Abstract:
The present invention relates to a jotting implement that infers hand-jotted information from a jotting surface. The hand-jotted information is any information marked on the jotting surface as a result of writing, jotting, drawing, sketching or in any other manner of marking or depositing marks on the jotting surface. Hand-jotted information is also information traced on the jotting surface without leaving any markings thereon or otherwise produced by the motions executed by the jotting implement with respect to the jotting surface while in contact with the jotting surface. The jotting implement has a nib for jotting and an arrangement for determining when the nib is jotting on the jotting surface. Further, the implement has an optical unit for viewing the jotting surface. The implement also has a processing unit for receiving optical data of said jotting surface from the optical unit and determining from it the physical coordinates of the nib with respect to at least one corner of the jotting surface and at least one edge of the jotting surface and/or other landmarks or optically recognizable features on the jotting surface.

Description:
RELATED APPLICATIONS  
       [0001]    This application claims priority from U.S.  
         [0002]    Provisional Patent Application No. 60/450,244 filed on Feb. 24 th , 2003. 
     
    
     
       FIELD OF THE INVENTION  
         [0003]    The present invention relates generally to acquisition of information written, drawn, sketched or otherwise marked on a jotting or writing surface by a user with the aid of a hand-held implement, such as a writing implement.  
         BACKGROUND OF THE INVENTION  
         [0004]    The art of writing and drawing is ancient and rich in traditions. Over the ages various types of implements have been used for writing down words as well as drawing, sketching, marking and painting. Most of these implements have a generally elongate shape, an essentially round cross-section and they are terminated at one end by a writing nib or tip. They are typically designed to be hand-held and operated by the user&#39;s preferred hand (e.g., by the right hand for right-handed persons). More specifically, the user moves the implement across a writing or jotting surface such that the writing nib leaves a visible trace marking its motion on the surface. The marking can be produced by a material deposited from the nib, e.g., through abrasion of the marking material (such as charcoal in the case of a pencil) or by direct wetting of the surface by an ink (as in the case of the pen). The marking can also include any other physical trace left on the surface.  
           [0005]    The most widely used writing and drawing implements include pens and pencils while the most convenient jotting surfaces include sheets of paper of various sizes and other generally planar objects capable of being marked. In fact, despite the tremendous advances in sciences and engineering, pen and paper remain among the simplest and most intuitive devices for writing, drawing, marking and sketching even in the electronic age.  
           [0006]    The challenge of communicating with electronic devices is in the very input interface to the electronic device. For example, computers take advantage of input devices such as keyboards, buttons, pointer devices, mice and various other types of apparatus that encode motion and convert it to data that the computer can process. Unfortunately, none of these devices are as user-friendly and accepted as pen and paper.  
           [0007]    This input interface problem has been recognized in the prior art and a variety of solutions have been proposed. Most of these solutions attempt to derive electronic, i.e., digital data from the motions of a pen on paper or some other writing surface, e.g., a writing tablet. Of these prior art teachings the following references are of note:  
                                                     U.S. Pat. Nos.                                4,471,162   4,896,543   5,103,486   5,215,397   5,226,091       5,294,792   5,333,209   5,434,371   5,484,966   5,517,579       5,548,092   5,661,506   5,577,135   5,581,276   5,587,558       5,587,560   5,652,412   5,661,506   5,717,168   5,737,740       5,750,939   5,774,602   5,781,661   5,902,968   5,939,702       5,959,617   5,960,124   5,977,958   6,031,936   6,044,165       6,050,490   6,081,261   6,100,877   6,104,387   6,104,388       6,108,444   6,111,565   6,124,847   6,130,666   6,147,681       6,153,836   6,177,927   6,181,329   6,184,873   6,188,392       6,213,398   6,243,503   6,262,719   6,292,177   6,330,359       6,334,003   6,335,723   6,335,724   6,335,727   6,348,914       6,396,481   6,414,673   6,421,042   6,422,775   6,424,340       6,429,856   6,437,314   6,456,749   6,492,981   6,498,604                  
 
           [0008]    [0008]                                                     U.S. Published applications:                                2002-0001029   2002-0028017   2002-0118181   2002-   2002-       2002-0163511           0148655   0158848                    
           [0009]    European Patent Specifications:  
           [0010]    0,649,549 
                                                 International Patent applications:                                WO 02/017222 A2   WO 02/058029 A2   WO 02/   WO 02/       WO 02/084634 A1       064380 A1   069247 A1                  
 
           [0011]    Although the above-referenced teachings provide a number of approaches they are cumbersome to the user. Many of these approaches provide the user with pens that are difficult to handle, impose special writing and/or monitoring conditions and/or they require cumbersome auxiliary systems and devices to track and digitize the information written on the writing surface. Thus, the problem of a user-friendly input interface based on a writing implement has not been solved.  
         SUMMARY OF THE INVENTION  
         [0012]    The present invention provides a jotting implement that infers hand-jotted information from a jotting surface. For the purposes of this invention, hand-jotted information comprises any information marked on the jotting surface as a result of any of the following actions: writing, jotting, drawing, sketching or in any other manner marking or depositing marks on the jotting surface. Additionally, hand-jotted information for the purposes of this application also means information traced on the jotting surface without leaving any markings on the jotting surface. The jotting implement has a nib for jotting and an arrangement for determining when the nib is jotting on the jotting surface. Further, the implement has an optical unit for viewing the jotting surface. The optical unit is preferably mounted at a distal end of the implement with respect to the nib and indexed to it. For the purposes of this invention indexed to the nib means that the optical axis of the optical unit is referenced to the nib, e.g., the optical axis of the optical unit passes through the nib. The implement also has a processing unit for receiving optical data of said jotting surface from said optical unit and for determining from said optical data the physical coordinates of the nib with respect to at least one corner of the jotting surface and at least one edge of the jotting surface.  
           [0013]    It should be noted that in contrast to the prior art the implement of the invention infers the physical coordinates of the nib indirectly, i.e., from the optical data of the jotting surface obtained from the optical unit. Therefore, any optical data about the jotting surface sufficient to make the determination of the physical coordinates of the nib can be used. For example, optical data of all corners or a number of corners, edges or portions thereof can be used. Alternatively, landmarks or any optically recognizable features on the jotting surface can be used as well.  
           [0014]    The arrangement for determining when the nib is jotting on the jotting surface preferably comprises a pressure sensitive unit mounted in the jotting implement. Strain gauges, mechanical pressure sensors, piezoelectric elements and other types of arrangements recognizing contact between the nib and the jotting surface can be used for this purpose.  
           [0015]    In the preferred embodiment the optical unit is an imaging unit for imaging the jotting surface or a portion thereof. It is further preferred that the imaging unit be equipped with a photodetector array for projecting an image of the jotting surface thereon. The processing unit has an edge detection unit or circuit (e.g., firmware in a microprocessor of the processing unit) for detecting edges and corners of the jotting surface in the image.  
           [0016]    The jotting implement is further equipped with an image transformation unit for applying one or more transformations to the image. Specifically, the image transformation unit can include appropriate physical optics (e.g., lenses) for correcting the image as well as software routines for correcting the image and performing various operations on the image. For example, the image transformation unit has an image deformation transformer that corrects the image for a plane projection. Alternatively, the image transformation unit has an image deformation transformer that corrects the image for a spherical projection. In the same or a different embodiment, the image transformation unit has an image transformer for determining Euler angles of the jotting implement with respect to the jotting surface.  
           [0017]    In the preferred embodiment the corrections and transformations are applied only to the edges and/or corners of the image that are identified by the edge detection unit. In other words, only a part of the image corresponding to the jotting surface and in particular its edges, corners, landmarks or other optically recognizable features and/or their portions are corrected and transformed.  
           [0018]    A ratio computation module belonging to the processing unit determines the physical coordinates of the nib from the image. Again, in the preferred embodiment this determination is made from the relevant part of the image corresponding to the jotting surface and in particular its edges, corners, landmarks or other optically recognizable features and/or their portions.  
           [0019]    The photodetector array can be any suitable array of photodetectors, including a photodiode or phototransistor array and preferably a CMOS photodetector array. The optics used by the imaging unit can include refractive and/or reflective optics and preferably include a catadioptric system. In any event, the field of view of the optics should be substantially larger than the area of the jotting surface such that the imaging unit can always detect at least one edge and one corner of the jotting surface for any possible position of the jotting implement when the nib is in contact with the jotting surface.  
           [0020]    In order to determine the physical coordinates of the nib at a sufficient rate to determine what the user has written, sketched or drawn the implement has a frame control unit.  
           [0021]    The frame control unit sets a certain frame rate at which the jotting surface is imaged. Preferably, this frame rate is at least 15 Hz, and more preferably it is in excess of 30 Hz.  
           [0022]    Finally, the jotting implement is provided with a device for communicating the physical coordinates of the nib with an external unit. The device for communicating these coordinates can include any type of data transmission port including but not limited to infra-red (IR) ports, ultrasound ports, optical ports and the like. The external unit can be a computer, a hand-held device, a network terminal, a downloading unit, an electronic gateway into a wide area network (WAN) (e.g., the internet) or a local area network (LAN), a storage device, a printer or any other external unit which can store, print, relay and/or further process the physical coordinates of the nib. It should be noted that, depending on the application and requirements, the physical coordinates of the nib can be processed in real time or not.  
           [0023]    In the preferred embodiment the implement is further equipped with an arrangement for initializing and recognizing the jotting surface. Of course, the sizes and types jotting surfaces can also be selected or input by the user. The arrangement for initializing and recognizing can include the optical unit and processing unit described above and a memory with standard sizes of likely jotting surfaces. For example, when the jotting surfaces are expected to be sheets of paper of standard sizes, the images of such sheets can be stored in the memory. Preferably, these stored images are taken at well-known positions and orientations of the jotting implement with respect to the jotting surface. In other words, they are taken at known physical coordinates of the nib on the jotting surface and known spatial orientation of the jotting implement (e.g., at known Euler angles).  
           [0024]    The details of the invention will now be explained in the attached detailed description with reference to the attached drawing figures. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0025]    [0025]FIG. 1 is a side view of a jotting implement in accordance with the invention where the jotting implement is shown in the plane of an inclination angle θ (Euler angle θ).  
         [0026]    [0026]FIG. 2 is a three-dimensional diagram illustrating the physical parameters of the jotting implement of FIG. 1 when in use.  
         [0027]    [0027]FIG. 3 is a plan side view of the jotting implement of FIG. 1 illustrating the principle of imaging.  
         [0028]    [0028]FIG. 4 is a block diagram of the processing unit of the jotting implement of FIG. 1.  
         [0029]    [0029]FIG. 5 is a diagram illustrating the image of the jotting surface projected onto a photodetector array belonging to the imaging unit.  
         [0030]    [0030]FIG. 6 is a diagram illustrating the process of edge and/or corner detection applied to the image of the jotting surface.  
         [0031]    FIGS.  7 A-D are diagrams illustrating the functions performed by the processing unit on the image to determine the orientation of the jotting implement with respect to the jotting surface in terms of Euler angles.  
         [0032]    [0032]FIG. 8 is a side view illustrating an alternative embodiment of a jotting implement having an orienting grip.  
         [0033]    [0033]FIG. 9 is a diagram illustrating the process of image correction and parametrization.  
         [0034]    [0034]FIG. 10 is a diagram illustrating the parameterized corrected image.  
         [0035]    [0035]FIG. 11 is a diagram illustrating the parametrized, corrected and transformed image from which the physical coordinates of the nib are determined.  
         [0036]    [0036]FIG. 12 is a diagram illustrating a correspondence between the image of the jotting surface and the physical jotting surface as can be used for initialization and cross-check purposes.  
         [0037]    [0037]FIG. 13 illustrates another embodiment of an optical unit using a catadioptric system.  
         [0038]    [0038]FIG. 14 illustrates the top portion of a writing implement employing the catadioptric system of FIG. 13.  
         [0039]    [0039]FIG. 15 is a three-dimensional diagram illustrating the use of alternative landmarks and features to determine the physical coordinates of the nib. 
     
    
     DETAILED DESCRIPTION  
       [0040]    The present invention will be best understood by initially referring to the side view of FIG. 1 illustrating a jotting implement  10  in accordance with the invention and the diagrams of FIGS. 2 through 4. Jotting implement  10  shown in FIG. 1 is a pen, more specifically an ink pen, and still more precisely a ball-point pen. However, it will be appreciated that jotting implement  10  can be a marker, a pencil a brush or indeed any other writing, sketching, drawing or painting implement that can jot information on a jotting surface  12 . Alternatively, jotting implement  10  can also be stylus or any device that jots information on jotting surface  12  by tracing that information without leaving any permanent markings or deformations on the jotting surface. Such jotting surface can include a pressure-sensitive digitizing tablet or any other surface provided specifically for input into an electronic data processing device. In the present embodiment jotting implement has a shape generally resembling known writing, sketching, drawing or painting devices. Specifically, jotting implement  10  has an elongate body  14  of generally round cross-section designed to be held in a user&#39;s hand  16 .  
         [0041]    In general, jotting surface  12  is a sheet of planar material on which implement  10  can perform a jotting function as defined above. For geometrical reasons, it is preferable that jotting surface  12  be rectangular. In the present embodiment jotting surface  12  is a sheet of paper of any standard or non-standard dimensions laying flat on a support surface  18 . In cases where jotting surface  12  is a digitizing tablet such as a tablet of a PDA device, a computer screen or any other sturdy surface then support surface  18  may not be required. It is important, however, that jotting surface  12  have optically recognizable features such as corners, edges, landmarks or the like. It is also important that these features not change their position with respect to the remainder of jotting surface  12  during the jotting operation.  
         [0042]    Implement  10  has a nib  20  terminating in a ball-point  22 . A pressure sensor  24  is mounted proximate nib  20  for determining when nib  20  is jotting. Jotting occurs when ball-point  22  is in contact with jotting surface  12 . Conveniently, pressure sensor  24  is a strain gauge. Alternatively, pressure sensor  24  is a mechanical pressure sensor or a piezoelectric element. A person skilled in the art will recognize that other pressure sensors can also be used. Implement  10  also has an initialization switch  26 . Switch  26  is provided for the user to communicating whether jotting is occurring on the same jotting surface  12  or on a new jotting surface (not shown).  
         [0043]    An optical unit  30  is mounted at a distal end  32  of implement  10 . Optical unit  30  is designed for viewing jotting surface  12  and it has a field of view  34  demarked by a delimiting line that extends beyond jotting surface, as described in more detail below. In the present embodiment optical unit  30  is mounted on three support members  36 . Members  36  can have any construction that ensures mechanical stability and obstructs a negligible portion of field of view  34 . Optical unit  30  has an optical axis  39  that is indexed to nib  20 . More specifically, optical axis  39  passes through nib  20 . Thus, field of view  34  of optical unit  30  is centered on nib  20 . Alternatively, optical axis  39  can be indexed to nib  20  at some predetermined offset. For reasons of symmetry of field of view  34 , however, it is preferred that optical unit  30  be indexed to nib  20  by passing optical axis  39  through nib  20  and through the center of ball-point  22 .  
         [0044]    Implement  10  has a device  38  for communicating with an external unit  40  (see FIG. 2). In the present embodiment device  38  is an infra-red (IR) port for transmitting and receiving data encoded in IR radiation  42 . Of course, any type of data transmission port including but not limited to ultrasound ports or optical ports can be used as device  38 . Meanwhile, external unit  40  can be a computer, a hand-held device, a network terminal, a downloading unit, an electronic gateway into a wide area network (WAN) (e.g., the internet) or a local area network (LAN), a storage device, a printer or any other external unit which can store, print, relay and/or further process the physical coordinates of nib  20 .  
         [0045]    Referring now to FIG. 2, the physical parameters of implement  10  are conveniently described in terms of a Cartesian coordinate system and a polar coordinate system. The origins of these coordinate systems coincide at the position of nib  20  and more specifically at the position where ball-point  22  contacts jotting surface  12 . The Cartesian system has its X- and Y-axes in the plane of jotting surface  12  and aligned with the width and length of jotting surface  12 . The Z-axis of the Cartesian system is perpendicular or normal to the plane of jotting surface  12 .  
         [0046]    A number of features  44 A,  44 B,  44 C are defined by corresponding vectors v 1 , V 2 , V 3  drawn from the origin of the Cartesian system. In the present case features  44 A,  44 B,  44 C are three corners of jotting surface  12 . Alternatively, features  44  can include any edge  43  of jotting surface  12  or any other optically recognizable landmark or feature of jotting surface  12 . It should be noted that features produced on jotting surface  12  by the user, including any marks jotted by implement  10 , are legitimate features for this purpose.  
         [0047]    The polar coordinate system is used to define the orientation of implement  10  with respect to jotting surface  12 . The Z-axis of the polar system is coincident with the Z-axis of the Cartesian system. Since optical axis  39  is indexed to nib  20  it passes through the origins of the two coordinate systems.  
         [0048]    Thus, in the polar system optical axis  39  defines the polar coordinate r and the length of r, i.e., |r| is the length of implement  10 . The inclination of implement  10  with respect to the Z-axis is expressed by polar angle θ, hereafter referred to as inclination angle θ. The angle of rotation of implement  10  about the Z-axis is expressed by polar angle φ.  
         [0049]    It is preferred that optical unit  30  be an imaging unit, as shown in the plan view of FIG. 3. Specifically, optical unit  30  is preferably an imaging unit capable of imaging objects present in its field of view  34  and in particular imaging jotting surface  12  with relatively low distortion. In the present embodiment imaging unit  30  has a refractive imaging optics  46  indicated by lenses  48 A,  48 B. It will be appreciated by a person skilled in the art that suitable refractive imaging optics  46  include lenses which afford a wide field of view with good off-axis optical performance, such as fish-eye lenses or wide-field-of-view lenses. For more specifics on such types of lenses the reader is referred to U.S. Pat. Nos. 4,203,653; 4,235,520; 4,257,678 as well as the article by James “Jay” Kumler et al., “Fisheye lens designs and their relative performance”, SPIE, all of which are herein incorporated by reference.  
         [0050]    Imaging optics  46  define an image plane  50  as indicated by the dashed line. Imaging unit  30  is further equipped with a photodetector array  52  positioned in image plane  50 . An image  12 ′ of jotting surface  12  is projected onto array  52  by imaging optics  46 . Preferably, array  52  is a CMOS photodetector array. Of course, other types of photodetector arrays including arrays employing photodiodes or phototransitors of various types can be used as photodetector array  52 . A CMOS photodetector array, however, tends to be more efficient, responsive and it tends to consume less power. In addition CMOS arrays have a small pitch thus enabling high resolution.  
         [0051]    Field of view  34  afforded by optics  46  is substantially larger than the area of jotting surface  12 . In fact, field of view  34  is large enough such that image  12 ′ of entire jotting surface  12  is always projected onto array  52 . This condition holds for any jotting position that may be assumed by jotting implement  10  during a jotting operation performed by the user, such as writing near an edge or corner of jotting surface  12  at a maximum possible inclination angle θ (e.g., θ≈40°). Thus, forward and backward portions y 1 , y 2  of jotting surface  12  are always imaged on array  52  as portions y′ 1 , y′ 2  as long as not obstructed by user&#39;s hand  16  or by other obstacles.  
         [0052]    It is noted that for purposes of clarity primed reference numbers are used herein to denote parts in image space corresponding to parts bearing the same but unprimed reference numbers in physical space. As additional transformations and operations are applied to parts in the image space, more primes are added to the reference numbers.  
         [0053]    Jotting implement  10  has a processing unit  54 , which is illustrated in more detail in FIG. 4. Processing unit  54  is designed for receiving optical data of jotting surface  12 . In this embodiment the optical data is represented by image  12 ′ of jotting surface  12 . From this optical data processing unit  54  determines the physical coordinates of nib  20  with respect to at least one corner and at least one edge of jotting surface  12 . In the present embodiment processing unit  54  is designed to determine vectors v 1 , V 2 , V 3  in the Cartesian coordinate system defined in FIG. 2.  
         [0054]    To achieve its function processing unit  54  is equipped with an image processor  56 , a frame control  58 , a memory  60  as well as an uplink port  62  and a downlink port  64 . Ports  62 ,  64  belong to communication device  38 . Image processor  56  preferably includes an edge detection unit  66 , an origin localization unit  68 , an image transformation unit  70  and a ratio computation unit  72 , as better shown in FIG. 5. In addition to these elements, image processor  56  has a demultiplexer  74  for receiving and demultiplexing raw image data  76  containing image  12 ′. Data  76  is delivered from the row  78 A and column  78 B multiplexing blocks of array  52 .  
         [0055]    During operation, the user moves implement  10 . Once nib  20  of implement  10  is brought in contact with jotting surface  12  pressure sensor  24  activates the acquisition mode of optical unit  30 . In the acquisition mode processing unit  54  receives optical data i.e.image  12 ′ of jotting surface  12  as imaged on the pixels of array  52 .  
         [0056]    Now, image processor  56  captures raw image data  76  of image  12 ′ at a certain frame rate. The frame rate is controlled by frame control  58 . The frame rate is fast enough to accurately track the jotting activity of the user. To achieve this the frame rate is set by frame control  58  at 15 Hz or even at 30 Hz or higher.  
         [0057]    In contrast with the prior art, the information jotted by the user is not determined by inspecting or imaging the information itself. Rather, the jotted information is inferred by determining the physical coordinates of nib  20  or, more precisely of ball-point  22  with respect to optically recognizable features of jotting surface  12 . These recognizable features can include corners, edges or any other landmarks or features produced by the user on jotting surface  12 . To determine all information jotted by the user the physical coordinates of nib  20  with respect to the recognizable features are acquired at the set frame rate whenever the acquisition mode is activated by pressure sensor  24 .  
         [0058]    In the present embodiment, the physical coordinates of nib  20  are determined with respect to three corners  44 A,  44 B and  44 C of jotting surface  12  parametrized with the aid of vectors v 1 , v 2  and V 3  (see FIG. 2). To accomplish this goal, processing unit  54  recovers vectors v 1 , v 2 , and V 3  from imaged vectors v′ 1 , v′ 2  and v′ 3  of image  12 ′ (see FIG. 5). This process requires a number of steps.  
         [0059]    In a first step image processor  56  of processing unit  54  demultiplexes raw image data  76  from row and column blocks  78 A,  78 B of array  52  with the aid of demultiplexer  74 . Next, image processor  56  sends image data  76  to edge detection unit  66 . Edge detection unit  66  identifies the edges and corners of image  12 ′ of jotting surface  12 . This process is better illustrated in FIG. 6 where unobstructed portions  80 ′ of imaged edges  43 ′ are used for edge detection. For more information on edge detection in images and edge detection algorithms the reader is referred to U.S. Pat. Nos. 6,023,291 and 6,408,109 and to Simon Baker and Shree K. Nayar, “Global Measures of Coherence for Edge Detector Evaluation”, Conference on Computer Vision and Pattern Recognition, June 1999, Vol. 2, pp. 373-379 and J. Canny, “A Computational Approach to Edge Detection”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 8, No. 6, November 1986 for basic edge detection all of which are herein incorporated by reference.  
         [0060]    In practice, user&#39;s hand  16  is an obstruction that obscures a portion of jotting surface  12 . Hence, a corresponding shadow  16 ′ is present in image  12 ′. Another shadow  17 ′ (or a number of shadows) will frequently be produced by other objects covering jotting surface  12  or located between jotting surface  12  and optical unit  30 . Such objects typically include the user&#39;s other hand and/or body parts such as hair (not shown). For the purposes of the present invention it is only necessary that image  12 ′ have a few unobstructed portions  80 ′ of imaged edges  43 ′, preferably including two or more corners, e.g.,  44 A′,  44 B′ and  44 C′ to enable recovery of vectors v 1 , v 2  and V 3  and consequent determination of the physical coordinates of nib  20 .  
         [0061]    Thus, despite shadows  16 ′ and  17 ′ several unobstructed portions  80 ′ of imaged edges  43 ′ are available to edge detection unit  66 . A number of pixel groups  82  whose optical data  76  can be used by edge detection unit  66  for edge detection purposes are indicated. It should be noted that in some circumstances a pixel group  83  which is obscured by a shadow, e.g., by shadow  16 ′ may become visible and can then be used to detect corner  44 D′.  
         [0062]    Edge detection unit  66  recognizes edges  43 ′ and describes them in terms of their vector equations or other suitable mathematical expressions with reference to a center  84  of field of view  34 . In order to serve as reference, center  84  is set with the aid of origin localization unit  68 . This can be performed prior to operating jotting implement  10 , e.g., during first initialization and testing of jotting implement  10  and whenever re-calibration of origin location becomes necessary due to mechanical reasons. The initialization can be performed with the aid of any suitable algorithm for fixing the center of an imaging system. For further information the reader is referred to Carlo Tomasi and John Zhang, “How to Rotate a Camera”, Computer Science Department Publication, Stanford University and Berthold K. P. Horn, “Tsai&#39;s Camera Calibration Method Revisited”, which are herein incorporated by reference and attached as appendices hereto.  
         [0063]    In accordance with the invention center  84  coincides with optical axis because optical unit  30  is indexed to nib  20 . Hence, for any orientation of jotting implement  10  in physical space, i.e., for any value of inclination angle θ and polar angle φ, center  84  of field of view  34  is always coincident with the position of nib  20  and its image  20 ′. Systems having this property are commonly referred to as central systems in the art and they include various types of central panoramic systems and the like. It should be noted that image  20 ′ of nib  20  is not actually visible in field of view  34 , because body  14  of jotting implement  10  obscures center  84  at all times.  
         [0064]    Due to optical effects including aberration associated with imaging optics  46 , the detected portion of image  12 ′ will exhibit a certain amount of rounding of edges  43 ′, as indicated in dashed lines. This rounding can be compensated optically by lenses  48 A,  48 B and/or by any additional lenses (not shown) as well as electronically by processing unit  54 . Preferably, the rounding is accounted for by applying a transformation to detected portion of image  12 ′ by image transformation unit  70 . For example, image transformation unit  70  has an image deformation transformer based on a plane projection to produce a perspective view. Alternatively, image transformation unit  70  has an image deformation transformer based on a spherical projection to produce a spherical projection. Advantageously, such spherical projection can be transformed to a plane projection with the aid of well-known methods, e.g., as described by Christopher Geyer and Kostas Daniilidis, “A Unifying Theory for Central Panoramic Systems and Practical Implications”, www.cis.upenn.edu, Omid Shakernia, et al., “Infinitesimal Motion Estimation from Multiple Central Panoramic Views”, Department of EECS, University of California, Berkeley, and Adnan Ansar and Kostas Daniilidis, “Linear Pose Estimation from Points or Lines”, Jet Propulsion Laboratory, California Institute of Technology and GRASP Laboratory, University of Pennsylvania which are herein incorporated by reference and attached as appendices hereto.  
         [0065]    Now, once image  12 ′ is recognized and transformed the orientation of jotting implement  10  is determined. This can be done in a number of ways. For example, when working with the spherical projection, i.e., with the spherical projection of unobstructed portions image  12 ′, a direct three-dimensional rotation estimation can be applied to recover inclination angle θ and polar angle φ. For this purpose a normal view of jotting surface  12  is stored in memory  60 , such that it is available to transformation unit  70  for reference purposes. The transformation then yields the Euler angles of jotting implement  10  with respect to jotting surface  12  by applying the generalized shift theorem. This theorem is related to the Euler theorem stating that any motion in three-dimensional space with one point fixed (in this case the point where nib  20  is in contact with jotting surface  12  is considered fixed for the duration of each frame) can be described by a rotation about some axis. For more information about the shift theorem the reader is referred to Ameesh Makadia and Kostas Daniilidis, “Direct 3D-Rotation Estimation from Spherical Images via a Generalized Shift Theorem”, Department of Computer and Information Science, University of Pennsylvania, which is herein incorporated by reference.  
         [0066]    Alternatively, when working with a plane projection producing a perspective view of unobstructed portions of image  12 ′ one can use standard rules of geometry to determine inclination angle θ and polar angle φ. Several geometrical methods taking advantage of the rules of perspective views can be employed in this case.  
         [0067]    One geometrical method is shown in FIG. 7A, where entire image  12 ′ is shown for clarity (disregarding obstructed portions or filling them in with equations of edges  43 ′ derived in the above step), two edges  43 ′ are extended to vanishing point  86 . A connecting line ψ from center  84  to vanishing point  86  is constructed. A line Σ in the plane of inclination angle θ is also constructed. Now, the angle between lines ψ and Σ is equal to polar angle φ. Meanwhile, the length of line ψ from center  84  to vanishing point  86  is inversely proportional to inclination angle  0 . Preferably, a look-up table with values of ψ corresponding to values of inclination angle θ is stored in memory  60  to facilitate rapid identification of angle θ during each frame. It should be noted that in order to keep track of the plane of inclination angle θ rotation of jotting implement  10  around optical axis  39  has to be known. This rotation can be established by providing a key e.g., in the form of a grip  90  on jotting implement  10 , as shown in FIG. 8. Grip  90  forces hand  16  of the user to hold jotting implement without rotating it around axis  39 .  
         [0068]    Another geometrical method is shown in FIG. 7B, where entire image  12 ′ is once again shown for clarity. Here, again, two edges  43 ′ are extended to vanishing point  86 . A connecting line ψ from center  84  to vanishing point  86  is constructed. A line Γ in the plane perpendicular to the plane of inclination angle θ is also constructed. Now, a line π is constructed from vanishing point  86  and perpendicular to line Γ. The angle between lines π and ψ is equal to polar angle φ. Meanwhile, the length of line π from intercept with line Γ to vanishing point  86  is inversely proportional to inclination angle Γ. Preferably, a look-up table with values of π corresponding to values of inclination angle θ is stored in memory  60  to facilitate rapid identification of angle θ during each frame. In this embodiment a key-mark  92  on array  52  or on some other part of jotting implement  10  is used to keep track of the plane perpendicular to the plane of inclination angle θ and it is indexed to an appropriate grip on the pen, e.g., as the one shown in FIG. 8.  
         [0069]    Yet another geometrical method is shown in FIG. 7C based on entire image  12 ′. Here, connecting line ψ is constructed from center  84  to vanishing point  86  defined by two edges  43 ′. A second vanishing point  94  is located by extending the other two edges  43 ′. Second vanishing point  94  is then joined by line Ω with vanishing point  86 . Line Σ is now constructed from center  84  to line Ω such that it intersects line Ωat a right angle. The angle between lines ψ and Σ is equal to polar angle φ and either the length of line ψ or the length of line Σ (or even the length of line Ω) can be used to derive inclination angle θ. Once again, the use of corresponding look-up tables is recommended for rapid processing. It should be noted that this embodiment does not require the use of a key-mark or grip since rotation of jotting implement  10  around optical axis  39  (which is also the center axis of jotting implement  10 ) does not affect this geometrical construction.  
         [0070]    Still another geometrical method is shown in FIG. 7D. In this case corner angles α, β, γ and δ (when unobstructed) as well as the area integral of image  12 ′ are used to determine θ and φ. Specifically, the values of corner angles α, β, γ and δ uniquely define angle θ. Likewise, the values of the area integral uniquely define θ. Corresponding look-up tables stored in memory  60  can be used for rapid processing and determination of angles θ, φ in this embodiment.  
         [0071]    In the case where imaging optics  46  invert image  12 ′ with respect to the physical orientation of jotting surface  12  image  12 ′ needs to be inverted, as illustrated in FIG. 9. This inversion can be performed by transformation unit  70  at any point in time. For example, image  12 ′ can be inverted before applying the above steps for determining θ and φ or after. If image  12 ′ is not inverted, then no inversion needs to be performed.  
         [0072]    A transformed and inverted (as necessary) image  12 ″ is illustrated in FIG. 10. At this point vectors v″ 1 , v″ 2  and v″ 3  are re-computed. An additional vector v″ n  from center  84  to a feature or landmark on an edge  43 ″ is also shown. Such landmark on edge  43  of jotting surface  12  can be used instead of a corner for determining the physical coordinates of nib  20 . This is especially important when two corners are obstructed by the user or any object(s) located between jotting surface  12  and optical unit  30 .  
         [0073]    At this point image  12 ″ is corrected for rotations by angles θ and φ to obtain final transformed and corrected image  12 ′″, as shown in FIG. 11. This is done by applying the appropriate inverse rotations to transformed (and inverted, as the case may be) image  12 ″. (These inverse rotations correspond to Euler rotations in physical space of jotting implement  10  with respect to jotting surface  12 . Standard Euler transformation is described in any classical mechanics textbook such as Goldstein,  Classical Mechanics ).  
         [0074]    Now the physical coordinates of nib  20  can be determined directly from vectors v′″ 1 , v′″ 2 , v′″ 3  and/or vector v′″ n  This function is performed by ratio computation unit  72 , which takes advantage of the fact that the proportions of image  12 ′″ to jotting surface  12  are preserved.  
         [0075]    Specifically, computation unit  72  employs the following ratios:  
             x   1       x   2       =       x   1   ′′′       x   2   ′′′         ,   and               y   1       y   2       =         y   1   ′′′       y   2   ′′′       .                           
 
         [0076]    These values can be obtained from the vectors and the scaling factor due to the magnification M of imaging optics  46  can be used, as shown in FIG. 12 as an additional cross-check and constraint to ensure that the values obtained are correct.  
         [0077]    Jotting implements according to the invention admit of numerous other embodiments. For example, an alternative optical unit  100  employing a catadioptic system with a parabolic (or hyperbolic) mirror  102  and a lens  104  is shown in FIG. 13. The construction of optical unit  100  has to be altered to accommodate optical unit  100  on a jotting implement  108  (only top part shown) as in FIG. 14. In this embodiment a photodetector array  106  is placed at a distal end  109  of a jotting implement  108 . Support members  110  are extended with extensions  111  in this embodiment.  
         [0078]    Jotting implement  10  can take advantage of features and landmarks other than corners and edges of a jotting surface  120 . For example, as shown in FIG. 15, jotting implement takes advantage of a feature  122  produced by the user.  
         [0079]    Feature  122  is in fact a letter “A” written by the user. In the present case a particularly easy-to-locate point on the letter (e.g., a point yielding high contrast for easy detection and tracking) is used for tracking and a vector v r  is constructed to this point from the origin of the Cartesian coordinate system. Jotting implement  10  also takes advantage of a landmark  124  located along an edge  126 . A vector v s  is constructed to landmark  122  from the origin. Finally, implement  10  uses a corner  128  of jotting surface  120  identified by corresponding vector v q .  
         [0080]    In this embodiment, during operation, edge detection algorithms described above and any other algorithms for detecting high-contrast points are applied to localize the lines and corners in the image and locate feature  122 , landmark  124  and corner  128 . Then, angles θ, φ are determined and the corresponding transformations applied to imaged vectors v′ q , v′ r  and v′ s , of the image of jotting surface  120 , as described above. The physical coordinates of nib  120  are determined from the transformed vectors.  
         [0081]    Of course, a person skilled in the art will recognize that the number of features and landmarks tracked will generally improve the accuracy of determining physical coordinates of nib  20  on jotting surface  120 . Thus, the more landmarks and features are tracked, the more processing effort will be required. If real-time operation of jotting implement  10  is required, e.g., in cases where the jotting action is transmitted from jotting implement  10  to a receiver in real time, the number of features and landmarks should be limited. Alternatively, if the information jotted down can be downloaded by the user at a later time and/or no real-time processing is required, then more landmarks and features can be used to improve the accuracy with which the physical coordinates of nib  20  are determined. This will generally lead to an improved resolution of jotting surface  120 . It should also be kept in mind, that the features and landmarks have to provide absolute references, i.e., their positions on jotting surface  120  can not change in time. However, it should be remembered that the landmarks or features being used for determining the physical coordinates of nib  20  need not be the same from frame to frame.  
         [0082]    It will be evident to a person skilled in the art that the present invention admits of various other embodiments.