Abstract:
A system for and method of obtaining rotation information is disclosed. The method comprises capturing a plurality of patterned images from a plurality of locations, correlating the plurality of patterned images to generate sets of linear differences, and using the sets of linear differences to generate the rotation information. Preferably, the plurality of locations comprise a first part of a fingerprint swipe sensor and a second part of the fingerprint swipe sensor, each part configured to capture a part of a fingerprint image. Each part captures a part of the fingerprint image at two positions and correlates the parts at the two positions to determine one set of linear differences. Together, the sets of linear differences are used to calculate the rotation information, which can be used to emulate a rotational device such as a steering wheel, a joystick, or a navigation bar.

Description:
RELATED APPLICATION  
       [0001]     This application claims priority under 35 U.S.C. § 119(e) of the co-pending U.S. provisional application Ser. No. 60/497,045, filed on Aug. 22, 2003, and titled “ROTATIONAL INPUT METHOD PATENT.” The provisional application Ser. No. 60/497,045, filed on Aug. 22, 2003, and titled “ROTATIONAL INPUT METHOD PATENT” is hereby incorporated by reference. 
     
    
     FIELD OF THE INVENTION  
       [0002]     This invention relates to the field of biometric sensors. In particular, this invention relates to systems and methods that use fingerprint images to emulate electronic positioning devices.  
       BACKGROUND OF THE INVENTION  
       [0003]     The emergence of portable electronic computing platforms allows functions and services to be enjoyed wherever necessary. Palmtop computers, personal digital assistants, mobile phones, portable game consoles, biometric/health monitors, remote controls, digital cameras, to name a few, are some daily-life examples of portable electronic computing platforms. The desire for portability has driven these computing platforms to become smaller and, consequently, to have longer battery life. A dilemma occurs when these ever-smaller devices require efficient ways to collect user input.  
         [0004]     Portable electronic computing platforms need these user inputs for multiple purposes, including (a) navigating a cursor or a pointer to a certain location on a display, (b) selecting (e.g., choosing or not choosing) an item or an action, and (c) orientating (e.g., changing direction with or without visual feedback) an input device.  
         [0005]     Concepts for user input from much larger personal computers have been borrowed. Micro joysticks, navigation bars, scroll wheels, touch pads, steering wheels and buttons have all been adopted, with limited success, in conventional devices. All these positioning devices consume substantial amounts of valuable surface real estate on a portable device. Mechanical positioning devices such as joysticks, navigation bars and scroll wheels can wear out and become unreliable. Their sizes and required movements often preclude optimal ergonomic placement on portable computing platforms.  
         [0006]     Prior art methods calculate rotation by rotating one frame with respect to another and then applying standard correlation methods. These methods require the selection of a pivot point (e.g., the origin), followed by additional computations. These computations are not helpful for determining linear motion (e.g., non-rotational movement in the x- and y-directions). Such a shortcoming makes prior art systems even more inefficient when used in portable devices, in which both rotational and linear movement are required, such as when emulating, respectively, a steering wheel and a pointing device.  
       SUMMARY OF THE INVENTION  
       [0007]     The present invention discloses a system for and method of obtaining rotation information from a patterned image, such as a fingerprint image. Embodiments of the present invention thus require smaller footprints than those that use joy sticks, steering wheels, and other, larger devices that require additional power. Embodiments of the present invention use linear correlation methods that are easier to use than rotational and other methods such as those using trigonometric functions. Embodiments of the present invention thus use simpler algorithms that can be performed faster and more reliably.  
         [0008]     In a first aspect of the present invention, a method of obtaining rotation information comprises capturing a plurality of patterned images from a plurality of locations, correlating the plurality of patterned images to generate sets of linear differences, and using the sets of linear differences to generate the rotation information. The plurality of locations comprise a first part of a sensor and a second part of the sensor. A first of the plurality of patterned images is captured in the first part of the sensor and a second of the plurality of patterned images is captured in the second part of the sensor.  
         [0009]     Preferably, the sensor is a biometric image sensor, such as a finger image sensor. The first of the plurality of patterned images and the second of the plurality of patterned images together correspond to a fingerprint image in a first position on the sensor. A third of the plurality of patterned images is captured in the first part of the sensor and a fourth of the plurality of patterned images is captured in the second part of the sensor. The third of the plurality of patterned images and the fourth of the plurality of patterned images together correspond to the fingerprint image in a second position on the sensor. In one embodiment, the rotation information corresponds to an angular difference between the first position and the second position.  
         [0010]     In one embodiment, correlating the plurality of patterned images comprises correlating the first patterned image with the third patterned image to generate a first set of linear differences from the sets of linear differences, correlating the second patterned image with the fourth patterned image to generate a second set of linear differences from the sets of linear differences, and correlating a first combination of the first patterned image and the second patterned image with a second combination of the third patterned image and the fourth patterned image to generate a third set of linear differences from the sets of linear differences. Correlating the first patterned image with the third patterned image, correlating the second patterned image with the fourth patterned image, and correlating the first combination with the second combination all comprise performing a cross correlation. In one embodiment, the cross correlation is either a normalized cross correlation or a standardized cross correlation.  
         [0011]     In one embodiment, the first part of the sensor and the second part of the sensor are contiguous. Alternatively, the first part of the sensor and the second part of the sensor are not contiguous.  
         [0012]     In one embodiment, the first part of the sensor comprises a first sub-frame of pixels and the second part of the sensor comprises a second sub-frame of pixels. In this embodiment, capturing the first patterned image comprises storing in the first sub-frame first data corresponding to the first patterned image, capturing the second patterned image comprises storing in the second sub-frame second data corresponding to the second patterned image, capturing the third patterned image comprises storing in the first sub-frame third data corresponding to the third patterned image, and capturing the fourth patterned image comprises storing in the second sub-frame fourth data corresponding to the fourth patterned image. Correlating the first patterned image with the third patterned image comprises correlating the first data with the third data to generate first and second linear differences from the first set of linear differences. Correlating the second patterned image with the fourth patterned image comprises correlating the second data with the fourth data to generate first and second linear differences from the second set of linear differences. And correlating the first combination with the second combination comprises correlating a combination of the first data and the second data with a combination of the third data and the fourth data to generate first and second linear differences from the third set of linear differences.  
         [0013]     In another embodiment, correlating comprises determining a lag to correlate elements of one of the first and second sub-frames, the lag and a difference between the elements corresponding to first and second linear differences from one of the sets of linear differences. Each element corresponds to a row of one of the first and second sub-frames. Alternatively, each element corresponds to a column of one of the first and second sub-frames.  
         [0014]     In another embodiment, the method further comprises filtering the first set of linear differences, the second set of linear differences, the third set of linear differences, and the rotation information. Filtering comprises multiplying by a scaling factor, performing a smoothing function, and performing a clipping function.  
         [0015]     Preferably, the finger image sensor is a finger swipe sensor. Alternatively, the finger image sensor is a finger placement sensor.  
         [0016]     In another embodiment, the method further comprises using the rotation information on a host platform having a display screen, the rotation information used to rotate an object on the display screen, thereby emulating a computer input device. The computer input device is selected from the group consisting of a steering wheel, a joystick, and a navigation bar. Emulating a computer input device comprises moving the object on the display screen at a rate related to the angular difference or the angular position.  
         [0017]     In accordance with a second aspect of the invention, a system for obtaining rotation information comprises means for capturing a plurality of patterned images from a plurality of locations and means for correlating the plurality of patterned images to generate sets of linear differences and for using the sets of linear differences to generate the rotation information.  
         [0018]     In accordance with a third aspect of the present invention, a method of emulating a rotational device using a pattern comprises capturing a first image of the pattern at a first orientation, capturing a second image of the pattern at a second orientation, correlating the first image with the second image to calculate linear differences between the first orientation and the second orientation, translating the linear difference into rotational data, and using the rotational data to emulate the movement of a rotational device.  
         [0019]     In accordance with a fourth aspect of the present invention, a system for emulating a positional device comprises a sensor for capturing an image of a pattern and a processor coupled to the sensor. The processor is configured to calculate linear differences between a first position of the image of the pattern and a second position of the image of the pattern and to translate the linear differences into rotational data corresponding to a rotation of the image of the pattern.  
         [0020]     In accordance with a fifth aspect of the present invention, a method of sensing rotation of an object on an image sensor comprises sensing a first image of the object, sensing a second image of the object, and comparing the first image with the second image to determine whether there is linear motion in each of at least two portions of an area containing the first image and the second image to determine whether the object remained stationary, moved in a linear manner, or rotated. 
     
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS  
       [0021]      FIGS. 1A and 1B  show how an electronic image is rotated by rotating a finger on a finger image sensor, in accordance with the present invention.  
         [0022]      FIG. 2  shows a fingerprint image where ridges are shown in black and valleys are shown in white and indicating areas of bifurcation and ridge endings.  
         [0023]     FIGS.  3 A-D shows left- and right-hand sections of a fingerprint sensor with a portion of a fingerprint image placed upon it as the fingerprint image is linearly moved and rotated in accordance with the present invention.  
         [0024]      FIG. 4  is a flowchart of a frame acquisition and image correlation procedure in accordance with the present invention.  
         [0025]      FIG. 5A  shows a finger image sensor in a horizontal orientation.  
         [0026]      FIG. 5B  shows a finger image sensor in a vertical orientation.  
         [0027]      FIG. 6  shows pixel data from a frame (slice) from a fingerprint sensor.  
         [0028]      FIG. 7  shows pixel data from a fingerprint sensor during different iterations of reconstruction in accordance with the present invention.  
         [0029]      FIGS. 8-12  show different partition configurations of a frame in accordance with the present invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0030]     The present invention is directed to systems for and methods of determining the rotational position and movement of an arbitrary patterned material imaged by an imaging sensor. Preferably, the arbitrary patterned material is a finger and the rotational position and movement of the image of the finger are determined.  
         [0031]     Embodiments of the present invention advantageously determine and collect finger rotational information for use in a digital device and most preferably in personal computing devices. Unlike prior art rotational position correlators, which are non-linear, requiring trigonometric functions like sine, cosine, and tangent calculations, embodiments of the present invention use a linear correlation method that is easier to implement and more computationally efficient. Embodiments of the present invention allow for extremely efficient calculation of linear motion from the components used to determine the rotational motion, thereby reducing the complexity of systems that require one sensor to be used to gather both linear and rotational movement inputs.  
         [0032]     A system in accordance with embodiments of the present invention reconstructs fingerprint images from swipe sensors, thereby efficiently providing rotational motion data along with data necessary to reconstruct the image. The system is particularly well suited for applications that do not require high precision rotational information. Methods of and systems for fingerprint sensing are described in detail in the U.S. patent application Ser. No. 10/194,994, filed Jul. 12, 2002, and titled “Method and System for Biometric Image Assembly from Multiple Partial Biometric Frame Scans,” and in the U.S. patent application Ser. No. 10/099,558, filed Mar. 13, 2002, and titled “Fingerprint Biometric Capture Device and Method with Integrated On-Chip Data Buffering,” both of which are hereby incorporated by reference in their entireties. In the preferred embodiment, the fingerprint sensor is an Atrua Wings ATW 100 capacitive swipe sensor by Atrua Technologies, Inc., at 1696 Dell Avenue, Campbell, California 95008.  
         [0033]     A key aspect of the present invention is determining rotation from linear correlation rather than prior art methods that determine rotation by rotating one frame with respect to another, and then applying standard correlation methods. The prior art methods require choosing a pivot point (center of origin) and then performing additional computation. Furthermore, such computation is not helpful for determining linear motion (non-rotational movement in the x- and y-directions). These computations are even more inefficient in portable electronic devices where it may be important to calculate both kinds of movement, for instance, when emulating a pointing device and a steering wheel on one component.  
         [0034]     Most of the prior art is concentrated on calculating exact rotational movement, and therefore requires the more precise steps outlined above. However, many applications do not require such precision, and it is these cases where the new invention is best suited. Embodiments of the present invention make use of the fact that, as a finger rotates clockwise, the left side of the image will appear to be moving upward, while the right half of the finger will appear to be moving downward. This is sometimes referred to as shear. The opposite is true of counterclockwise motion. Furthermore, in both cases, the left side will appear to be moving toward the right, and the right side will appear to be moving toward the left, as shown in  FIGS. 2B and 2C . On a typical swipe type of finger imaging sensor, which is mounted horizontally so that its height is much smaller than its width, the upward and downward motion is easily observed and exploitable, but because the sensor is so small in height, observing the motion in the x-direction is more difficult. If a swipe sensor is mounted vertically, then it will be easier to observe motion in the x-direction than in the y-direction due to the device&#39;s small width in this case. The invention is equally applicable to both cases. It is also equally applicable on a large fingerprint placement sensor, where movement in both the x- and y-directions is easily observable and can be exploited.  
         [0035]     Using the observations outlined above, embodiments of the present invention use the simpler linear correlation methods to determine rotational movement, which will occur when motion of the left side of a finger image is in an opposite direction to that of the right side. For instance, if the left half is moving upward and the right half downward, there is clockwise rotational movement as shown in  FIG. 2D , discussed below. If the linear movement detected at the left edge and right edge of the sensor are substantially equal but opposite, the center of rotation is at or near the center of the sensor. If the linear movement is not equal but opposite, the center of rotation can be calculated and will be closer to the end of the sensor with the smaller amount of linear movement. If the linear movement is not equal but opposite, the center of rotation can be calculated. If both sides are moving in the same direction, as in  FIG. 2B , then likely only overall linear movement is observed. It will be appreciated that the present invention can determine an angle of rotation even if the center of rotation is displaced, as when a finger slides along the sensor as it rotates.  
         [0036]     Accordingly, the present invention offers a reliable and computationally-efficient solution to obtain high-resolution rotational information about a user&#39;s finger as it contacts a finger imaging sensor, so that such a sensor can, for example, emulate a steering wheel for use in gaming, or rotate the image of a map for easier viewing on a display.  
         [0037]      FIG. 1A  shows a system  10  used to illustrate one embodiment of the present invention. The system  10  comprises a finger image sensor  20  coupled to a display device  11 , displaying a triangular electronic image  15 . The display device  11  can be a monitor used with a personal computer, a screen on a personal digital assistant (PDA) or game device, or any other kind of display device.  FIG. 1A  also shows a finger  30  placed on the finger image sensor  25 . It will be appreciated that the finger  30  has patterns on a surface contacting the finger image sensor  25  and that the finger image sensor  25  captures images of those patterns. A coordinate axis  20  makes an angle α 0  with an edge  21  of the triangular image  15 . A coordinate axis  35  makes an angle β 0  with a line segment  36  associated with the finger  30 .  FIG. 1B  shows the system  10  after the finger  30  has been rotated so that the coordinate axis  35  makes an angle β 1  with the line segment  36 . In accordance with the present invention, the triangular image  15  is rotated so that the coordinate axis  20  makes an angle α 1  with the edge  21 . Thus, in accordance with one embodiment, rotating the finger  30  through an angle β 1 −β 0 (Δβ) results in rotating the triangular electronic image through an angle α 1 −α 0 (Δα).  
         [0038]     It will be appreciated that Δα can correspond to Δβ in any number of ways. For example, Δα can equal Δβ, Δα can be a multiple of Δβ, Δα can be a fraction of Δβ, Δα can be a multiple of Δβ plus some offset, etc. It will also be appreciated that in accordance with one embodiment, the finger  30  does not have to maintain a pivot point on the finger image sensor  25 . The finger  30  can be moved horizontally or vertically on the finger image sensor  25  before, while, or after it is rotated so that the line segment  36  is displaced horizontally, or vertically, or both, and the angle Δβ still determined. It will also be appreciated that vertical and horizontal movements of the finger  30  can also captured to vertically and horizontally displace the triangular image  15  on the display device  11 . It will also be appreciated that the triangular image  15  can be moved at a rate related to Δβ (called the rate mode) or at a rate related to β 1 .  
         [0039]     While the finger image sensor  25  is depicted as a placement sensor, it will be appreciated that other types of sensors can be used in accordance with the present invention. Preferably, the finger image sensor  25  is a swipe sensor, described in more detail below.  
         [0040]      FIG. 2  shows a typical fingerprint image, including physical ridges and valleys on the surface of the finger. The pattern of ridges and valleys has proven to be unique among very large populations of human beings, especially the ridge endings and bifurcations called “minutiae.” Fingers also often have other measurable surface features such as pores, scars, and wrinkles. It is the overall pattern of features—not the unique individual features—that are tracked to measure the distance, rotation, direction, or speed that a fingerprint has moved on the finger image sensor.  
         [0041]     Many prior art electronic finger imaging sensors actively sense the entire surface of a fingerprint at the same time. Whether based on optical or electrical sensing methods, these sensors have a surface area at least as large as a typical person&#39;s fingertip pad (typically 15 mm×15 mm). Using these sensors the user simply places his finger on the sensor until the image is captured. These sensors, now known as placement sensors, contain rows and columns and can capture large images, typically ranging from 250-500 rows and 200-500 columns depending on the sensor&#39;s capabilities and size. Such devices are capable of sensing rotational input, and can indeed be used with the new invention to collect rotational information, but they are larger than today&#39;s more miniaturized finger sensors.  
         [0042]     The most promising of the miniaturized sensors is one that is fully sized in one direction (typically in width) but abbreviated in the other (typically height). This results in a sensor that only is capable of sensing a small rectangular portion of the fingerprint at any one time.  
         [0043]     Such smaller sensors are better suited for use with the present invention, not only because they are more apropos for portable devices, but also because they produce smaller images. The smaller images have less data in them, making the computations less intense. While it is possible to ignore or mask off data from a larger sensor to make it resemble a smaller one, such an approach is not ideal, because it does not guarantee that the finger of the user is even touching the area of interest. With a swipe sensor, this is not an issue.  
         [0044]     Embodiments of the present invention can acquire rotational position data from any device capable of imaging the surface of a human finger or other patterned material and is therefore not limited to use with placement or swipe finger image sensors, which typically provide at least 250 dots per inch resolution. The present invention will also work with lower or higher resolution devices that may become available in the future.  
         [0045]      FIG. 3A  shows the left half  205 A and the right half  205 B of a finger image sensor  205 . The finger image sensor  205  has placed upon it a finger identified by the fingerprint image  203  having identifiable ridge portions  201  and  202 .  FIG. 3A  also shows an x-coordinate axis and a y-coordinate axis, with the arrow of each axis pointing in a direction of increasing values for the respective axis.  FIG. 3A  shows the fingerprint image  203  in a first orientation on the finger image sensor  205  and thus in a first orientation with respect to the x-coordinate axis and the y-coordinate axis.  FIG. 3B  shows the fingerprint image after it has been moved linearly in a vertical position, in a direction of decreasing values for the y-coordinate.  FIG. 3C  shows the fingerprint image  203  after it has been rotated counter-clockwise on the finger image sensor  205 . It is seen by comparing the orientations of the fingerprint image  203  from  FIG. 3B  to  FIG. 3C  that the y-coordinates of the identifiable portions  201  and  202  in the left half  205 A have both decreased and that the y-coordinates in the right half  205 B have both increased.  FIG. 3D  shows the fingerprint image  203  after it has been rotated clockwise on the finger image sensor  205 . It is seen by comparing the orientations of the fingerprint image  203  from  FIG. 3C  to  FIG. 3D  that the y-coordinates of the identifiable portions  201  and  202  in the left half  205 A have both increased and that the y-coordinates in the right half  205 B have both decreased.  
         [0046]      FIG. 4  is a flowchart for an algorithm  210  for determining rotational movement or placement in accordance with a preferred embodiment of the present invention. In the start step  211 , a user is prompted by an operating system or application executing on a host (not shown). Next, in the step  212 , a finger image sensor (not shown) in accordance with the present invention is initialized, readied for reading data. This step  212  comprises powering on the sensor on and making sure it is ready to capture a fingerprint image. Step  212  can also include setting contrast and brightness levels, setting the sensor to a desired data acquisition mode, calibrating the sensor, or otherwise initializing the sensor. It will be appreciated that step  212  is not required if the sensor has already been initialized.  
         [0047]     Next, in the step  213 , a frame is read by the sensor at a rate supported by it or by the hardware platform&#39;s computing power and bandwidth. In the step  215 , the properties of the frame are estimated to determine whether it is useful. The metrics of the frame are analyzed in the step  220 , to determine whether the frame is useful. If the frame is useful, it is kept and processing continues in the step  225 ; otherwise, the frame is disregarded, and processing continues in the step  255 . As described in more detail below, in a preferred embodiment the usefulness of a frame is determined by measuring image statistics such as the average value and the variance of pixel data in the frame. The usefulness of a frame is directly related to whether or not a finger is present on the sensor. It will be appreciated that the step  215  can be eliminated if a less efficient implementation is acceptable, or when the sensor only generates frames when a finger is present on it.  
         [0048]     In the step  225 , the current frame (e.g., the frame most recently read and currently being processed) is correlated with the last stored useful frame. On the very first iteration, since there is no “last useful frame,” the current frame is copied to the last useful frame. In a preferred embodiment, the frame is divided into a left half and a right half. It will be appreciated, however, that a frame can be divided into any number of parts. Next, in the step  230 , the linear movement of the left half of the frame and the linear movement of the right half of the frame are both calculated. In the step  235 , using the linear movement of the left half of the frame and the linear movement of the right half of the frame, the overall linear movement of the frame is calculated. This calculation is described in more detail below. In the step  240 , the calculations made in the step  235  are used to calculate the rotational movement of the fingerprint image.  
         [0049]     Next, in the step  245  the process checks whether there was any movement, linear or rotational, of the fingerprint image. If there was movement, the process continues in the step  250 , otherwise it continues in the step  255 . In the step  250 , the last frame useful frame is updated, and in the step  251 , the last useful frame is stored. Processing then continues in the step  225 .  
         [0050]     In the step  255 , the process checks whether more frames are to be acquired. If more frames are to be acquired, the process continues to the step  260 , where a counter is incremented, and then continues on to the step  213 . If no more frames are to be acquired, the process continues to the step  265 , where it stops.  
         [0051]     As described above, the pixels for the current frame are correlated to the pixels of the last useful frame to determine the amount of rotational or linear motion. If overall linear movement has been calculated in the step  235 , data corresponding to the movement are sent to whatever downstream process needs it. For example, a program (e.g., an application program, a device driver, or an operating system) can use the corresponding data to linearly position a pointer on a display screen. If any overall rotational movement has been calculated in the step  240 , data corresponding to the movement are sent to whatever downstream process needs it. For example, a program can use the corresponding data to rotate an image on the display screen. Once it is determined that movement has occurred, the last useful frame is replaced by the current frame and the algorithm continues by acquiring new image data from the sensor.  
         [0052]     In a preferred embodiment, the system iterates in real time. Alternatively, the system stores all the frames in a memory buffer and calculates movement after multiple frames are acquired from the sensor. Preferably, the iteration halts when either the application or operating system tells it to stop. When the system is used as a pointing device for an operating system, the process can continue indefinitely.  
         [0053]     The algorithm starts whenever there is a need for rotational feedback, such as power up of a device or start of a game. The algorithm terminates when rotational information is no longer needed.  
         [0054]     In a preferred embodiment, the system executes on a computing device that is connected to a swipe fingerprint sensor  310  shown in  FIG. 5A . The swipe sensor  310  is mounted horizontally with respect to the x and y directions so that image frames as shown in  FIG. 6  are captured. The x direction is along the longest side of the sensor  310  while the y direction is perpendicular to the x direction. It will be appreciated that the sensor  310  can be mounted in any orientation. For consistency, the length of the sensor along the x-axis will always denote the length of the sensor.  FIG. 5B  shows a sensor  315  having a second orientation used in accordance with the present invention. The sensor  315  is mounted vertically with respect to the x and y directions. In the preferred embodiment, the fingerprint sensor (e.g.,  310  or  315 ) provides a single frame of data to a program upon request. As described below, a single frame can be logically divided into any number of smaller sub-frames. Sensors that can provide more than one frame per request can also be used in accordance with the present invention. It will also be appreciated that fingerprint sensors in accordance with the present invention can be mounted at orientations other than those shown in  FIGS. 5A and 5B .  
         [0055]     Typically, swipe sensors are capable of delivering anywhere from 250 to 3000 frames per second (the “frame rate”), depending on the sensor&#39;s capabilities, the interface used and the speed of the host personal computer.  
         [0056]      FIG. 6  shows image data  400  captured by a finger image sensor in accordance with the present invention. The image data  400  comprises N rows by M columns of picture elements, or pixels, with each pixel typically represented by a single byte (8 bits) of data. M can be any positive value (100-300 is typical, depending on resolution) and N must be at least 2 (the typical number of rows in a frame is 8-32). Preferably, N=8 and M=192. A value of a pixel is a gray level, such that the image frame resembles a finger image when displayed on a computer monitor. Typically, this value ranges from 0 to 255, with 0 representing black and indicating the presence of a fingerprint ridge, and 255 representing white and indicating the presence of a valley. Other ranges of data and other representations of such data are possible without affecting the nature of the invention.  
         [0057]     It is possible, in alternative embodiments, to use the system with little or no modification, with other similar types of sensors, such as optical document scanners. In one embodiment, the system of the present invention executes in specialized hardware or firmware instead of in software. In another embodiment, the algorithm executes on a general-purpose CPU and other portions execute solely in hardware.  
         [0058]      FIG. 7  shows a current frame and the last useful frame for several iterations of the algorithm  210  in  FIG. 3 . Iteration  1 , shown in column  401 , shows a last useful frame  405  and a current frame  410 . No rows of the frame  405  correspond to the frame  410 , so no recognizable movement can be identified. Iteration  2 , shown in column  402 , shows a last useful frame  410  and a current frame  415 . It will be appreciated that the last useful frame  410  corresponds to the current frame from the previous iteration, iteration  1 . Row 0 of frame  410  (indicated by an arrow) corresponds to row 1 of frame  415  (also indicated by an arrow). Linear movement in a y direction is thus detected. Iteration  3 , shown in column  403 , shows a last useful frame  415  and a current frame  420 . Frame  415  is identical to the frame  420 , so zero motion is recognized. (E.g., the finger has not been moved on the finger image sensor.) In this example, the last useful frame does not have to be updated. Iteration  4 , shown in column  404 , shows a last useful frame  420  and a current frame  425 . It will be appreciated that the last useful frame  420  corresponds to the current frame from iteration  3 . Row 1 of frame  420  (indicated by a straight arrow) corresponds to row 2 of frame  425  (also indicated by a straight arrow). This vertical shift in rows (i.e., tracking images of fingerprint patterns as they and hence a finger moves from row 1 to row 2) indicates a downward movement of a finger on a finger image sensor, referred to as movement in a positive y direction. Furthermore, column 2 of frame  420  (indicated by a squiggly arrow) corresponds to column 1 of frame  425  (also indicated by a squiggly arrow). This horizontal shift in columns (i.e., tracking images of fingerprint patterns as they and hence a finger moves from column 2 to column 1) indicates a left movement of a finger on a finger image sensor, here labeled movement in a negative x-direction. In this example, because a positive y-movement and a negative x-movement has been detected, a clockwise rotation of the fingerprint image is recognized.  
         [0059]     It will be appreciated that signs (positive or negative) assigned to a particular direction in an x-direction and a y-direction are arbitrarily chosen for the sake of explanation. The signs can be reversed.  
         [0060]     The algorithm  210  in  FIG. 4  is now described in more detail. As described above, the algorithm  200  iterates, requesting new frames of data (step  210 ) and correlating them to a previous image frame (step  225 ) stored in a buffer for just this purpose. At the i th  iteration of the algorithm  210 , one frame of data is requested from the sensing device (e.g., a finger image sensor). Once the frame is collected, it is analyzed to determine its usefulness. If the frame is deemed useful, it is saved in local memory for later use; if it is deemed useless, it is simply disregarded.  
         [0061]     In the preferred embodiment, the usefulness of a frame is determined by ensuring the frame contains at least some finger image information. For instance, if a frame is collected when no finger is on the device, that frame likely will contain only noise or a blank image. This is done using rules based on measuring image statistics of the frame, namely the average value and the variance. Some sensors provide information on finger presence, and that can be used in systems where it is available, either by itself or in conjunction with the above statistics.  
         [0062]     Mathematically, if the pixel in the n th  row and m th  column is given by frame[n,m], then:  
             FrameAverage   =     Φ   =         ∑     n   =   1     N     ⁢       ∑     m   =   1     M     ⁢     frame   ⁡     [     n   ,   m     ]             N   ×   M                     FrameVariance   =     Ψ   =         ∑     n   =   1     N     ⁢       ∑     m   =   1     M     ⁢       (       frame   ⁡     [     n   ,   m     ]       -   Φ     )     2           N   ×   M                   
 
 For the purposes of efficiency, the Metrics (calculated in the step  215 ) can also be calculated just using portions of the frame (rather than the entire frame), where the portions are arbitrary sub-images or are obtained by skipping every p th  pixel in the calculation. 
 
         [0064]     The frame is considered noise, and thereby disregarded, if: 
        Φ≧Noise_average_threshold_high or if     Φ≦Noise_average_threshold_low or if     Ψ≦Variance_average_threshold 
 
 In other words, if the average is above or below a certain level (e.g., a threshold), or if the variance is less than expected for a normal finger, it may indicate—depending on the sensor used—that no finger exists on the device at that moment. In the preferred embodiment, typical values of these thresholds are: 
    Noise_average_threshold_high=240     Noise_average_threshold_low=30     Variance_average_threshold=10 
 
 Note that other values can be used to tune the algorithm to the desired performance, and other more complicated combinations of the above statistics can also be used to determine the usefulness of a frame. Of course, other metrics, alone or in combination with the above, can also be used. 
       
 
         [0073]     Once the current frame has been found useful, it is next correlated to the last useful frame (stored in the step  251 ) to determine the finger movement, if any, that occurred. Once it is determined that finger movement has occurred, the last useful frame (step  251 ) is replaced by the current frame and the algorithm continues by acquiring a new frame from the sensor.  
         [0074]     In accordance with the present invention, a new frame (“cF”) is correlated with an older one stored in memory (“oF”). Correlation is well known by any person skilled in the art, but it is described in more detail here to better explain the present invention.  
         [0075]     Standard cross-correlation SCC of row R of the last useful frame with row S of the current frame is mathematically expressed as:  
               SCC_whole   ⁢     (     R   ,   S   ,   d     )       =       ∑     m   =     d   +   1         M   -   d       ⁢     (       oF   ⁡     [     R   ,   m     ]       ×     cF   ⁡     [     S   ,     m   -   d       ]         )               [     Equation   ⁢           ⁢   1     ]             
 
 where d is referred to as the “lag” or “offset.” The lag is related to the horizontal movement of the data in one frame with respect to the data in another, and can also be thought of as a velocity. Typically, the lag is −L&lt;=d&lt;=+L, where L is much less than M. All of the equations in this description are written assuming d&gt;=0 to keep the equations clear. It will be appreciated, however, that negative lag values can be processed by interchanging the column indices on oF and cF as shown below:  
         SCC_whole   ⁢     (     R   ,   S   ,   d     )       =       ∑     m   =          d        +   1         M   -        d            ⁢     (       oF   ⁡     [     R   ,     m   -        d            ]       ×     cF   ⁡     [     S   ,   m     ]         )           
 
 where |d| is the absolute value of d. 
 
 This interchange method is valid for all correlation equations in this document, not just SCC but also normalized cross-correlation NCC, discussed below. 
 
         [0079]     Though it is feasible to use standard correlation, the preferred embodiment uses a slightly modified version of the correlation called Normalized Cross Correlation NCC, defined in Equation 2 below, which is better suited to image registration tasks like fingerprint image reconstruction. Unlike standard correlation, NCC is invariant to changes in image intensity, has a range that is independent of the number of pixels used in the calculation, and is more accurate because it is less dependent on local properties of the image frames being correlated.  
                     NCC_whole   ⁢     (     R   ,   S   ,   d     )       =                           ∑     m   =     d   +   1         M   -   d       ⁢     [       {       oF   ⁡     [     R   ,   m     ]       ×     cF   ⁡     [     S   ,     m   -   d       ]         }       (     M   -     2   ⁢   d       )       ]       -                     oFsum   ⁡     [     R   ,   d     ]         (     M   -     2   ⁢   d       )       ×       cFsum   ⁡     [     S   ,   d     ]         (     M   -     2   ⁢   d       )         }                       [       {       ∑     m   =     d   +   1         M   -   d       ⁢         {     oF   ⁡     [     R   ,   m     ]       }     2       (     M   -     2   ⁢   d       )         }     -       {       oFsum   ⁡     [     R   ,   d     ]         (     M   -     2   ⁢   d       )       }     2       ]     ×               [       {       ∑     m   =     d   +   1         M   -   d       ⁢         {     cF   ⁡     [     S   ,     m   -   d       ]       }     2       (     M   -     2   ⁢   d       )         }     -       {       cFsum   ⁡     [     S   ,   d     ]         (     M   -     2   ⁢   d       )       }     2       ]                         where   ⁢     :                   oFsum   ⁡     [     R   ,   d     ]       =       ∑     m   =     d   +   1         M   -   d       ⁢     {     oF   ⁡     [     R   ,   m     ]       }                     [     Equation   ⁢           ⁢   2     ]             
 
 is the sum along the row R from column d+1 through column M−d, and  
         cFsum   ⁡     [     S   ,   d     ]       =       ∑     m   =   1       M   -     2   ⁢   d         ⁢     {     cF   ⁡     [     S   ,   m     ]       }           
 
 is the sum along row S from column 1 through column M−2d. 
 
         [0082]     The above equations are in terms of rows of each frame, but it is more general to think of “patches” of each frame, where a patch can be some subset or superset of a row. While the patches of each frame to be correlated can be any arbitrary set of pixels, the preferred embodiment uses a patch centered in the middle of each frame. While any row or subset of a row could be used, if the patch is too small, the statistical significance of the cross-correlation value will erode.  
         [0083]     Since the lag, or offset, of the information in the current frame to that in the last frame corresponds to an unknown amount of movement in the x-direction, NCC_whole(R,S,d) must typically be calculated for multiple values of d to find the one that corresponds to the best fit. Therefore, in one embodiment: 
 
 PeakNCC   whole ( R,S,L )=MAX{ NCC   —   whole ( R,S,d )}for  d=−L  to  d=L.   [Equation 3]
        d peakwhole (R,S,L)=the value of d at which the above equation is satisfied. 
 
 In the preferred embodiment, L=8, but L should be chosen so that it is as large as the maximum x-velocity that can occur from frame to frame. A smaller L is more computationally efficient, but will produce inaccurate results if the finger shifts more than ±L from one frame to the next. In an alternative embodiment, L can be a function of the d peakwhole  from the previous iteration i−1. For example, 
 
 L (at iteration  i )= d   peakwhole (at iteration  i− 1)+ e , where e is typically equal to 1 or 2. 
 
 In yet another embodiment, L can be a function of the row number in the frame (i.e. R and/or S). Also note that it is possible to use scaled versions of the NCC equations so that floating-point operations can be avoided, and that for computing purposes it is also possible to use NCC-squared to avoid an expensive square-root operation. 
       
 
         [0087]     The PeakNCC whole  corresponds to the correlation coefficient of the best fit, while d peakwhole  corresponds to the amount of movement in the x direction. A method to obtain the amount of motion in the y direction is described below.  
         [0088]     The NCC calculation in Equation 2 below can be restated, for last frame oF and current frame cF,  
                     NCC_whole   ⁢     (     R   ,   S   ,   d     )       =                           ∑     m   =     d   +   1         M   -   d       ⁢     [       {       oF   ⁡     [     R   ,   m     ]       ×     cF   ⁡     [     S   ,     m   -   d       ]         }       (     M   -     2   ⁢   d       )       ]       -                   oFsum   ⁡     [     R   ,   d     ]         (     M   -     2   ⁢   d       )       ×       cFsum   ⁡     [     S   ,   d     ]         (     M   -     2   ⁢   d       )                           [       {       ∑     m   =     d   +   1         M   -   d       ⁢         {     oF   ⁡     [     R   ,   m     ]       }     2       (     M   -     2   ⁢   d       )         }     -       {       oFsum   ⁡     [     R   ,   d     ]         (     M   -     2   ⁢   d       )       }     2       ]     ×               [       {       ∑     m   =     d   +   1         M   -   d       ⁢         {     cF   ⁡     [     S   ,     m   -   d       ]       }     2       (     M   -     2   ⁢   d       )         }     -       {       cFsum   ⁡     [     S   ,   d     ]         (     M   -     2   ⁢   d       )       }     2       ]                         as   ⁢     :                   NCC_whole   ⁢     (     R   ,   S   ,   d     )       =                         [       (     M   -     2   ⁢   d       )     ⁢           ⁢       ∑     m   =     d   +   1         M   -   d       ⁢     [     {       oF   ⁡     [     R   ,   m     ]       ×     cF   ⁡     [     S   ,     m   -   d       ]         }     ]         ]     -                 oFsum   ⁡     [     R   ,   d     ]       ×     cFsum   ⁡     [     S   ,   d     ]                           [       {       (     M   -     2   ⁢   d       )     ⁢           ⁢       ∑     m   =     d   +   1         M   -   d       ⁢       {     oF   ⁡     [     R   ,   m     ]       }     2         }     -       {     oFsum   ⁡     [     R   ,   d     ]       }     2       ]     ×               [       {       (     M   -     2   ⁢   d       )     ⁢           ⁢       ∑     m   =     d   +   1         M   -   d       ⁢       {     cF   ⁡     [     S   ,     m   -   d       ]       }     2         }     -       {     cFsum   ⁡     [     S   ,   d     ]       }     2       ]                           [     Equation   ⁢           ⁢   2     ]             
 
 where the numerator and denominator have both been multiplied by (M−2d) 2  to make it simpler to compute and understand. 
 
         [0090]     This can be separated into left and right halves of each row as: 
 
 NCC   —   whole ( R, S, d )=( A−B )/( C   1/2   ×D ) 
 
           where             A   =     [       (     M   -     2   ⁢   d       )     ⁢     {         ∑     m   =     d   +   1         M   /   2       ⁢     [     {       oF   ⁡     [     R   ,   m     ]       ×     cF   ⁡     [     S   ,     m   -   d       ]         }     ]       +                                 ⁢       ∑     m   =       M   /   2     +   1         M   -   d       ⁢     [     {       oF   ⁡     [     R   ,   m     ]       ×     cF   ⁡     [     S   ,     m   -   d       ]         }     ]       }     ]             where             B   =       ⌊         oFsum   left     ⁡     [     R   ,   d     ]       +       oFsum   right     ⁡     [     R   ,   d     ]         ⌋     ×                         ⁢     ⌊         cFsum   left     ⁡     [     S   ,   d     ]       +       cFsum   right     ⁡     [     S   ,   d     ]         ⌋               where             C   =     [         (     M   -     2   ⁢   d       )     ⁢     {         ∑     m   =     d   +   1         M   /   2       ⁢       {     oF   ⁡     [     R   ,   m     ]       }     2       +       ∑     m   =       M   /   2     +   1         M   -   d       ⁢       {     oF   ⁡     [     R   ,   m     ]       }     2         }       -                           ⁢       {         oFsum   left     ⁡     [     R   ,   d     ]       +       oFsum   right     ⁡     [     R   ,   d     ]         }     2     ]               and   ,   where               D   =         (     M   -     2   ⁢   d       )     ⁢     {         ∑     m   =     d   +   1         M   /   2       ⁢       {     cF   ⁡     [     S   ,     m   -   d       ]       }     2       +       ∑     m   =       M   /   2     +   1         M   -   d       ⁢       {     cF   ⁡     [     S   ,     m   -   d       ]       }     2         }       -                         ⁢       {         cFsum   left     ⁡     [     S   ,   d     ]       +       cFsum   right     ⁡     [     S   ,   d     ]         }     2                 where   ⁢     :                   oFsum   right     =       ∑     m   =       M   /   2     +   1         M   -   d       ⁢     {     oF   ⁡     [     R   ,   m     ]       }                 
 
 is the sum along row R from column M/2+1 through column M−d,  
         oFsum   left     =       ∑     m   =     d   +   1         M   /   2       ⁢     {     oF   ⁡     [     R   ,   m     ]       }           
 
 is the sum along row R from column d+1 through column M/2,  
         cFsum   right     =       ∑     m   =       M   /   2     -   d   +   1         M   -     2   ⁢   d         ⁢     {     cF   ⁡     [     S   ,   m     ]       }           
 
 is the sum along row S from column M/2−d+1 through column M−2d, and  
         cFsum   left     =       ∑     m   =   1         M   /   2     -   d       ⁢     {     cF   ⁡     [     S   ,   m     ]       }           
 
 is the sum along row S from column 1 through column M/2−d. 
 
         [0095]     Furthermore, the NCC for the left and right halves of each row can be determined using:  
               NCC_left   ⁢     (     R   ,   S   ,   d     )       =               [       (     M   -     2   ⁢   d       )     ⁢     {       ∑     m   =     d   +   1         M   /   2       ⁢     [     {       oF   ⁡     [     R   ,   m     ]       ×     cF   ⁡     [     S   ,     m   -   d       ]         }     ]       }       ]     -                 [     oF   ⁢           ⁢       sum   left     ⁡     [     R   ,   d     ]         ]     ×     [     cF   ⁢           ⁢       sum   left     ⁡     [     S   ,   d     ]         ]                         [         (     M   -     2   ⁢   d       )     ⁢     {       ∑     m   =     d   +   1         M   /   2       ⁢       {     oF   ⁡     [     R   ,   m     ]       }     2       }       -       {     oF   ⁢           ⁢       sum   left     ⁡     [     R   ,   d     ]         }     2       ]     ×                     [         (     M   -     2   ⁢   d       )     ⁢     {       ∑     m   =     d   +   1         M   /   2       ⁢       {     cF   ⁡     [     S   ,     m   -   d       ]       }     2       }       -       {     cF   ⁢           ⁢       sum     left   ,       ⁡     [     S   ,   d     ]         }     2       ]                     [     Equation   ⁢           ⁢   5   ⁢   a     ]                 NCC_right   ⁢     (     R   ,   S   ,   d     )       =               [       (     M   -     2   ⁢   d       )     ⁢     {       ∑     m   =       M   /   2     +   1         M   -   d       ⁢     [     {       oF   ⁡     [     R   ,   m     ]       ×     cF   ⁡     [     S   ,     m   -   d       ]         }     ]       }       ]     -                 [     oF   ⁢           ⁢       sum   right     ⁡     [     R   ,   d     ]         ]     ×     [     cF   ⁢           ⁢       sum   right     ⁡     [     S   ,   d     ]         ]                         [         (     M   -     2   ⁢   d       )     ⁢     {       ∑     m   =       M   /   2     +   1         M   -   d       ⁢       {     oF   ⁡     [     R   ,   m     ]       }     2       }       -       {     oF   ⁢           ⁢       sum   right     ⁡     [     R   ,   d     ]         }     2       ]     ×                     [         (     M   -     2   ⁢   d       )     ⁢     {       ∑     m   =       M   /   2     +   1         M   -   d       ⁢       {     cF   ⁡     [     S   ,     m   -   d       ]       }     2       }       -       {     cF   ⁢           ⁢       sum   right     ⁡     [     S   ,   d     ]         }     2       ]                     [     Equation   ⁢           ⁢   5   ⁢   b     ]             
 
 In addition, the PeakNCC for the left and right sides is given by: 
 
 PeakNCC   left ( R,S,L )=MAX{ NCC   —   left ( R,S,d )}for  d=−L  to  d=L.   [Equation 6a]
        d peakleft (R,S,L)=the value of d at which the above equation is satisfied. 
 
 PeakNCC   right ( R,S,L )=MAX{ NCC   —   right ( R,S,d )}for  d=−L  to  d=L.   [Equation 6b]
    d peakright (R,S,L)=the value of d at which the above equation is satisfied. 
 
 These equations allow the left and right sides of the sensor array to be treated separately, and efficiently determine the rotational movement as described below. 
       
 
         [0100]     Once all the NCC terms for left and right sides are calculated for the left and right sides in Equations 5a and 5b, only a few addition and division operations are required to calculate NCC_whole for the entire sensing array using Equation 4. Then, overall linear motion can be calculated using Eq. 3 as before, while rotational movement is calculated using the linear motion for the left and right sides of the sensing array.  
         [0101]     Using PeakNCC(R,S,L) defined above in Equation 3 or Equations 6a and 6b, the calculation of exact x and y motion is straightforward. The last useful frame at iteration i has rows numbered 1 through N, as shown in  FIG. 4 , where N is the number of rows supplied by the sensor. Similarly, the current frame to be processed has rows 1 through N.  
         [0102]     For a given row R in the last frame, PeakNCC and d peak  are calculated as in Equations 3, 6a and 6b with respect to rows 1 through N of the current frame, and take the d peak  that corresponds to the maximum PeakNCC. Preferably, this is done for two values of R: R=1 and R=N. In this way, both upward and downward motion in the y direction can be determined while maximizing the speed at which a user can move his finger. It is also possible to choose only one R, at R=N/2 (or very near the middle row). However that is sub-optimal. It is also possible to choose values other than 1 or N, such as R=2 and R=N−1, which may be advantageous for accuracy reasons since they are not on the edge of the sensor array.  
         [0103]     Table 1 shows the pseudo-code for performing a single frame iteration for a given value of R. Although the calculations are carried out separately for the left side, right side, and whole row, only the generic case is described by the pseudo-code in Table 1.  
                                                                             TABLE 1                           Step 0: START       Step 1: Set R=1 ///// start with R=1 and then do R=N       Step 2: Set L=8 ///// lag value fixed at 8 columns       Step 3: Set bestS = 0 ///// initialize       Step 4: set MaxPeakNCC = 0 ///// initialize       Step 5: set d peak Max = 0 /////initialize       Step 6: Loop from currentRow = 1 through N //loop over N rows       of current frame       {                Step 6.1: set tmp = PeakNCC(R,currentRow,L)           Step 6.2: if tmp greater than MaxPeakNCC then                {           Step 6.3: set MaxPeakNCC = tmp //keep largest           Step 6.4: set d peak Max = d peak (R,currentRow,L)           Step 6.5: set bestS = currentRow           Step 6.6: set bestR = R           }            }       Step 7: if R equals 1 then                {                Step 7.1: set R = N           Step 7.2: Go to Step 2                }            Step 8: STOP                  
 
         [0104]     The pseudo-code in Table 1 can be summarized as: 
 
 MaxPeakNCC=NCC   —   whole ( bestR, bestS, d   peak ( bestR,bestS,L ))  [Equation 6c]
 
 d   peak   Max=dpeak ( bestR,bests,L )  [Equation 6d]
 
 Thus, after the above calculations, the following information is obtained: 
        1. MaxPeakNCC, the value of the correlation of the best pair of matching rows in the current frame and the last frame     2. bestR, the row of the last frame that results in MaxPeakNCC     3. bestS, the row of the current frame that results in MaxPeakNCC     4. d peak Max, the correlation lag where MaxPeakNCC is reached 
 
 bestR and bestS are the pair of rows that yield the highest correlation value (MaxPeakNCC). 
       
 
         [0111]     Typically, MaxPeakNCC will be close to 1.0 (the closer to 1.0, the stronger the correlation), but if the finger being analyzed is moved too quickly, it is possible that the current frame does not have any rows in common with the last frame (i.e. a non-overlapping case). Therefore, MaxPeakNCC must be checked to ensure that it is large enough.  
         [0112]     Using the above information, the following calculations are performed: 
        if MaxPeakNCC&gt;corr_threshold: 
            1. Δx(i)=d peak Max, which is the x-velocity at iteration i     2. Δy(i)=bestS−bestR, which is the y-velocity at iteration i    
            otherwise 
            3. Δx(i)=0     4. Δy(i)=0 
 
 where corr_threshold is used to make sure the correlation is high enough to indicate an overlap at all. Preferably, corr_threshold=0.75, but other values can be used to tune the performance of the algorithm. If the correlation is below a threshold, it is impossible to determine actual values for the x- and y-velocities, so the algorithm simply outputs no motion vector. However, in accordance with alternative embodiments other values can be output as the default, such as maximum movements of N rows and M columns, or combinations thereof. 
   
               
 
         [0120]     In any case, after x and y motion have been calculated for the left side, right side, and whole rows for the current iteration i—denoted by Δx left (i) and Δy left (i); Δx right (i) and Δy right (i); Δx whole (i) and Δy whole (i), respectively-are calculated, the rotational movement Δtheta(i) can now be determined. The Δx whole (i) and Δy whole (i) are made available to the host requiring the rotational information, and represent the overall linear x- and y-motion.  
         [0121]     Table 2 shows the pseudo code for determining rotational movement. The pseudo code continues iterating until told to stop by the application program or operating system using the rotational data.  
                                                                                 TABLE 2                           Step 0: START       Step 1: set cumulativeDelY left  (0) = 0       Step 2: set cumulativeDelY right  (0) = 0       Step 3: Loop from iteration i = 1 through infinity                {           Step 3.1: Acquire a frame and calculate Δy left  (i) and Δy right  (i)           Step 3.2: Set cumulativeDelY left  (i)=cumlativeDelY left  (i−1)+Δy left  (i)           Step 3.3: Set cumulativeDelY right  (i)=cumlativeDelY right             (i−1)+Δy right  (i)           Step 3.4: If absolute value (cumulativeDelY left  (i) −                cumulativeDelY right  (i)) &gt;= THRESH,           then           {                Step 3.5: Set Δtheta (i) = [cumulativeDelY left  (i) −           cumulativeDelY right  (i)]           Step 3.6: Set cumulativeDelY left  (i) = 0           Step 3.7: Set cumulativeDelY right  (i) = 0                }           Else:                Step 3.8: Set Δtheta (i) = 0                }            where THRESH can be any value &gt;= 1. Preferably, THRESH=1.                  
 
         [0122]     It will be appreciated that there are alternative ways to compute the rotational delta, including arbitrary functions of the Δy left (i) and Δy right (i). For alternative mountings of the sensor, where the x and y directions are transposed, Δx left (i) and Δx right (i) are used in the pseudo code in Table 2. On full size placement sensors, more accuracy can be achieved using both Δx left (i), Δx right (i) and Δy left (i), Δy right (i). This is achieved in one embodiment by calculating a Δtheta(i) using the pseudo code in Table 2 using Δx values and again using Δy values. The resulting two estimated values can be averaged together or otherwise combined to form the final Δtheta(i). The Δtheta(i) are made available to the host application and/or operating system.  
         [0123]     In other embodiments a standard correlation is used instead of normalized cross correlation. Standard cross correlation given in Equation 1 could be used instead of Normalized Cross Correlation. It is straightforward to split Equation 1 into terms from the left and right sides of each row.  
               SCC_whole   ⁢     (     R   ,   S   ,   d     )       =         ∑     m   =     d   +   1         M   /   2       ⁢     (       oF   ⁡     [     R   ,   m     ]       ×     cF   ⁡     [     S   ,     m   -   d       ]         )       +       ∑     m   =       M   /   2     +   1         M   -   d       ⁢     (       oF   ⁡     [     R   ,   m     ]       ×     cF   ⁡     [     S   ,     m   -   d       ]         )                 [     Equation   ⁢           ⁢   7     ]             
 
 In this case, which is much simpler than the NCC case in the preferred embodiment, the SCC value for the entire row is simply the sum of the correlation values of each half. 
 
         [0125]     It will also be appreciated that the maximum standard cross-correlation between a row S of a frame and a row R of the last useful frame can be given by other expressions. For example, weighted or voting schemes can be used. In one embodiment, 
 
 PeakSCC   whole ( R,S,L )= Weighted   —   MAX{SCC   —   Whole ( R,S,d )} for  d=−L  to d=L  [Equation 8]
 
 where Weighted_MAX is a function that assigns a plurality of predetermined weights to its elements before generating a value, d peakwhole (R,S,L) is the value of d at which Equation 8 is satisfied, and L is approximately equal to the maximum horizontal speed from the last useful frame to the current frame. 
 
         [0127]     While the preferred embodiment splits each row into a left and right side of equal length, alternative embodiments use any arbitrary division of each row, including more than 2 equal parts instead of 2, and also using divisions that are of differing length. It is also not necessary to have each division touch the next.  FIGS. 8-12  show some of the possibilities, each with advantages over the other.  
         [0128]     For example,  FIG. 8  shows a fingerprint sensor having a left half (sub-frame)  605  contiguous with a right half  610 .  FIG. 9  shows a fingerprint sensor having a first section (sub-frame)  615 , a second section  620 , a third section  625 , and a fourth section  630 . Section  615  is contiguous with section  620 , section  620  is contiguous with  625 , and section  625  is contiguous with section  630 .  FIG. 10  shows a finger image sensor having two sections  631  and  632  that are not contiguous.  FIG. 11  shows a finger image sensor having four sections  635 ,  640 ,  645 , and  650 , none of which are contiguous. And  FIG. 12  shows a finger image sensor having a section  655  contiguous with a section  660 , and a section  665  contiguous with a section  670 . It will be appreciated that other configurations are also possible, each preferably having more than one single division and using linear correlation to determine rotational movement. The number and configurations of the sections can be chosen based on production cost, surface area of the finger image sensor, computational algorithms, processor configuration, speed required, and other criteria.  
         [0129]     In other embodiments, it is desirable to modify the raw values Δx whole (i), Δy whole (i), and Δtheta(i) before sending it to the host. These types of modifications involve three different mathematical transformations, generically called filtering, where the transformed output is noted by the notation: 
        1. Scaling: applying a linear or non-linear scaling factor to multiply the original movement values to obtain scaled versions more appropriate to the displayed coordinate system of the host. An example is to multiply all values by a factor of 2. Another example is to multiply x movement by a factor of 2 and y movement by a 0.5.     2. Smoothing: applying a smoothing (low-pass) filter to successive movement values in order to make the values less jagged over time. Examples are: 
 
Linear Average=Δx′ whole ( i )=[Δx whole ( i )+Δx whole ( i− 1)+Δx whole ( i− 2)]/3 
 
Exponential average=Δtheta′( i )=[Δtheta′( i− 1)+Δtheta( i )]/2 
    3. Clipping: limiting values of the movement to arbitrary values. An example is: 
 
If Δ y ( i )&gt; T , then Δ y′ ( i )= T . Otherwise Δ y ′( i )=Δ y ( i ). 
 
 These operations can be combined in many ways in accordance with the present invention. Here, “filtering” is used to describe the function of processing an input in a well-defined way to produce an output. 
       
 
         [0134]     Those skilled in the art will recognize that correlation is computationally intensive. Accordingly, in one embodiment, the calculation of Δtheta(i) and/or the Δx(i), Δy(i) for the left, right, and whole array are performed on a separate processor or dedicated hardware. In this embodiment, the hardware can be integrated into the silicon fingerprint sensor itself. The hardware performing the correlation must have access to the current frame and the last useful frame, both of which can be stored in memory on the device. If, for example, this is integrated into the finger image sensor, such a device would obviously have access to the current frame (since the device itself created it), and it could save the last useful frame in volatile memory registers. In such a case the device would also need to determine whether a frame is useful or not, using the method described here in the preferred embodiment. In such an embodiment the host computing device is not necessary. Obviously, such a hardware implementation could also be used to reconstruct fingerprint images since doing so only requires the Δx(i) and Δy(i) for the whole array.  
         [0135]     It will be readily apparent to one skilled in the art that various modifications may be made to the embodiments without departing from the spirit and scope of the invention as defined by the appended claims.