest in an image that represents a large brightness change in two dimensions. 
     A video segment includes a sequence of frames. Each frame represents an image (simplistically, this can be viewed as a picture taken with a camera). If a sequence of frames is taken of an image that is not moving with a video camera that is not moving, each pair of consecutive frames will be almost exact (note there may be some change due to hand jitter and other factors). 
     On the other hand, if the sequence of frames are taken of a moving object, or the video camera is moving, or both, consecutive frames capture different images. If there is smooth motion, then it is possible to select a feature in a first frame, find the corresponding pixel or pixels associated with that feature in subsequent frames, map the points on a graph (e.g., an X-Y graph), and obtain a smooth path when the positions of the features are connected. When there is unwanted motion, however, a feature across frames does not follow a smooth path. This results in “jitters” when viewed by the human eye. The video stabilization system of the invention identifies the trajectory of a set of features and adjusts them to “ideal positions” that results in a smooth video segment. 
     The video stabilization system reduces and/or removes the unwanted motion (also referred to as a “high frequency portion”) without affecting normal motion (also referred to as a “low frequency portion”). Therefore, a camera need not be ideally static or have only one type of motion. 
     The software solution has many advantages over a hardware solution (e.g., liquid lens). For example, the video stabilization system can classify the “normal” camera motion and jittering or unwanted motion. The video stabilization system can correct larger displacement (e.g., caused by a fast moving camera) than hardware. The video stabilization system can stabilize video from any video camera, rather than from high-end products, as is the case with hardware solutions. Furthermore, software production also costs less than hardware manufacturing. 
       FIG. 1  is a block diagram that illustrates components that may be used in one embodiment of the invention. In one embodiment, a video camera  100  records an image  110 . The video camera  100  and/or the image may be in motion. The video camera  100  includes data storage that stores the video segment. The video segment is transferred to a computer  120 , which includes video stabilization system  130  stored, for example, on a hard drive of the computer  120  or a CD-ROM (compact disc-read only memory) inserted into the CD-ROM drive of the computer  120 . In other embodiments, the video stabilization system  130  may be implemented as a hardware video stabilizer or as a combination of hardware and software. 
     In one embodiment, the video camera  100  is a digital video camera. Digital video cameras offer many advantages. For example, digital images are easier to manipulate and easier to distribute over electronic media (e.g., the Internet or e-mail). In another embodiment, the video camera  100  is an analog video camera using film to record images. The film can be converted to digital images for processing with the video stabilization system  130 . In yet another embodiment, a still picture camera, rather than video camera  100 , is used to take a series of pictures that are either digitally recorded or converted to digital images. The series of pictures are transformed into a video segment that may be processed with the video stabilization system  130 . 
     The video stabilization system works with both gray scale or color images. For example, each image can be a two-dimensional array of RGB (red-green-blue) pixels or YUV pixel values representing color pixels. YUV is defined by the Commission International de L&#39;Eclairage (CIE), which is an international committee for color standards. YUV is often used in Phase Alternation Line (PAL) television (an analog television display standard), where the luminance and the chrominance are treated as separate components. In YUV systems, a luminance signal (represented with “Y”) typically occupies the maximum bandwidth, while chrominance signals (represented by “U” and “V”) typically occupy half the bandwidth each (i.e., because the eye is less sensitive to color detail). 
     In one embodiment, the images are represented in Microsoft Windows™ 24-bit BITMAP format. In this format, each pixel has three adjacent bytes for Blue, Green, and Red channels respectively. In one embodiment, each of the source images is W (i.e., width) by H (i.e., height) pixels. For example, the dimensions may be 720×480 pixels or 352×288 pixels. 
       FIG. 2  is a flow diagram that illustrates processing of a video segment in one embodiment of the invention. In particular, block  200  represents the video stabilization system  130  receiving a video segment. Block  202  represents the video stabilization system  130  performing video stabilization to remove unwanted motion from the video segment. For example, the video stabilization system  130  processes the data to reduce the jitter caused by unintended camera motion. Block  204  represents the video stabilization system  130  outputting a stabilized video segment. The stabilized video segment may be output to local data storage, remote data storage, to a user monitor, to television transmitters, or to another device. The digital images may be converted to analog images. Also, the stabilized video segment may be output to other software for additional processing. 
     In an alternative embodiment, as a video camera  100  captures images, the video camera  100  transfers data directly to computer  120 , which has sufficient memory to hold the data. The computer  120  processes the data in real time to reduce jitter, and, for example, transfers the data to storage, to a user monitor, or to television transmitters. 
     The computer  120  may be a personal computer, workstation, laptop computer, personal digital assistant, mainframe computer, or other processing device. Also, the computer  120  may be a general purpose or a special purpose computer. For example, computer  120  may be a computer having a Pentium® chip, available from computer vendors such as International Business Machines Corporation, Inc., of Armonk, N.Y. or Apple Computer, Inc. of Cupertino, Calif. The computer  120  may include an operating system, such as Microsoft® Windows® 2000 from Microsoft Corp. of Redmond, Wash. 
     Given ongoing advances in the data processing industry, it is conceivable that the storage and processing features illustrated in  FIG. 1  may be incorporated on integrated circuits, microprocessors, and other electronics small enough to fit within a handheld video camera. Therefore, the video stabilization system  130  may be incorporated into the video camera  100  as software, hardware, or a combination of hardware and software. Nevertheless, merely reducing the size or altering the location of elements of this invention does not depart from the spirit and scope of the invention. 
       FIGS. 3A ,  3 B, and  3 C illustrate frames in a video segment in one embodiment of the invention. In  FIG. 3A , a scene is the subject of a video camera recording resulting in frame  300 . In the scene, one or more objects (e.g., cars) may have been in motion. Additionally, the video camera may have been in motion (e.g., panning, zooming or tilting). This is referred to as normal motion. In addition, there may be unintended motion of the camera caused by, for example, the camera person walking while recording. 
     In  FIG. 3A , multiple points of interest (POIs) have been detected in frame  300 . Although points of interest are illustrated in  FIGS. 3A ,  3 B, and  3 C, other features may be used in accordance with the technique of the invention. In this illustration, crossbars (i.e., +) are used to indicate points of interest, such as  310 ,  312 , and  314 . In one embodiment, at least 3 points of interest are tracked through a video segment.  FIGS. 3B and 3C  illustrate subsequent frames to  FIG. 3A  in a video segment. 
       FIGS. 4A and 4B  are flow diagrams that illustrate video stabilization processing in one embodiment of the invention. For ease of illustration, the flow diagrams refer to a point of interest, which is one type of feature. It is to be understood that the technique of the invention is applicable to any type of feature or distinguishing characteristic between frames. 
     Block  400  represents the video stabilization system  130  initializing memory and variables. Initialization is performed to initialize variables, allocate memory, and open an input video file, such as an Audio Video Interleaved (AVI) file. In one embodiment, a video file is one in which motion picture and audio are interleaved. 
     Block  401  represents the video stabilization system  130  determining whether the video camera motion was fast or slow. In one embodiment, a user submits input indicating whether the camera moved fast or slow. In another embodiment, the video stabilization system  130  compares one or more points in a series of frames and determines whether the motion was fast or slow based on the amount of distance each point moved from one frame to another. 
     For example, if the video stabilization system  130  finds that point ( 3 , 3 ) in frame  1 , is in location ( 30 , 30 ) in frame  2 , the video stabilization system  130  detects that the camera motion was fast. While, for example, if the same point ( 3 , 3 ) in frame  1  is in location ( 4 , 4 ) in frame  2 , the video stabilization system  130  detects that the camera motion was slow. 
       FIG. 5  illustrates motion of points of interest of an image when motion is slow versus when motion is fast in one embodiment of the invention. Image  500  is a first image having three points of interest  502 ,  504 , and  506 . Image  510  represents a second image captured when motion is slow, and points of interest  502 ,  504 , and  506  have moved horizontally relative to their positions in image  500 . Image  520  represents a third image captured when motion is fast, and points of interest  502 ,  504 , and  506  have moved horizontally relative to their positions in image  500 . In image  520 , point of interest  506  has partially moved off of the image. Points of interest  502 ,  504 , and  506  have moved more in image  520  than in image  510 . 
     The video stabilization system  130  processes groups of pictures in the video segment. Block  402  represents the video stabilization system  130  retrieving a sequence of frames of a video segment from storage or memory. In particular, the video stabilization system  130  selects a video segment made up of a sequence of frames and designates this as a group of pictures (GOP). In one embodiment, a group of pictures may include frames captured during 2–3 seconds of recording, and approximately 25–30 frames may be captured each second. So, a group of pictures may include 50–90 frames. 
     In another embodiment, a set number of frames (e.g., 60 frames) are selected as a group of pictures. At this point, the length of the group of pictures is calculated. 
     In either embodiment, the video stabilization system  130  may start with a long video segment (e.g., 3 seconds or 90 frames). If the video stabilization system  130  determines that many (e.g., more than half) of the points of interest in the first frame are missing from the last frame in the sequence, then the video stabilization system  130  may truncate the video segment and process a smaller sequence of frames. Then, the next video segment processed would begin at the truncated position. For example, if the video stabilization system  130  initially took a video segment having 90 frames and truncated the video segment to work with 40 frames, the next video segment would start at the 41 st  frame. 
     Block  404  represents the video stabilization system  130  determining whether the video segment has been completely processed (i.e., to its end). If not, processing continues to block  408 . Otherwise, processing continues to block  406  and post-processing is performed. Post-processing includes freeing memory and closing the output .avi file. 
     Block  408  represents the video stabilization system  130  computing points of interest (POIs) for the first frame. For example,  FIG. 3A  illustrates a first frame with points of interest. These points of interest may be selected using, for example, the Harris technique for corner and edge detection or the Kitchen-Rosenfeld technique for corner detection. For more information on the Harris technique, see “A Combined Comer and Edge Detector,” by C. Harris and M. Stephens, Fourth Alvey Vision Conference, pp. 147–151, 1988, which was available for download from the website of the Department of Electrical Engineering of the University of Leuven, which is incorporated herein by reference in its entirety and is listed in Appendix A. For more information on the Kitchen-Rosenfeld technique, see “Gray-Level Corner Detection,” by L. Kitchen and A. Rosenfeld, Pattern Recognition Letters, 95–102, December, 1982, which is incorporated herein by reference in its entirety. 
     Alternatively the Hough transform technique for line detection (rather than point of interest detection) may be used. For example, if the Hough transform technique were used, lines would be detected and compared in frames, rather than points of interest.  FIG. 6  illiterates lines in a frame  600  in one embodiment of the invention. For example, vertical line  602  is found along a telephone pole, horizontal line  604  is found along a sidewalk, and horizontal lines  606  and  608  are found along parking space markings. Although the lines depicted in  FIG. 6  extend across much of frame  600 , the lines could be shorter segments in alternative embodiments. 
     For more information on the Hough transform technique, see “Fundamentals of Digital Image Processing,” by Anil K. Jain, Prentice-Hall, Inc., page 362, 1989 or “Digital Image Processing,” by Rafael C. Gonzalez and Richard E. Woods, page 432–438, each of which is incorporated herein by reference in its entirety. In one embodiment, the positions of the points of interest of the first frame may be stored in a linked list. However, alternative data structures such as tables may be used. For ease of illustration, a table will be used to provide an example. The following Table A is a sample table of positions of points of interest in a first frame (e.g., frame  300  of  FIG. 3A ): 
     
       
         
           
               
               
               
             
               
                 TABLE A 
               
               
                   
               
               
                 Frame 1 
                 X-coordinate 
                 Y-coordinate 
               
               
                   
               
             
            
               
                 Point 1 
                 7 
                 3 
               
               
                 Point 2 
                 8 
                 7 
               
               
                 Point 3 
                 9 
                 8 
               
               
                   
               
            
           
         
       
     
     For each pair of consecutive frames, the video stabilization system  130  identifies positions for corresponding points of interest (blocks  410 – 426 ). In particular, the video stabilization system  130  identifies estimated positions for points of interest in blocks  418  and  424 . Then, in block  420 , the video stabilization system  130  identifies tracked positions for the points of interest. The tracked positions are more accurate than the estimated positions. 
     In an alternative embodiment, a selected frame, such as the first frame or the middle frame in a group of pictures, may be compared to every other frame. This alternative works well when there is little change between the compared frames. Block  410  represents the video stabilization system  130  selecting the next frame in the group of pictures, starting with the second frame. Block  412  represents the video stabilization system  130  setting a current-frame variable to the selected next frame and setting a previous-frame variable to the frame before the current-frame. Initially, the video stabilization system  130  works with a first frame and a second frame (which represent the previous and current frames, respectively, in one iteration of the process). 
     Block  414  represents the video stabilization system  130  determining whether all the frames in the group of pictures have been selected and processed. If so, processing continues to block  427 . Otherwise, processing continues to block  416 . Block  416  represents the video stabilization system  130  determining whether the camera was moving fast when the video segment was recorded (this information is determined in block  401 ). 
     If the intended motion of the camera (e.g., pan, zoom, or tilt) is slow, then global tracking is performed in the second frame with respect to the points of interest selected for the first frame. If the motion is fast, a new set of points of interest are detected in the second frame and matching (rather than tracking) is performed in the first frame for these points of interest. In one embodiment, global tracking refers to selecting a point of interest in a first frame, such as ( 3 ,  3 ), and searching a large area in the second frame around this point, such as searching a 16×16 area around ( 3 ,  3 ) in the second frame, for a point of interest corresponding to the point of interest in a first frame. In one embodiment, matching refers to selecting points of interest in a first frame, selecting points of interest in a second frame, and attempting to match the points of interest in the first frame to those in the second frame. 
     In one embodiment, frames are examined in consecutive pairs. One pair includes a first frame and a second frame (which are also referred to as a previous frame and a current frame, respectively). 
     In block  418 , the video stabilization system  130  performs global tracking. There are many techniques that may be used to perform tracking (global or local). One technique is described in “Making Good Features Track Better, by Tiziano Tommasini, Andrea Fusiello, Emanuele Trucco, and Vito Roberto, pages 1–6, which is incorporated herein by reference in its entirety. For global tracking, the points of interest from the first frame are tracked in a large area in the second frame to estimate the global movement between the first frame and the second frame. For global tracking, initially, a first point of interest in a first frame is selected. For this point of interest, the video stabilization system  130  attempts to find a point of interest within an area of a second (e.g., consecutive) frame that estimates the position of the point of interest in the first frame. This estimated position of the point of interest in the second frame may not be the point of interest that actually corresponds to the point of interest in the first frame due to possible errors with the tracking technique. The estimated position is only an estimate of where the point of interest from the first frame is in the second frame, considering there may have been camera and/or object motion. As will be discussed with respect to local tracking in block  420 , additional processing is done to confirm that the estimated position of the point of interest actually corresponds to the point of interest in the first frame. 
     For example, the video stabilization system  130  may search a 16×16 pixel area around the location of the first point of interest in the second frame. For example, if the first point of interest is ( 8 ,  8 ) in the first frame, then the area formed by corner points ( 0 ,  0 ), ( 0 ,  16 ), ( 16 ,  0 ), and ( 16 ,  16 ) may be searched for a corresponding point of interest in the second frame. The result is an estimated position of the point of interest in the second frame. 
       FIGS. 7A ,  7 B, and  7 C illustrate tracking in one embodiment of the invention. Once, point of interest is identified in a first frame, such as frame  700  in  FIG. 7A , then a 3×3 “window” is used to obtain the pixel value of each pixel in the 3×3 area  710  in which the point of interest  702  is the center pixel. Each pixel has a value associated with it. For example, when an image represented with a two-dimensional array of RGB (red-green-blue) pixels, each pixel has a value associated with it ranging from 0–255. A larger pixel value may be indicative of, for example, a brighter, more colorful pixel. In alternative embodiments, the area  710  selected may be smaller or larger than 3×3. 
     Next, for a second frame  720  in  FIG. 7B , the video stabilization system  130  selects a large area, such as area  721 . Within 8×8 area  721 , for each pixel, the video stabilization system  130  selects a pixel, designates the selected pixel as a center pixel of a 3×3 area, and identifies the pixel value of each pixel in the 3×3 area. For example, for pixel  722 , the video stabilization system identifies the pixel values of each pixel in the 3×3 area designated by brackets  724  and  726 . Once, this is done for each pixel in area  721 , the video stabilization system attempts to find the pixel in the second frame  720  which is most similar to the point of interest  702  in the first frame  700 . 
     In one embodiment, the video stabilization system  130  will compare the differences between the 3×3 area  710  in the first frame with each 3×3 area surrounding each pixel in the second frame to determine which pixel in the second frame has “neighboring” pixels (i.e., pixels that are one position away from the center pixel in any direction) that are most similar to the point of interest in the first frame. 
     After global tracking, the video stabilization system  130  has identified estimated positions for the points of interest in the second frame that estimate points of interest in the first frame. At this time, these are estimated positions for points of interest because the positions could be inaccurate. That is, the tracking technique of looking at neighboring pixel values may result in finding a pixel in the second frame that does not correspond to the point of interest in the first frame. Local tracking, performed in block  420 , attempts to confirm whether global tracking found the correct position of the point of interest in the second frame. Local tracking is described below with reference to  FIG. 7C . 
     In one embodiment, the estimated positions of points of interest may be stored in a linked list. However, alternative data structures such as tables may be used. For ease of illustration, a table will be used to provide an example. The following Table B is a sample table of estimated positions of points of interest in a second frame that correspond to points of interest in the first frame (illustrated in Table A) after global tracking has been performed (block  418 ). 
     
       
         
           
               
             
               
                 TABLE B 
               
             
            
               
                   
               
               
                 Estimated Positions from Global Tracking 
               
            
           
           
               
               
               
            
               
                 Frame 2 
                 X-coordinate 
                 Y-coordinate 
               
               
                   
               
               
                 Point 1 
                 8 
                 3 
               
               
                 Point 2 
                 9 
                 8 
               
               
                 Point 3 
                 10  
                 9 
               
               
                   
               
            
           
         
       
     
     In one embodiment, global tracking may be performed using epipolar geometric constraints to narrow down the tracking area and to remove outliers (i.e., points of interest that are far away from other points of interest). For more information on epipolar geometry, see “A Robust Technique for Matching Two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry,” by Zhengyou Zhang, pages 1–38, May 1994, which is incorporated herein by reference in its entirety. 
     On the other hand, if camera motion is fast, a new set of points of interest are selected in the second frame (block  422 ). Then, for each of these points, the video stabilization system  130  attempts to match points of interest in the second frame to points of interest in the first frame to estimate global movement between the first and second frames (block  424 ). 
     In one embodiment, for two frames, points of interest are calculated in each frame. Then, for each point of interest in each frame, the video stabilization system  130  computes a neighbor (i.e., another point of interest in that frame) distribution in terms of distance and direction. For example, in  FIG. 3C , for frame  350 , the video stabilization system  130  identifies an area  360  around point of interest  362 . The area  360  may be, for example, a circular area having a specified radius. Then, the video stabilization system  130  generates a distance histogram (indicating the distance of each neighbor in the area  360  from the point of interest) and a direction histogram (indicating the direction of each neighbor, such as above and to the left, relative to the point of interest). The area  360  may be partitioned into sections for ease in generating the histograms. The histograms are generated by the video stabilization system  130  for each point of interest in the first and second frames. The video stabilization system  130  determines that a point of interest in a first frame corresponds to a point of interest in a second frame if they have the most similar neighbor distributions (e.g., two points of interest have neighbors at approximately the same distance and direction away from them). In this example, point of interest  362  at estimated position ( 7 ,  4 ) corresponds to point of interest  310  in the first frame illustrated in  FIG. 3A . 
     In an alternative embodiment, the matching technique described in “A Fast Matching Method for Color Uncalibrated Images Using Differential Invariants,” British Machine Vision Conference, by V. Gouet, P. Montesinos, D. Pel, pages 367–376 may be used, and this article is incorporated herein by reference in its entirety. 
     In other embodiments, matching can be implemented using any correlation technique known in the art. For example, a description of image matching by correlation can be found in “Digital Image Processing” by R. Gonzales and R. Woods, Addison-Wesley Publishing Co., Inc., 1992, pages 583–586. Correlation is a technique for matching two images by finding, for an observed region on the first image, the corresponding region on the second image. Correlation may be performed by selecting an observed region defined by a window in the first image. Then, the second image is searched by moving the window around the entire image area and computing the correlation between the observed region and each of the areas in the second image. The similarity between two areas are determined using correlation criteria and a match between the two areas is found when the correlation yields the largest correlation value. When a match between the observed region and the match region is found, the distance from the observed point and its match is called “disparity” having units in pixels. 
     In another embodiment, the correlation process further includes a brightness normalization operation to account for the fact that first and second images may be captured at different times with different exposure parameters. 
     Block  426  represents the video stabilization system  130  updating the current positions of points of interest to their estimated positions in a data structure. In one embodiment, this information may be stored in a linked list. However, alternative data structures such as tables may be used. For ease of illustration, a table will be used to provide an example. In this example, The following Table C is a sample table of estimated positions of points of interest in a second frame that match points of interest in the first frame (illustrated in Table A): 
     
       
         
           
               
             
               
                 TABLE C 
               
             
            
               
                   
               
               
                 Estimated Positions from Matching 
               
            
           
           
               
               
               
            
               
                 Frame 2 
                 X-coordinate 
                 Y-coordinate 
               
               
                   
               
               
                 Point 1 
                 7 
                 4 
               
               
                 Point 2 
                 9 
                 7 
               
               
                 Point 3 
                 10  
                 8 
               
               
                   
               
            
           
         
       
     
     Whether camera motion is slow or fast, it is possible that a first point of interest in a first frame is no longer in the second frame (i.e., it has moved completely off the frame). Therefore, it may be that not every point of interest in one frame has a corresponding point of interest in a second frame. Additionally, there may be new points of interest in the second frame that do not have corresponding points of interest in the first frame. 
     Next, the video stabilization system performs local tracking (block  420 ) on estimated positions of points of interest. In one embodiment, local tracking may be performed using epipolar geometric constraints to narrow down the tracking area and to remove outliers (i.e., points of interest that are far away from other points of interest). For more information on epipolar geometry, see “A Robust Technique for Matching Two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry,” by Zhengyou Zhang, pages 1–38, May 1994, which is incorporated herein by reference in its entirety. 
     In particular, the estimated positions of points of interest (from either global tracking in block  418  or matching in block  424 ) are tracked again, but in a smaller area, such as an area 2×2 pixels in size. For example, in frame  730  of  FIG. 7C , 2×2 area  731  is tracked. That is, the 3×3 window used for frame  700  is applied to each pixel in the 2×2 area  731 . Each pixel in area  731  is treated as the center of a 3×3 area, and the values of the pixels in the 3×3 area are identified. Then, the pixel values in each 3×3 area are compared to the pixel values in the 3×3 area  710  of frame  700 . The result may be that the estimated position of a point of interest in a second frame is found to be the correct position that corresponds to the point of interest in the first frame, taking into consideration motion of the camera and/or object. Thus, local tracking adjusts the estimated position of points of interest for improved accuracy, resulting in tracked positions of points of interest. 
     The result of blocks  410 – 426  is a table illustrating, for each point of interest, a tracked position for each corresponding point of interest in each subsequent frame. 
     The following Table D is a sample table illustrating tracked positions of points of interest for a second frame after local tracking has been performed (block  420 ): 
     
       
         
           
               
             
               
                 TABLE D 
               
             
            
               
                   
               
               
                 Tracked Positions from Local Tracking 
               
            
           
           
               
               
               
            
               
                 Frame 2 
                 X-coordinate 
                 Y-coordinate 
               
               
                   
               
               
                 Point 1 
                  9 
                 4 
               
               
                 Point 2 
                 11 
                 8 
               
               
                 Point 3 
                 10 
                 8 
               
               
                   
               
            
           
         
       
     
     After determining the motion of the points of interest, the video stabilization system  130  draws a motion trajectory (block  427 ) for each point of interest across multiple frames. In particular, the video stabilization system  130  selects a point of interest. For the selected point of interest, the video stabilization system  130  plots the tracked positions (identified in block  420 ) of the point of interest across a sequence of frames on an X,Y coordinate graph. Next, the video stabilization system  130  connects the first position to the last position in the graph using a linear or non-linear connection (e.g., a line or a curve, respectively). The linear or non-linear connection is referred to as a motion trajectory. All positions on the motion trajectory are considered to be ideal positions, while positions of the point of interest that do not fall on the motion trajectory are considered to include unwanted motion. 
       FIGS. 8A and 8B  illustrate sample graphs  800  and  850  showing motion trajectories in embodiments of the invention. Each graph  800  and  850  illustrates a motion trajectory for one point of interest across five frames. The motion trajectories are drawn using the tracked positions of one point of interest. If each of the positions were connected together, the result may be a line that is not smooth, which represents a combination of normal motion and unwanted motion. The video stabilization system  130  removes the unwanted motion from the combination, leaving only the normal motion. The normal motion of a point of interest may be linear (e.g.,  FIG. 8A ) or nonlinear (e.g.,  FIG. 8B ). 
     In one embodiment, as illustrated by  FIG. 8A , the video stabilization system  130  uses linear interpolation for each point of interest across five frames in a group of pictures. In particular, after plotting the tracked positions of one point of interest, the video stabilization system  130  draws a line from the first position of the point of interest to the last position of the point of interest. Then, the video stabilization system  130  determines that the ideal positions for a point of interest across the frames fall on the line. 
     In graph  800 , a motion trajectory for one point of interest, referred to as Point  1 , is illustrated. For this example, Point  1  has position ( 7 ,  3 ) in a first frame (Table A), tracked position ( 11 ,  8 ) in a second frame (Table D), tracked position ( 19 ,  8 ) in a third frame, tracked position ( 27 ,  6 ) in a fourth frame, and tracked position ( 35 ,  13 ) in a fifth frame. These positions are plotted in graph  800 . Then, a line is drawn that connects the position of Point  1  in the first frame of the video segment to the position of Point  1  in the fifth frame of the video segment. In graph  800 , the combined motion is represented by line  810 , while the normal motion is represented by line  820 . For the tracked position ( 11 ,  8 )  830  of the point of interest in the second frame (labeled “Frame 2”), the ideal position is ( 11 ,  5 )  840 . The difference between the tracked position ( 11 ,  8 ) and the ideal position ( 11 ,  5 ), which is a vertical 3 pixel change, represents the unwanted motion that is removed. In one embodiment, the ideal position of a point of interest has the same X-coordinate and a different Y-coordinate when compared to the tracked position of the same point of interest. 
     Table E is a sample table illustrating ideal positions of one point of interest across three frames: 
     
       
         
           
               
             
               
                 TABLE E 
               
             
            
               
                   
               
               
                 Ideal Positions 
               
            
           
           
               
               
               
            
               
                 Point 1 
                 X-coordinate 
                 Y-coordinate 
               
               
                   
               
               
                 Frame 1 
                  7 
                 3 
               
               
                 Frame 2 
                 11 
                 5 
               
               
                 Frame 3 
                 19 
                 7 
               
               
                 Frame 4 
                 27 
                 10  
               
               
                 Frame 5 
                 35 
                 13  
               
               
                   
               
            
           
         
       
     
     In an alternative embodiment, a curve may be drawn to connect the positions of the points of interest with a smoothening technique.  FIG. 8B  illustrates that the normal motion of a point of interest may be nonlinear. For example, in graph  850 , the combined motion is represented by line  860 , while the normal motion is represented by curve  870 . The tracked position  880  of the point of interest in the second frame (labeled “Frame 2”) differs from the ideal position of the point of interest  890 . 
     Once the motion trajectories are drawn (block  427 ), each frame in a group of pictures is again examined. Block  428  represents the video stabilization system  130  selecting the next frame in the current group of pictures, starting with the first frame. Block  432  represents the video stabilization system  130  computing ideal positions of each point in a frame according to motion trajectories. 
     Image stabilization is completed by computing transform parameters from motion trajectories (block  434 ) for each frame and by transforming the current frame by moving points from current positions to ideal positions (block  436 ) using the transform parameters. Then, the transformed frame is output (block  438 ). 
     The transform parameters are calculated using affine transformation. For more information on affine transformation, see “Computer Graphics Principles and Practice,” by James D. Foley, Andries van Dam, Steven K. Feiner, and John F. Hughes, Second Edition, Addison-Wesley Publishing Company, page 207, 1990; “Affine Transformation,” pages 1–8, which was available for download from the website of the School of Informatics at the University of Edinburgh on Oct. 25, 2001; and “Affine Transform Matrices,” pages 1–7, which was available for download from the website of the Libart Library on Oct. 25, 2001; each of which is incorporated herein by reference in its entirety. 
     A matrix is used to solve the transform parameters “a,” “b,” “c,” “d,” “m,” and “n” for the ideal positions of points of interest (x′, y′) and the tracked positions of points of interest (x, y). The ideal positions of points of interest (x′, y′), are determined by the video stabilization system  130  in block  432  (e.g., see Table E). The tracked positions of points of interest (x, y) are determined by the video stabilization system  130  in block  420  (e.g., see Table D). An image being recorded may be represented using an X, Y coordinate graph. The transform parameters “a,” “b,” “c,” and “d” represent rotation, scaling, and/or shearing information, while the transform parameters “m” and “n” represent translation information. Once the transform parameter values are obtained for the points of interest, these values are applied to all pixels in the frame. The result is a frame in which unwanted motion has been removed. 
     A general affine transformation maybe written as Equation (1): 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             x 
                             ′ 
                           
                         
                       
                       
                         
                           
                             y 
                             ′ 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               a 
                             
                             
                               b 
                             
                           
                           
                             
                               c 
                             
                             
                               d 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               x 
                             
                           
                           
                             
                               y 
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           
                             m 
                           
                         
                         
                           
                             n 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   (_1_) 
                 
               
             
           
         
       
     
     For example, in order to transform a tracked position of a point of interest such as ( 11 ,  8 ) to an ideal position of the point of interest ( 11 ,  5 ), the transform parameters are calculated using equation (2). 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             11 
                             ′ 
                           
                         
                       
                       
                         
                           
                             5 
                             ′ 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               a 
                             
                             
                               b 
                             
                           
                           
                             
                               c 
                             
                             
                               d 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               11 
                             
                           
                           
                             
                               8 
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           
                             m 
                           
                         
                         
                           
                             n 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   (_2_) 
                 
               
             
           
         
       
     
     Equation (1) may be written with pairs of equations (3) for three pairs of points of interest. Each pair of points of interest includes a tracked position of the point of interest (e.g., (x 1 , y 1 )) and an ideal position of the point of interest (e.g., (x′ 1 , y′ 1 )).
 
 x′   1   =ax   1   +by   1   +m  
 
 y′   1   =cx   1   +dy   1   +n  
 
 x′   2   =ax   2   +by   2   +m  
 
 y′   2   =cx   2   +dy   2   +n  
 
 x′   3   =ax   3   +by   3   +m  
 
 y′   3   =cx   3   +dy   3   +n   (3)
 
     For example, for tracked position of a point of interest such as ( 11 ,  8 ) and ideal position of the point of interest ( 11 ,  5 ), equations (4) may be used to solve for the transform parameters:
 
11=11 a+ 8 b+m  
 
5=11 c+ 8 d+n   (4)
 
     The pairs of equations (3) may be rewritten as equation (5): 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   x 
                                   1 
                                 
                               
                               
                                 
                                   y 
                                   1 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   x 
                                   1 
                                 
                               
                               
                                 
                                   y 
                                   1 
                                 
                               
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   x 
                                   2 
                                 
                               
                               
                                 
                                   y 
                                   2 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   x 
                                   2 
                                 
                               
                               
                                 
                                   y 
                                   2 
                                 
                               
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   x 
                                   3 
                                 
                               
                               
                                 
                                   y 
                                   3 
                                 
                               
                               
                                 0 
                               
                               
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                                 1 
                               
                               
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                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   x 
                                   3 
                                 
                               
                               
                                 
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                                   3 
                                 
                               
                               
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                                   x 
                                   4 
                                 
                               
                               
                                 
                                   y 
                                   4 
                                 
                               
                               
                                 0 
                               
                               
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                                 0 
                               
                               
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                                   x 
                                   4 
                                 
                               
                               
                                 
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                                   4 
                                 
                               
                               
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                                 1 
                               
                             
                             
                               
                                 
                                   x 
                                   5 
                                 
                               
                               
                                 
                                   y 
                                   5 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
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                                   x 
                                   5 
                                 
                               
                               
                                 
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                                   5 
                                 
                               
                               
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                           ) 
                         
                         ⋮ 
                       
                       
                         ︸ 
                         M 
                       
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             
                               a 
                             
                           
                           
                             
                               b 
                             
                           
                           
                             
                               c 
                             
                           
                           
                             
                               d 
                             
                           
                           
                             
                               m 
                             
                           
                           
                             
                               n 
                             
                           
                         
                         ) 
                       
                       
                         ︸ 
                         a 
                       
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               x 
                               1 
                               ′ 
                             
                           
                         
                         
                           
                             
                               y 
                               1 
                               ′ 
                             
                           
                         
                         
                           
                             
                               x 
                               2 
                               ′ 
                             
                           
                         
                         
                           
                             
                               y 
                               2 
                               ′ 
                             
                           
                         
                         
                           
                             
                               x 
                               3 
                               ′ 
                             
                           
                         
                         
                           
                             
                               y 
                               3 
                               ′ 
                             
                           
                         
                         
                           
                             
                               x 
                               4 
                               ′ 
                             
                           
                         
                         
                           
                             
                               y 
                               4 
                               ′ 
                             
                           
                         
                         
                           
                             
                               x 
                               5 
                               ′ 
                             
                           
                         
                         
                           
                             
                               y 
                               5 
                               ′ 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                       
                       ) 
                     
                     
                       ︸ 
                       b 
                     
                   
                 
               
               
                 
                   (_5_) 
                 
               
             
           
         
       
     
     Linear equation (5) may be written as equation (6) as follows:
 
Ma=b  (6)
 
     The matrix M contains x rows and y columns. If the number of rows exceeds the number of columns, then a linear equation is referred to as over-constrained. For example, for more than three points of interest, there is an over-constrained linear system illustrated in equation (5), which is rewritten as equation (6). The solution to over-constrained equation (5) may not exist in an algebraic sense, but it is valuable to determine a solution in an approximate sense. The error in this approximate solution is then illustrated with equation (7):
 
 E=Ma−b   (7)
 
     In one embodiment, the approximate solution is selected by optimizing this error in some manner. One useful technique for optimizing this error is referred to as the least squares method. For more information about the least squares method, see, for example, “The Method of Least Squares,” which was available for download from the website of eFunda on Oct. 25, 2001, which is incorporated herein by reference in its entirety. The least squares method minimizes the residual sum of squares (rss), which is represented as equations (8)–(10) follows:
 
rss=e T e  (8)
 
=[ a   T   M   T   b   T   ][Mab]   (9)
 
= a   T   M   T   Ma  2  a   T   M   T   b+b   T   b   (10)
 
     Setting the partial derivative of rss with respect to a (i.e., ∂rss/∂a) to zero gives equation (11):
 
∂ rss/∂a= 2 M   T   Ma− 2 M   T   b= 0  (11)
 
     Thus, solving for M T Ma=M T b or a=(M T M) −1  M T b, the solution vector “a” provides the solution of Ma=b according to the least squares method. Note that M −1  represents inversion of matrix M, while M T b represents transposition. 
     For example, for tracked position of a point of interest such as ( 11 ,  8 ) and ideal position of the point of interest ( 11 ,  5 ), the video stabilization system  130  may apply the least squares method to determine that the transform parameter values are: a=1, b=0, c=0, d=1, m=0, and n=−3. 
     For each frame all image elements are then transformed to their ideal positions (block  436 ). In particular, the values of “a,” “b,” “c,” “d,” “m,” and “n,” which provide rotation, scaling, shearing, and/or translation information (referred to as transformation information), are applied to each pixel of a frame. The result is a frame in which unwanted motion has been removed. Equation (12) may then be used for each pixel in the first frame, represented as (xf, yf), to obtain its position in the second frame, represented as (xs, ys). In one embodiment, the first frame and the second frame are consecutive frames. 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           xs 
                         
                       
                       
                         
                           ys 
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               1 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               1 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               xf 
                             
                           
                           
                             
                               yf 
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           
                             0 
                           
                         
                         
                           
                             
                               - 
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     Continuing with  FIG. 4B , block  440  represents the video stabilization system  130  determining whether all frames in the group of pictures have been selected. If so, processing continues to block  402 . Otherwise, the next frame is selected and processing continues to block  428 . 
     In an alternative embodiment, frame averaging and/or frame sharpening may be performed after block  402  and/or after block  436  to remove noise and detect more interesting points of interest. In particular, some details in a video segment may be unclear due to noise, motion blur, and other distortions. Frame averaging may be used to combine data across frames when a scene is relatively stationary to about one pixel or less of variation across several frames at a time. After frame averaging, some degree of blur may remain (e.g., the stabilized frames are imperfectly aligned with one another). Frame sharpening refers to using a sharpen filter to remove this blur. Some additional fine tuning to adjust brightness offset may also be used in yet other alternative embodiments. 
     Noise in an image usually refers to the pixels whose values are not related to (i.e., not part of) ideal image content. For example, a recorded image may show reflection of sunlight, which is “noise” that may be removed. Since most of the image noise is related to single points, frame averaging can reduce the effect of noise, while frame sharpening can increase image contrast. The result of frame averaging and frame sharpening provides an image in which it is easier to detect real feature points. In particular, if an image has a lot of noise, some techniques for finding feature points may select some points that are not actually features. 
     Microsoft and Windows 2000 are trademarks of Microsoft, Inc. of Redmond, Wash. 
     Although the invention has been described with reference to particular embodiments, the description is only an example of the invention&#39;s application and should not be taken as a limitation. 
     Additionally, the invention may be tangibly embodied as software in a computer-readable device or media, such as memory, data storage devices, and/or data communication devices, thereby making a product or article of manufacture according to the invention. As such, the terms “article of manufacture” and “computer program product” and “computer-readable storage medium” as used herein are intended to encompass software accessible from any computer readable device or media. Using the present specification, the invention may be implemented as a machine, process, or article of manufacture by using programming and/or engineering techniques to produce software, firmware, hardware, or any combination thereof. 
     Various other adaptations and combinations of features of the embodiments disclosed are within the scope of the invention as defined by the claims.