Abstract:
Hardware and software configurations, optionally, for performing profilometry of an object are disclosed. An advantageous imaging device is described. An advantageous approach to determining imager position is also described. Each aspect described may be used independently of the other. Moreover, the teaching may find use in other fields including velocimetry, etc.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application is a National Phase application of PCT application No. PCT/US2010/057532, filed Nov. 19, 2010, which claims priority to U.S. Provisional Application No. 61/380,094, filed Sep. 3, 2010, each of which is incorporated herein by reference in its entirety. 
     
    
     BACKGROUND 
       [0002]    A number of patents, each including Gharib as an inventor and assigned to California Institute of Technology, cover useful hardware configurations for performing profilometry employing multi-aperture defocusing in connection with a single imager lens and one or more cameras/imagers. These patents include U.S. Pat. Nos. 6,278,847; 7,006,132; 7,612,869 and 7,612,870—all of which are licensed by the assignee hereof and incorporated by reference herein in their entireties. Defocusing principles in which two-dimensional scan data is employed to generate three-dimensional coordinate information can be appreciated in reference to these patents. Further-improved hardware for applying these defocusing principles is described herein. 
         [0003]    Irrespective of such hardware improvements, keen positional information is required to aggregate the three dimensional information determined through defocusing in order to map the surface of an object. Such positional information—often referred to as the camera “pose”—may be obtained in different ways. U.S. Pat. No. 7,605,817 to Zhang (assigned to 3M) describes one approach and US Publication No. 2009/0295908 to Gharib (assigned to California Institute of Technology) describes another. Neither approach offers the benefits of the pose techniques described herein. 
       SUMMARY 
       [0004]    Accordingly, hardware and software configurations, optionally, for performing profilometry of an object are disclosed. An advantageous imaging device (i.e., imager, camera or scanner) is described. An advantageous approach to determining imager position is also described. While advantageously used together, each aspect described may be used independently of the other. Moreover, the teaching may find use in other fields including velocimetry, etc. 
         [0005]    Three-dimensional information may be obtained using a hand-held imager/camera/scanner. Sometimes the subject to be scanned is larger than the field of view of the scanner and/or the subject is scanned from different vantage points. To capture such information, the pose of the scanner device changes at different times. A combined or aggregated image scene may then be prepared in connection with determining camera pose on a spatially-related basis across any number of image scenes. Given the fidelity of the camera pose determination, it is hereinafter referred to as the “True Pose” of the camera. 
         [0006]    This implementation for determining camera position operates by comparing scenes for which information has already been determined indicating the scenes are potentially matchable. (Wherein the matching may be carried out through various techniques including cross correlation, least mean squares, super-resolution PIV or as including warping/dewarping approach as further elaborated upon below). The determination of True Pose for a final or actual (i.e., for the purpose of combining data sets for system output) camera position is performed in a post-processing setting after image capture. 
         [0007]    Scenes are indicated as potentially matchable based on a roughly-accurate camera position determination (i.e., a “Rough Pose”) performed during image capture (i.e., as in “real time”). Processing and other action conducted in “real time” is performed such that a user does not recognize a lag in system performance. When possible, the Rough Pose is generated by matching (as above) data sets based given Tentative Pose information. 
         [0008]    Initial camera position information (i.e., the “Tentative Pose”) to be used in determining the Rough Pose (and no longer relied upon) can be generated in a number of ways. Generally, Tentative Pose is found employing a robust process. One approach is to use the standard technique of comparing a reduced data set of easily recognizable features derived from one frame to a reduced data set of easily recognizable features from a/the subsequent frame. See, e.g., US Patent Publication 2008/0201101 at ¶0010 (describing the state of the state of the art prior to the application priority date). However, such an approach can be altered and augmented by comparing such features in a current frame from those accumulated or aggregated from previous (e.g., 20 to 100) frames. 
         [0009]    In any case, the Tentative Pose is not itself used in the methods described in any manner for combining the subject data to produce the scanner output. Its resolution falls far short of the requirements of the present system to deliver a workable image file output as desired for dental crown production and/or other high-precision profilometry applications. However, in some circumstances, the Tentative Pose data may stand-in for the Rough Pose data in carrying out True Pose determination through spatial/global matching. 
         [0010]    To use an analogy, the Tentative Pose provides location data akin to indicating the state for United States postal delivery. Closer position—akin to calling out the zip code of a region—is determined through the Rough Pose procedure. True Pose—akin to a particular PO Box location—is, alone, used to provide the final deliverable. 
         [0011]    Using True Pose for image aggregation thus avoids the error stack-up and data/package loss associated with imprecise address information. Using the Tentative or Rough Pose makes finding the True Pose computationally feasible (this is especially so when employing Rough Pose in longer scans—as in a scan of a complete jaw—for which the enhancement in Rough Pose spatial accuracy is more evident). 
         [0012]    More directly, “Tentative Pose” is positional information used for the time-being, but is quite uncertain and preliminary. The “Rough Pose” is still uncertain, but more accurate—roughly accurate—in terms of describing camera position. The “True Pose” is the camera position determination that is accurate to the degree required to meet the system specifications for the intended purpose. As an example, this accuracy is such that it can deliver a profilometry output file with the following specification: an RMS error for a single tooth about 35 microns or better, and an RMS error for 3 teeth of about 40 microns or better. 
         [0013]    In delivering such results, the inventors hereof have discovered that it is important to refine the Tentative Pose to generate Rough Pose, when possible, for further use in determining True Pose because reliance on sequential/time-wise generated positional information (i.e., Tentative Pose) results in a stacking or build-up of error. When scanning a significant/relevant region (as in scans for dental crown production) the error generated can be too great to accurately aggregate information to produce a relevant model. 
         [0014]    Another aspect considered herein is the manner of performing the matching itself. Various techniques are employed. These include a cross-correlation technique as described below, as well as optionally incorporating a rotational element in an overall “Pose-Based Matching” process. The rotation of one frame to more closely match another with a somewhat-known (i.e., tentatively or roughly know) spatial relation allows for cross-correlation that could not otherwise occur. 
         [0015]    As for the advantageous hardware implementation, it employs a single lens with multiple apertures as do the referenced approaches. A preferred embodiment, employs the different color channels of a commercially available sensor to capture different wavelengths of light (optionally emitted by single-color light sources such as LEDs) with simplified hardware. As such, no additional beam splitters, alignment controllers with lock-downs or other cumbersome hardware is required, thereby allowing production of a highly compact and robust (against shock, thermal cycling, etc.) imager handpiece. 
         [0016]    The present invention includes the subject devices and methods including the hardware and software embodying the same. More detailed discussion is presented in connection with the figures below. 
         [0017]    This filing claims the benefit of U.S. Provisional Patent Application 61/380,094 filed Sep. 3, 2010 and entitled, “Three-Dimensional Image System with Multiple Determinations,” which application incorporated by reference herein in its entirety. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    The figures provided herein are not necessarily drawn to scale, with some components and features exaggerated for clarity. Variations of the invention from the embodiments pictured are contemplated. Accordingly, depiction of aspects and elements of the invention in the figures are not intended to limit the scope of the invention. 
           [0019]    In the figures, 
           [0020]      FIG. 1A  shows a block diagram of the hardware of an embodiment and  FIG. 1B  illustrates filter characteristics associated with a commercially available color sensor; 
           [0021]      FIG. 2  shows a summary flowchart; 
           [0022]      FIGS. 3A-3C  shows a more detailed flowchart of the real-time activity in  FIG. 2 ; 
           [0023]      FIGS. 4A and 4B  detail cross-correlation matching;  FIG. 4C  is a flowchart illustrating 3-D point location determination; 
           [0024]      FIG. 5  diagrammatically illustrates a scanning procedure; 
           [0025]      FIG. 6  illustrates the use of multiple different libraries in connection with obtaining images of a subject&#39;s teeth; 
           [0026]      FIG. 7  shows the way in which global matching is carried out; 
           [0027]      FIG. 8  illustrates frame finding and translating in the process of pose based warping as referenced in  FIGS. 3C and 7 ; and 
           [0028]      FIG. 9  functionally details the technique of pose-based warping. 
       
    
    
     DETAILED DESCRIPTION 
       [0029]    Various exemplary embodiments of the invention are described below. Reference is made to these examples in a non-limiting sense. They are provided to illustrate more broadly applicable aspects of the present invention. Various changes may be made to the invention described and equivalents may be substituted without departing from the true spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation, material, composition of matter, process, process act(s) or step(s) to the objective(s), spirit or scope of the present invention. Such modifications are intended to be within the scope of the claims made herein. 
       Imaging Hardware 
       [0030]      FIG. 1A  shows a block diagram of a hardware embodiment. A hand-held scanner  100  is used to image an object  99 . The scanner  100  has an outer housing  102  which holds a number of optical and electrical items. The scanner can include any type of camera  140  or any other device which receives optical information and converts that optical information into electrical information. For example, this may include a CCD camera, CMOS image sensor, or any other kind of photosensor that converts light photons into electrical signals. The camera  140  produces output information indicative of one or both of two dimensional information and/or three-dimensional information. The two-dimensional information may be referred to as x and y coordinates, defined as coordinates that are perpendicular to a z axis direction  111  between the imaging device and the object being imaged. The third dimensional information may include z-axis coordinates that are orthogonal to the x and y coordinates and are indicative of the distance between the camera  110  and the object being imaged. As conventional, the axes can also be tilted and/or reversed, as there is not intent to limit to this specific coordinate layout. 
         [0031]    The image information may be stored as x, y and z coordinates or may be stored in any other form, such as a three-dimensional point cloud, a three-dimensional mesh, or any other form that can represent two-dimensional and/or three-dimensional information. 
         [0032]    A window  105  is formed in the portion of the scanner  100  which allows scanning of three-dimensional objects  99 . In an embodiment, this may be used for scanning dental objects such as teeth, to form a map of the teeth. While the embodiment describes scanning teeth, the imaged object  99  may be any object, collection of objects, portion of an object, or other subject matter. For example, in a dental imaging application, the object  99  may include a tooth, a quadrant of teeth, or a full collection of teeth from which a virtual dental impression is desired. In other embodiments, the object may be some other medical subject, e.g., an eye, nose, head, ear, or other. 
         [0033]    An illuminator comprising different color light elements  115 ,  116  provides light onto the teeth  99 . The image of the illuminated object is also received through the window  105 . A corner mirror  120  reflects the received radiation to an optical system  125 . In other embodiments, the system may operate without a corner mirror. 
         [0034]    The optical system may include a lens  130 , and a mask with multiple apertures  135 . The apertures  135  may be color coded, that is one aperture may pass only or predominately a blue color and the other may pass only the light through which has a red color. The illumination  115 ,  116  may provide colors that match the colors of the mask, here blue illumination from  115  and red illumination from  116 . This produces two different channels of information, one through each of the two apertures. The processing described herein distinguishes between these two different channels to obtain different information from the two channels. 
         [0035]    The light through the apertures  135  is provided to an electronic camera  140  that produces electronic outputs indicative of the light received through the apertures. The camera is connected by a cable  145  to a computing device  150  that includes software for driving the camera and analyzing the information. The wires  145  may include power for driving the camera, and may also receive information from the camera. 
         [0036]    The computing device  150  can be a general purpose processor with a microprocessor  153  operating according to a stored program that is described according to the techniques of the present application. The computing device may also or alternatively include a graphics processing unit, or GPU  155 , e.g., in a video card that drives a display  160 . The GPU  155 , for example, can be an ATI or an Nvidia video card. The computing device may also or alternatively include a field programmable memory, (e.g., a gate array) or any custom hardware or custom logic. 
         [0037]    In one embodiment, the portable hand-held scanner in  FIG. 1A  can be moved, while still obtaining information about the scanned area. As the camera moves at each of the plurality of different times, new information about that new camera position is obtained. This allows the overall object  99  that is finally imaged to be larger than the window  105 . 
         [0038]    The camera  140  may be a standard color camera (e.g., ⅓-Inch SOC Megapixel CMOS Digital Image Sensor as produced by Micron Technology, Inc.) that uses a color filter array that is already part of an image sensor within the camera  140  to separate the colors. The filters on the color filter array portion of the camera  140  separate between the color rays (here red and blue channels) to obtain the information and to distinguish between the color rays passed by the color filters on apertures  135 . The information from each colored filtered aperture is picked-up only by the appropriate filter portion of the camera  140 . 
         [0039]    The color filter array can be a Bayer filter such as described in U.S. Pat. No. 3,971,065 or alternatively can be a different kind of color filtering such as the CYGM filter and the RGBE filter or a custom filter array (e.g., if there are two apertures which are coded as blue and red the filter array would have alternating filters of blue and red). A camera incorporating a custom two-color filter would have the advantage of using all of the available sensor area in connection with a two-color two-aperture system. 
         [0040]    In use of such a standard imager, however, only two (R, B) of the three channel colors (RGB) available are used. This means that part of the real estate of the photosensor is in essence wasted: the area where the non-used color is located. In theory, such an approach reduces the dynamic range of the system by a ratio equivalent to the amount of the photosensor surface that cannot be used. With a conventional Bayer filter, this amounts to roughly half the sensor area. 
         [0041]    Surprisingly, such an approach is none-the-less advantageously implemented. The conventional concern of recording a sub-optimal data set does not problematically hinder system utility. Indeed, by selecting red and blue channels only, less noise is introduced from a processing standpoint than if a third green-coded aperture and green channel recorded. This fact is illustrated in reference to  FIG. 1B . Namely, the separation of the red (R) and blue (B) filters illustrated for the sensor essentially ensures (for a given intensity cutoff or threshold) that light passed through the red-coded aperture is only recorded on the red channel of the sensor and vice versa for blue. If a green channel were introduced, the light from the green aperture would be more readily absorbed by each of the red and blue sensor channels and the green sensor channel (G) would more readily absorb (again, at a given threshold) light from each of the red and blue coded apertures due to transmission spectrum overlap. 
         [0042]    It has been discovered that avoiding such “cross-talk” for the sake of cleaner sensor data more than compensates for the (effective) reduction in pixel count. Essentially, the sub-selection of channels enables producing a high quality image system with low cost (because they are available off-the-shelf) sensor components. 
         [0043]    While the inventive hardware aspects focus on the above, it is to be understood that the inventive software and associated methodology may employ different numbers of apertures and/or colors. In either case, composite colors (such as amber or white) can be employed even though discreetly colored emitters are discussed above. Notably, dropping the green channel out of use to achieve further separation between the color channels that are ultimately used may have even more pronounced benefits in this last scenario. 
       Defocusing 
       [0044]    As generally referred to herein, a number of references (including patents noted to Gharib) discuss the “defocusing” concept. In the broadest sense, “defocusing” involves imaging through a plurality of pin-hole camera type apertures of a known spatial relation. The apertures restrict the image received by a camera sensor system. Whether using a single sensor or multiple coordinated sensors, differences in x, y coordinates of features identified from the images received through each aperture are compared to determine z-coordinate values for those features. 
         [0045]    Scalar differences between features recorded at one distance from a scanned object are compared to those at another distance. For example, the difference between resultant triangular patterns imaged through a triangular arrangement of apertures is used to determine the z-axis differences. Further, a calibration set can be used to improve the accuracy of the results. By imaging a known grid pattern, and storing a calibration table, nonlinearities of the recorded image data can be accounted for by “dewarping” the image feature positions. 
       Margin Definition 
       [0046]    In scanning an irregular body (e.g., one or more teeth) to produce a three-dimensional data output file (e.g., an STL file for use in crown manufacturing) it is useful to define a boundary up to which three-dimensional scan data is populated. Such a boundary (or “margin”) definition can be helpful for defining the extent to which a user is directed to concentrate scanning activity on an area to generate a full scan. Also, in some instance in which scanning is not complete, but a margin has been defined, an approximation of the unscanned area can instead be filled-in by interpolation. Still further, a well-defined boundary helps in point outlier filtering (i.e., points outside of the view of the margin are not considered in the calculation of the surface inside). 
         [0047]    User definition of a margin offers certain benefits. When performed by drawing a line or line segments digitally (using a wand, touch screen interface or other means) over a digital representation of the object that is being scanned or has been scanned, the user can make judgment calls based on observation and experience. Utilizing the human capacity in this manner may help avoid the need to implant costly or cumbersome programming and/or introducing error that the qualitative “eye” of a user can otherwise avoid. 
         [0048]    In the approach to user-produced margin definition described above, x and y coordinate information is recorded in the reference plane of the screen. In doing so, line(s) or a curve is drawn by a user upon the image of the body (scanned or to be scanned) displayed. So each (say, blue channel) x,y point in this plane intersects with multiple potential z values. Then, in connection with the dense point cloud/set information from scanning and the calibration set, true x,y,z can be determined. Accordingly, the activity generates a three-dimensional feature based upon user-input two-dimensional information. 
       Image Determination Software Overview 
       [0049]      FIG. 2  shows a general flowchart of the operation of image determination and processing. At  200 , the system obtains image information at a first time t 1 . 
         [0050]    In an embodiment, this information is a capture of multiple images through multiple apertures, in a way that allows distinguishing between the apertures. In the embodiment illustrated above, color filters are used to separate between the channels. One of the apertures can be associated with a red filter to only or predominately pass the red light, with the other aperture can be associated with a blue filter to only or predominately pass the blue light. This approach forms two channels of information, one having passed through each of two separated apertures. According to another embodiment, rather than separating the channels by colors, the apertures are arranged in a specified arrangement such as an equilateral triangle, and the processor  153  recognizes that equilateral triangle in the final image to find the image parts attributable to the apertures. According to another embodiment, the different channels can be formed by modifying polarizations of different channels, by putting different polarizations on the different apertures and camera sensors, thereby using polarizations on both the apertures and on the camera. This embodiment uses those different polarizations as the different channels. The channels can be formed in different ways by providing different physical mask shapes (shaped apertures), or by time division changing the aperture (e.g. by moving it from place to place). 
         [0051]    Regardless of the implementation, at  205 , a robust feature detector (e.g., the robust feature detector can use the off-the-shelf “SIFT” software or a simply-implemented custom software) is used to determine references on the current image frame using a reduced data set—in this example—from the blue channel. Note that the image frame obtained at any one time will be smaller than the overall image frame. The references are referred to herein as being “keypoints,” but any reference that can be recognized in different images can be used. The robust feature detector finds two-dimensional information (x, y) of the position of the keypoints as well as a feature vector style descriptor for those keypoints. That feature vector style descriptor will stay constant at any scale rotation and lighting for the points. 
         [0052]    The feature vector style descriptor can be obtained by extracting interesting points on the object to provide a “feature description” of the object. This description has enough information that can be used to identify the object when attempting to locate the object in other images containing other objects and/or from when imaging from different view/vantage points. The features extracted from the training image are selected to be robust to changes in image scale, noise, illumination, and local geometric distortion to perform reliable recognition. This may use techniques, for example, described in U.S. Pat. No. 6,711,293. The commercially available scale invariant feature transform (SIFT) software can be used for this detection. Three dimensional point information for each of the keypoints is also determined using defocusing principles and equations of the type described herein and described in U.S. Pat. Nos. 6,278,847 and 7,006,132. 
         [0053]    At  210 , the next frame is obtained, where the next frame can be frame number  2  at time t 2 . In general, the frames can be incremented to get the next frame. 
         [0054]    At  215  a Tentative Pose map is formed of the different ts. It matches the different parts of the three dimensional information corresponding to the keypoints in order to obtain a transformation T (translation and rotation) between the t&#39;s. This represents a transformation between a core time t, and any other times tn, which can include multiple ns, e.g., (t n1 , t n2  . . . ) via the combined information. 
         [0055]    At  220 , a dense point cloud for each obtained frame t n  is obtained. The dense point cloud can obtain three-dimensional image information using defocusing applying the techniques described above. The finding of the dense set (the points and their positions) and the identification of robust features can be determined in parallel. The finding of the 3D coordinates of the robust features may be done after other information has already been determined. 
         [0056]    At  225 , the linear transformation T associated with the Tentative Pose between the different times is used to transform and/or cross correlate between the 16×16 pixel windows of the images that surround dense point clouds obtained at the different times to obtain a Rough Pose. This is done by either cross correlating a current dense point set (e.g., a 16×16 pixel window around a central point) with a previous dense point set, or by using robust feature detection on a sparse point set (e.g., the blue channel) to match to a previous set of frames to find a match. At  225 , therefore, the 3D information, and the Rough Pose have both been obtained. 
         [0057]    Based on that Rough Pose, at  230  it is determined if the current information is close enough to a reference frame to cross correlate the two frames. If so, then cross correlation is carried out. If no frames are close enough, then the current frame is rejected. If the current information is close enough to the reference frame to cross correlate the two frames but the new frame is outside some threshold distance at  235 , it is also rejected but added as a new reference frame. A pose recovery operation may then be used to establish or refine the Tentative Pose. 
         [0058]    In operation, the processor is programmed to process a point collection along with the defocusing equations to obtain a 3-D image. The red and blue channels are cross correlated with a multi-grid as described herein. At  226  the frames are organized by location. 
         [0059]    At  227 , the transformation information representing the Rough Pose of the scanner is determined through post processing in order to obtain different and more accurate information positional information (i.e., the “True Pose”). The post processing may use a less robust but more accurate technique than employed for either of the previous pose determinations. For example, less robust techniques may make it more computationally expensive to match pixel differences more than a certain amount, but may provide more information about that matching. 
         [0060]    The inventors found that cross correlation techniques may be extremely robust, and may provide very accurate values between the different transformations. However, it is not computationally feasible to use this more robust technique to recover poses that have large pixel shift between poses (thus the value of using the Rough Pose vs. the purely Tentative Pose). Using current Nvidia GPUs, more than 64 or 128 pixels of shift between the poses would not be computationally feasible in real time. 
         [0061]    The post processing at  227  recognizes that once these frames are “transformed” to have shifted so that there is less pixel shift, a more accurate technique can be used for post processing. Accordingly, in an embodiment, steps  200 - 225  are carried out in real time, and  226  and  227  in non-real time, after the real time Rough Pose has been calculated. The first part of the operation thus calculates the Tentative Pose and Rough Pose in real time, while the next parts refine those pose estimates. 
       Cross Correlation 
       [0062]    The cross-correlation or “CC” operation referenced throughout the specification is illustrated in  FIG. 4A . This may be a robust cross-correlation operation (e.g., when using robust features) or it may be used to match point cloud data. The operations of  FIG. 4A  may be carried out, for example, in a processor such as the microprocessor  153  or GPU  155 . 
         [0063]    Item  400  is shown at a first time/pose in  415 , and at a second time/pose in  416 . The different times/poses can be different color channels of the same frame, for example, or can use other channel separating techniques. The points can be natural points, or can be applied, for example, by a fixed illuminator, or can be applied using a contrast agent. This can also investigate arbitrary locations that are areas of the surface that have a certain brightness, contrast or look. 
         [0064]    Each frame  415 ,  416  is subdivided into a number of subdivisions such as  401 . Subdivision  401  in  415  is shown compared with another of the subdivisions  411  in  416 . These two subdivisions  401 / 411  are shown as being compared in  FIG. 4A , but it should be understood that this operation is carried out for each of a plurality of subdivisions. 
         [0065]    At  420 , the two subdivisions  401 ,  411  are correlated. Each correlation represents a number of different shifts of the image. Each correlation creates a correlation image at  425  which includes a number of pixels. Each pixel in the correlation image represents the result of one correlation shift. For example, cross correlating  401  and  411  gives a single cc image  425  representing all the shifts. Note that the cross correlation technique used can be any kind of cross correlation type, including circular, zero padded, fast fourier transform (FFT) based, or any other kind. 
         [0066]    For example, the pixel  427  represents a pixel which is shifted in the x direction by zero but shifted down (in the y direction) by three. Each pixel value in the correlation image represents one whole shift and one whole multiplication by the amount in the location of the pixel in the correlation image. Each of these values can be calculated, for example, in shaders of the GPU or in a processor, or in dedicated logic such as gate arrays or custom hardware. 
         [0067]    The brightest pixel in the correlation plane is found. This is done by investigating the pixels and the surrounding pixels are used to find the sub pixel location of the peak. Any of a number of different peak fitting techniques can be used in this way. A most common peak fitting assumes a Gaussian shape. 
         [0068]    Subpixel Gaussian peak fitting can be used.  FIG. 4B  shows how this technique is used to find the correspondence of a grid of points in the blue channel to their corresponding points in the second channel. 
         [0069]    At  445 , the brightest pixel in the grid of correlation images represents the location of best match between the images. This match is used to represent the offsets between the images. Bicubic splines can be used to interpolate between grid points. 
         [0070]    At  450 , the set of coarse offsets has been found (at  445 ). One of the images (e.g., the red) is then warped at  450  to look like the other image (e.g., the blue) based on the offset. This creates a composite image  455 . 
         [0071]    At  460 , the images have been warped to be closer to one another. A finer subdivision grid is obtained. The correlation operations  420 ,  425  are then repeated to get a new warp between images for the finer grid. 
         [0072]    A new grid is then formed again, representing a finer subdivision. This procedure is done some number of times (e.g., 4), reflecting the desired accuracy balanced with the computational accuracy available at  465  in the embodiment. Or the iterations may continue for some other number of iterations (e.g., until reaching a 16×16 pixel size). At this point,  470 , the final image information obtained. It includes x,y (or “bx, by” expressed as the location information for the blue channel information) and dx, dy (the shift in position between the blue and red channel) 
       3-D Point Location Resolution 
       [0073]    In one embodiment, 3-D point clouds are generated (per  325  in  FIG. 3A ) in connection with the cross-correlation technique. In general, cross-correlation is employed between the blue and red channels to find numerous corresponding image pixels between these channels. With point location information obtained through cross-correlation (e.g., as per above), corresponding 3-D point locations can be obtained in connection with the scanner calibration information. 
         [0074]    For a calibration procedure, an initial operation is carried out to define a calibration set or table based on a calibration grid. More specifically, for a calibration grid imaged at each of a plurality of “z values”, a value in the blue channel is compared to the value in the red channel. For example, the location 0,0 in the blue channel will have a corresponding location in the red channel. This calibration set/table represents an offset from the blue channel to the red channel. 
         [0075]    These offsets dx and dy (which are offsets to the red channel) are known at  475 . For each value, a translation to the x,y,z position is also known from the calibration procedure. Therefore, for any bx, by (i.e., x and y in the blue channel) and dx, dy a corresponding x, y, z value can be determined using the calibration table by applying linear algebra. Stated otherwise, with (bx, by, dx, dy) the z can be determined tracking back through the deformations used to match the blue and red images per  480  in  FIG. 4B . 
         [0076]    Namely, in  FIG. 4B , each warping/deformation iteration ( 450 - 465 ) represents a difference from the previous image to the next deformation. These deformations are added to one another to obtain final image information at  470  (optionally expressed in terms of x, y, dx, dy). At  480 , the calibration set is used as a function applied to this information to obtain x, y and z position information in defining the dense point cloud. Accuracy is thereby improved by reducing from four dimensions to three dimensions using the calibration information that is individual for the specific camera. 
       Pose Based Warping 
       [0077]    The cross-correlation technique also offers a tool in connection with a “Project Planes” feature. “Pose Based Warping” may be regarded as the action of Projecting Planes and then Cross-Correlating. 
         [0078]    When images cannot be directly cross-correlated because of gross movement (e.g., large in/out of plane rotation and/or translation), it becomes computationally infeasible to recover the pose using cross correlation or other similar image matching algorithms. With some knowledge of R and T (e.g., Tentative or Rough Pose depending on the point of implementation in the current method) cross correlation is possible after adjusting one of the images to be cross-correlated even when the offset is larger than 64 pixels. 
         [0079]    The Project Planes feature used to carry out the adjustment is described in connection with  FIG. 8 . At  800 , close-by vectors are identified. At  802 , vectors that are as distant as possible are identified for cross-correlation. At  805 , one frame is shifted (translated/rotated) based on less-refined pose information to look like the other frame en route to determining more-refined pose information. 
         [0080]    More specifically, for first and second images (I 1 , I 2 ) an Image I 2 ′ is generated as a prediction of what I 2  will look like in the plane of I 1 . So, taking a representative point in I 2 ′, it is translated and rotated (i.e., projected) in 3-space (using the calibration set, available pose information and dense point cloud information) to find its position in I 2 . For all of the integer points considered f(x,y) represents such activity as a continuous function. 
         [0081]    Ultimately, the Project Planes operation in Pose Based warping optionally used in determining Rough and True Pose has the goal of creating data from multiple different images that look more like one another for cross-correlation. For example, looking at  FIG. 6 , different poses of the camera may be looking at the same item and even the same place on the item, but from different viewpoints. For example, image  1  at pose  1  (R 1 , T 1 ) may have been found as  650 . Image  2  at pose  2  (R 2 , T 2 ), however, may have been found at  652 . While these may both be looking at the same actual item,  650  may look as shown in  651 , while  652  looks as shown in  653 . At this point, these values may be too different and far apart to cross correlate. 
         [0082]    Per  FIG. 9 , a function f(x,y) is used to map Image  2 ′ into Image  2 , where Image  2 ′ has similar pose parameters to Image  1  (as represented in the Project Planes process  800 ). Then, through a cross-correlation process  400 , flowchart element  900  finds the function that warps Image  2 ′ into the coordinate system of Image  1 , to provide Image  1  and Image  2 ′ both in the same coordinate system. 
         [0083]    In notation per element  905 , in cross correlating image  1  to image  2 ′, image  2 ′ has already been inverted, so no inverses need to be found for this function. This creates a simplified warp. Such a warp assumes that all of the Z values are zero. 
         [0084]    Since this is typically not the case, however, the calculation of f(x,y) at  900  can also account for the differing z-axis depth by fitting a least squares plane to the transformation f(x,y)-&gt;(x′, y′, z′), where 
         [0000]    
       
      
       x′ 
       i 
       ; =a 
       x 
       x 
       i 
       :+b 
       x 
       y 
       i 
       :+c 
       x  
      
     
         [0000]    
       
      
       y′ 
       i 
       ; =a 
       y 
       xi; +b 
       y 
       y 
       i 
       ; +c 
       y  
      
     
         [0000]        z′   1 = . . . . 
         [0000]    This can be written in matrix form. 
         [0085]    The shape can then be smoothed by creating a new grid of points using the new x,y,z correspondence. The new grid of points creates a relationship between f(x,y) and (x,y,z) based on spline (“Sp”) interpretation. This uses the relationship 
         [0000]      ( x,y )→ x  Sp x  
 
         [0000]      ( x,y )→ y  Sp y  
 
         [0000]      ( x,y )→ z  Sp z  
 
         [0000]    therefore, the plane maps to a 3-D smoothed spline. 
         [0086]    As referenced above, using the calibration set obtained for the camera, the points for the blue channel can be converted to x,y,z. The transformation is not a completely linear function, since the pose changes the magnification as x,y and z change. By calculating these values in a matrix form, the amount of nonlinearity can be compensated in this way. 
       Image Capture and Real-Time Pose Determination Details 
       [0087]      FIGS. 3A-3C  define a flowchart or real-time activity in an implementation of a program that is run on the processor  153  and/or GPU  155 . At  300 , at a time frame t 0 , the system captures two images in that one time frame t 0 . These two images form the two channels which are used herein. After obtaining the two images (color-coded in this case), two parallel paths  305  and  306  of processing are carried out. The path  305  is used (as per  FIG. 3B ) to determine camera pose and to carry out a coarse determination of the camera information and hence find preliminary translation information (i.e., the Tentative Pose). Path  306  is used to determine dense 3-D information. While this application describes these as being carried out in parallel, it should be understood that these computations can be carried out at any time. 
         [0088]    At  310 , keypoints are obtained using a more robust but less accurate technique such as the scale invariant feature transform “SIFT” software or other means as noted above. In any case, a feature vector descriptor is typically determined for each of a plurality of keypoints. That feature vector descriptor describes what the keypoint looks like. The features selected are invariant to image translation, scaling, and rotation, partially invariant to illumination changes and robust to local geometric distortion. This may be done, for example, using a maxima and minima of the result of difference of Gaussians function applied in scale-space to a series of smoothed and re-sampled images. 
         [0089]    In one embodiment, the imaging may be carried out using painted-on features, for example features that are applied using contrast. In an embodiment, a contrast may be used of white and black particles sprayed with an aerosol. 
         [0090]    In an embodiment, the extraction of keypoints is carried out on the blue channel image. Then, at  315 , information from the other color channel, here the red channel, can be used to find the corresponding features. Such feature-finding can employ cross-correlation as described herein. 
         [0091]    At  320 , the keypoints that have been obtained in this way have information about their 3-D location determined in the current time frame using defocusing. Each keypoint therefore is processed to obtain three-dimensional information corresponding to that keypoint, as well as its associated descriptors. This information forms a set of sparse keypoints with descriptors for the time frame t 0 . 
         [0092]    In parallel with the Tentative Pose determination path  305 , the dense point cloud path  306  is carried out to determine dense 3-D information, however, without descriptors. For the time period t 0 , step  325  starts by determining a dense 3-D cloud of points, using defocused information. This may be done by cross correlating between the blue and red channels at  330  to find many corresponding points or image pixels between these channels. The 3-D locations of these points are obtained at  335 . The defocused information from the two channels is used to determine this 3D information. 
         [0093]    At  340 , both the pose and 3-D point cloud determination have been carried out. At timeframe t 0 , there are now two sets of 3-D point clouds: a sparse set with descriptors (from the path  305 ) and a dense cloud without descriptors (from the path  306 ). 
         [0094]    At  345 , the next part of the operation proceeds that finds the next t, called t 1 . The process continues to iterate to find multiple different values at multiple different time frames. 
         [0095]    According to the operation, there are multiple different libraries of dense and sparse point sets for the overall object. For example,  FIG. 6  shows how this would be used to obtain images of a scan subject&#39;s teeth such as  600 ,  602 ,  604 ,  606  and others. A first library  1  at  610  represents the field of view that can be obtained from the scanner from a single scan. This may image, for example, teeth  600 ,  602 . However, tooth  604  is not within the field of view of the scanner within library one  610 . Therefore, library  2  shown as  620  may be used to capture the image of the teeth  604 ,  606 . The different libraries may each represent a different reference. 
       Pose Methodology Overview 
       [0096]    The initial camera position determination (yielding the “Tentative Pose”) provides rotation and translation R &amp; T in real-time matched in the t dimension. This employs one or more robust matching techniques (e.g., carried out through cross-correlation as described above and/or by comparing keypoints) that is accepting of differences between points. Subsequent to this activity, feature matching, optionally, through pose based warping refines the pose (yielding the Rough Pose) between matchable frames. Post-processing typically uses that Rough Pose information. The Rough Pose provides more information about a selected frame and allows full matching, again—optionally, through pose based warping to spatially-related frame(s) to determine more accurate pose points (yielding the “True Pose”) by taking advantage of the additional a priori knowledge. 
       Tentative Pose Determination 
       [0097]    In  FIG. 3B , the operation of determining the Tentative Pose is started. At  350 , the current point set is compared with the previous point set via cross-correlation techniques. At  355 , a determination is made if there is a cross-correlation or “CC” match between the point sets. If so, then 360 determines that there are two matched dense point clouds, and control passes to node  3 C, step  390 , which carries out a processing operation shown in  FIG. 3C  which represents the comparing and forming of the libraries. 
         [0098]    If there is not a CC match at  355 , then control passes so that at  365  robust descriptors (e.g., SIFT descriptors) of the previous group of frames are used, where the group of frames can be, for example, between 20 frames and 100 frames. At  370 , it is determined if there is a match on the previous 20-100 frames and the current frame. If so, this establishes a match between sparse point clouds at  375 , and control passes to the library node  3 C ( FIG. 3C ). 
         [0099]    If there is no match between the current frame and the previous 20-100 frames, then pose recovery is carried out at  380  using the descriptors on a stored library of key points. This compares the robust descriptors with the entire library of keypoints that has been created. If there is a match, then this is taken as the Tentative Pose, and control passes to the library determination at  3 C. If there is no match at  385 , this means, at  386 , that all reference frames are too far away from the current frame. At this point, the current frame is rejected (i.e., discarded). 
       Rough Pose Determination 
       [0100]      FIG. 3C  continues pose determination using the Tentative Pose which has been found in  FIG. 3B . This begins with step  391 , which obtains the Tentative Pose information, and then at  392  determines if there is a close CC frame. If the result of the action at  392  is that there is no close enough CC frame, then all the frames are too far away and the frame is discarded. Or it may be added as a library reference for future CC activity. However, if there is a close enough CC frame, then it is obtained at  393  and the new frame is warped to the older frame (i.e., the frames are projected at  393  and cross-correlated at  394 ). 
         [0101]    Generally, the operation is an attempt to find, for a plurality of different vectors (scene position values), which vectors are most close by. The object is to cross correlate vectors which are as distant as possible, as long as they are still correlatable.  FIG. 8  graphically details the frame finding and translating involved in projecting the planes as referenced above. 
         [0102]    Returning to  FIG. 3C , after the projection at  393 , R 0 , T 0  is used to cross correlate the current frame to the found frame. This is used to find the new pose (the Rough Pose) R and T. If the R and T can be found at  395 , then this more-refined pose can be used for aggregating 3-D point cloud data, at  399 , for the purpose of display on a user interface device (e.g., computer monitor). If not, the current frame is compared to the SIFT references at  396 . If R and T are not found at this stage  397 , it is added as a SIFT reference at  398 . Otherwise, the processing is complete, and operation proceeds to get the next point at step  3 A. 
         [0103]    Note in the above that the three dimensional points and keypoints in the current frame are matched to keypoints in multiple different previous time frames via the descriptors. That is, for each core frame tn, each keypoint is matched to each of a plurality of previous frames t(n−x), where x can be a set number. For example, x may be set to any number between 0 and 10000 depending on available processing power and memory. In the embodiment, this is described as being between 20 and 100 frames. This thereby matches each of a number of frames to the core frame. 
         [0104]    At  350 , the matches are used to find a transformation from the current frame to the previous frames. This operation determines a transformation Tn (translation and rotation) between frame n, and all other frames that are going to be compared to frame n. This same information also represents the transformation for the dense points. In this way, all of the frames end up in a single coordinate system called the reference coordinate system. The reference coordinate system is arbitrary, but in general stays the same throughout all reference frames. The reference frame can change from time to time, as described herein, when the motion of the camera causes an image of the subject has moved too far from its original location. 
         [0105]    According to another embodiment, many different frames can be used as base/reference frames, so that there are many different transformations. For example, there can be new base frames every specified time. In yet another embodiment, transformations can be found, so that there can be intermediate frames. In still another embodiment, instead of combining the transformations, an average of the transformations may be used. 
         [0106]    At  360  (in  FIG. 3B ), the transformation is made between the reference frame and any other frame tn. This forms a library of data that is all in the same coordinate system. All of the data is in a single coordinate system, where that coordinate system is in essence randomly selected. 
         [0107]    This serial transformation may minimize the number of transformations that are combined for any given frame to thereby minimize error propagation. 
         [0108]    After the dense sets have been transformed to enable production of a full resolution image in  FIGS. 3A-3C  (e.g., for display purposes only during scanning as user feedback during the process), a post-processing of the pose is carried out as shown in  FIG. 7 . This post-processing may use a “global matching technique” to allow better frame matching while minimizing error propagation to find the True Pose as defined above and deliver a final scan output product (e.g., a STL file embodied in computer-readable medium) for producing a physical object from the representative data by CNC or other production techniques. 
       Further-Refined/True Pose Determination 
       [0109]    As a preface to describing this global matching approach,  FIG. 5  shows how a camera may be moved between different positions as it images a larger area. The top part in  FIG. 5  shows the camera moving in direction  500 , while the bottom part is shown going in direction  505 . Frames are obtained in the order shown 1, 2, 3 . . . 254, 255, 256. As one is going through the images sequentially, one might take an image 10 times a second. While frames  1  and  2  are close in time, there may actually be more similarities between frames  1  and  256 . For example, the camera may be spatially closer in 1/256 than at ½. 
         [0110]    The present approach accounts for this possibility by pursuing the best spatial matches in comparing image data to determine the camera pose information used to combine the images. Other systems (e.g., Zhang) focus on closest time matches (i.e., sequential frames) in determining pose. 
         [0111]    In actual practice, the inventors found that there is indeed no way to predict in advance which of the different frames produce the best spatial match. The best information is actually obtained by finding a tentative/provisional match, and then refining that tentative match to a collection of different frames. 
         [0112]    In recognition of this issue, the referenced post processing is carried out globally. Rather than automatically comparing one frame with the next frame, the processing of this embodiment looks at the entire library of different frames. For example, you might get more information about the current frame from an old frame because it is spatially closer. 
         [0113]    The inventors found the unexpected result that matching concurrently to multiple frames produces better results than matching to consecutive frames. This global matching system in essence looks at the entire point library to keep track of the same points across multiple frames as far as can be done, and averaging that information. All of the descriptors in that whole library can be compared, to find the “best descriptor” to compare the points that have those best descriptors. Since that point is on the item being imaged, averaging that point across multiple frames provides more information about that point. Because of the averaging, the multiple frames each contribute pose information to other spatially nearby frames. Averaging may also be used to more accurately find their true locations by eliminating various kinds of stochastic noise. 
         [0114]    The post-processing uses global matching between the different frames from as far away as possible. Different frames containing different views of the same point represent that same point. Since those points are always the same, averaging between them will increase their accuracy. According to the present system, the points are averaged without accumulating errors of the point locations between the frames. 
         [0115]    Such post-processing is shown in detail with reference to the flowchart of  FIG. 7 . At  700 , the best existing rotation and translation R, T (typically, the Rough Pose) have been obtained. This has created a map of all places where the camera was at all times. Each place at each time corresponds to a specific 3D pose. 
         [0116]    At  705 , a pose is selected as the root node for this library. This can be selected in essence at random, for example by selecting the first pose in the list. Alternatively, a criteria can be selected, for example by taking the centroid point as the root node pose. 
         [0117]    At  710 , the operation continues by finding all neighbors that are close to the chosen pose. The operation creates information that represents a graph of all 3D poses based on proximity. 
         [0118]    First, pose based warping is carried out at  706  to warp the poses to look more like one another. The pose based warping is described in detail with reference to  FIG. 9 , herein. 
         [0119]    After the warping, all neighbor poses that are within T 1  of the starting pose are found at  710 . Each of these neighbor poses are removed and labeled. T 1  is a value that is chosen to be the maximum workable distance to reduce error propagation, but still limited by feasibility of the calculations. 
         [0120]    At  715 , after the neighbor poses have been removed, a second threshold T 2  is used to find child poses. All of the poses that are left are not neighbors to the root node. The threshold T 2  is such that there is minimal or no overlap between the images in a different reference plane. T 2  is larger than T 1  and is chosen as the maximum distance for which you can find a pose via pose based warping. The points that are within T 2  to the root node are called Children nodes. Anything beyond T 1 +T 2  is too far from the root, and hence the T 1  of the child will not be affected by the parent. 
         [0121]    All the points are analyzed in this way. Flowchart element  720  represents continuing this operation, until all children are found. At  725 , all the nodes within the library are either a child or a neighbor. At this point, this subprocess is called “complete”. 
         [0122]    At  730 , each of the neighbors to the root node are averaged in with the root node. Each of the neighbors to the children are also averaged with all of its children. This creates heavyweight nodes that have been an averaged with a number of different neighbors forming an average pose value. 
         [0123]    At this point, the translation between the children and the root are determined. The children are translated to determine where the child node is in the parent node. The heavyweight child nodes are then translated and averaged in with the parent. Such action forms very heavyweight nodes that are based on many different poses. The pose as averaged in this way provides a very accurate depiction of the root node that has been improved by averaging. The new R,T obtained at  735  is a heavyweight average between the root node selected as  705 , and all of its neighbors and children. 
         [0124]    This new R and T is used as a post processed pose (the most refined, True Pose), to re-calculate the 3-D value with greater accuracy. 
         [0125]    An advantage of this system is that the same points from multiple frames can be averaged with one another without the error stack up as would possibly occur from a temporal technique. Also, the operations are carried out only one layer deep, so error does not propagate through layers. This means that the cross-correlation point identification error does not propagate. 
       Variations 
       [0126]    One embodiment carries out certain parts of the image processing, including interpolating between values, using a bicubic spline function. According to an embodiment, the bicubic spline function forms a set of spline coefficients. Each coefficient is used to calculate the next coefficient. The list of coefficients is causal in that one coefficient effects values of other coefficients. 
         [0127]    According to an embodiment, the bi cubic spline function is simplified by using only some previous number of coefficients as a sliding window across the spline coefficients. The inventors found that this sliding window can be selected (here by 16 blocks) to a value that does not effect the bicubic spline calculation. For example, by using 16 blocks, the error in coefficients can be less than the precision of the floating-point variable. However, by reducing the result in this way, each item can be simultaneously calculated in shaders of the GPU. This allows massively parallel processing, so that each single shader can calculate a part using only the 16 coefficients in this way, therefore allowing each shader to calculate a value for one pixel. 
         [0128]    Importantly, the inventors found when a process such as this is done on the GPU, it is important to maintain all of the values in the shader. For example, some of the calculations such as the bicubic spline can be carried out faster on the shader, but other calculations such as sorting and comparing may be carried out faster on a processor. However, the inventors found that writing between the shaders and the main processor takes more time, and therefore it is faster to do everything in the shader, even those things which are less efficiently carried out in the shader. The pose based warping uses bicubic spline calculations as described above, and parts or all of this calculation may also be more efficiently carried out in the GPU, according to one embodiment. 
         [0129]    Another operation, carried out before the CC operation, may weight the center, left and right values more than the others. 
         [0130]    Another operation may take the standard deviation of all values in the final 16×16 square carried out as part of the cross-correlation operation. Any standard deviation values higher than a specified peak of the images are truncated so that those peaks do not bias the data. This removes the abnormally bright pixels to avoid biasing the data. 
         [0131]    Another operation may take advantage of the known value that the blue/red apertures are shifted in only one dimension. Therefore, for the cross-correlation subdivisions, this one dimension shift may represent the maximum displacement that can occur. Any displacement which is greater than this can be detected in the cross-correlation subdivisions, and used to weight the final value. 
         [0132]    Although only a few embodiments have been disclosed in detail above, other embodiments are possible and the inventors intend these to be encompassed within this specification. The specification describes specific examples to accomplish a more general goal that may be accomplished in another way. This disclosure is intended to be exemplary, and the claims are intended to cover any modification or alternative which might be predictable to a person having ordinary skill in the art. For example, other forms of matching other than cross-correlation can be used. 
         [0133]    Those of skill would further appreciate that the various illustrative logical blocks, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the exemplary embodiments of the invention. 
         [0134]    The various illustrative logical blocks, modules, and circuits described in connection with the embodiments disclosed herein, may be implemented or performed with a general purpose processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. The processor can be part of a computer system that also has a user interface port that communicates with a user interface, and which receives commands entered by a user, has at least one memory (e.g., hard drive or other comparable storage, and random access memory) that stores electronic information including a program that operates under control of the processor and with communication via the user interface port, and a video output that produces its output via any kind of video output format, e.g., VGA, DVI, HDMI, display port, or any other form. 
         [0135]    A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. These devices may also be used to select values for devices as described herein. 
         [0136]    The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in Random Access Memory (RAM), flash memory, Read Only Memory (ROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In the alternative, the processor and the storage medium may reside as discrete components in a user terminal. 
         [0137]    In one or more exemplary embodiments, the functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media may be any available media that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. The memory storage can also be rotating magnetic hard disk drives, optical disk drives, or flash memory based storage drives or other such solid state, magnetic, or optical storage devices. Also, any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and blu-ray disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media. 
         [0138]    Operations as described herein can be carried out on or over a website. The website can be operated on a server computer, or operated locally, e.g., by being downloaded to the client computer, or operated via a server farm. The website can be accessed over a mobile phone or a PDA, or on any other client. The website can use HTML code in any form, e.g., MHTML, or XML, and via any form such as cascading style sheets (“CSS”) or other. 
         [0139]    Also, the inventors intend that only those claims which use the words “means for” are intended to be interpreted under 35 USC 112, sixth paragraph. Moreover, no limitations from the specification are intended to be read into any claims, unless those limitations are expressly included in the claims. The computers described herein may be any kind of computer, either general purpose, or some specific purpose computer such as a workstation. The programs may be written in C, or Java, Brew or any other programming language. The programs may be resident on a storage medium, e.g., magnetic or optical, e.g. the computer hard drive, a removable disk or media such as a memory stick or SD media, or other removable medium. The programs may also be run over a network, for example, with a server or other machine sending signals to the local machine, which allows the local machine to carry out the operations described herein. 
         [0140]    Where a specific numerical value is mentioned herein, it should be considered that the value may be increased or decreased by 20%, while still staying within the teachings of the present application, unless some different range is specifically mentioned. While many of these embodiments discuss 64 bits, 128 or 256 bit processors or processing can alternatively be used. Where a specified logical sense is used, the opposite logical sense is also intended to be encompassed. 
         [0141]    The previous description of the disclosed exemplary embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these exemplary embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.