Patent Publication Number: US-8988445-B2

Title: Systems and methods for capturing and recreating the feel of surfaces

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Patent Application No. 61/369,254, entitled “SYSTEMS AND METHODS FOR CAPTURING AND RECREATING THE FEEL OF SURFACES,” filed on Jul. 30, 2010, the contents of which are incorporated herein by reference in their entirety. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to haptic human-computer interfaces, which enable a user to interact with virtual objects through motions and forces. More particularly, the invention relates to “haptography” (or “haptic photography”), which involves using a human-computer interface to capture and recreate the feel of real surfaces. 
     BACKGROUND OF THE INVENTION 
     The ability to touch the surface of an object allows one to feel and determine a number of structural characteristics about the object, such as its shape, stiffness, friction, texture, or other characteristics. Humans are adept at eliciting and interpreting these feelings, called haptic feedback, during physical interaction with an object. 
     Haptic interfaces seek to extend the normal reach of the human hand to enable interaction with virtual objects, either by direct touch or through tool-mediated contact. Haptic interfaces measure the motion of the human hand and map it into a virtual environment. For example, a control computer may be programmed to determine when and how a user is touching objects in the virtual environment. When contact occurs, the system may employ actuators to provide the user with haptic feedback about the virtual object. 
     However, current haptic interfaces require extensive tuning or adjustment, and do not feel authentic, which limits the usefulness and applicability of such systems. Accordingly, improved systems and methods are desired for capturing and recreating the feel of surfaces. 
     SUMMARY OF THE INVENTION 
     Aspects of the present invention are related to systems and methods for capturing and recreating the feel of surfaces. 
     In accordance with one aspect of the present invention, a method for capturing a feel of a surface is disclosed. The method comprises the steps of contacting the surface with a handheld tool; recording the acceleration experienced by the tool, the force experienced by the tool, and the speed of the tool while the tool contacts the surface; and generating a texture model of the surface based on the recorded acceleration, force, and speed. The handheld tool includes at least one accelerometer configured to measure an acceleration experienced by the tool, at least one force sensor configured to measure a force experienced by the tool, and at least one speed sensor configured to measure a speed of the tool. 
     In accordance with another aspect of the present invention, a method for recreating a feel of a surface is disclosed. The method comprises the steps of contacting a virtual surface with a handheld tool; determining an estimated contact force based on the measured force experienced by the tool and an estimated contact speed based on the measured speed of the tool; generating a vibration waveform from a texture model based on the estimated contact speed and the estimated contact speed of the tool; and actuating at least one actuator of the tool according to the vibration waveform. The handheld tool includes at least one actuator configured to provide an acceleration to the tool, at least one force sensor configured to measure a force experienced by the tool, and at least one speed sensor configured to measure a speed of the tool. 
     In accordance with still another aspect of the present invention, a system for capturing and recreating a feel of a surface is disclosed. The system comprises a handheld tool, a storage device, and a processor. The handheld tool includes at least one accelerometer configured to measure an acceleration experienced by the tool, at least one force sensor configured to measure a force experienced by the tool, and at least one speed sensor configured to measure a speed of the tool. The storage device is in communication with the tool. The storage device is operable to store the acceleration experienced by the tool, the force experienced by the tool, and the speed of the tool over a period of time. The processor is in communication with the storage device. The processor is programmed to generate a texture model of the surface based on the acceleration, force, and speed stored in the storage device. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention is best understood from the following detailed description when read in connection with the accompanying drawings. It is emphasized that, according to common practice, the various features of the drawings are not to scale. On the contrary, the dimensions of the various features may be arbitrarily expanded or reduced for clarity. Included in the drawings are the following figures: 
         FIG. 1A  is a block diagram depicting an exemplary system for capturing and recreating the feel of the surface of an object in accordance with an aspect of the present invention; 
         FIG. 1B  is a diagram of an exemplary tool for use with the system of  FIG. 1A ; 
         FIG. 1C  is an image of another exemplary tool for us with the system of  FIG. 1A ; 
         FIG. 1D  is an image of still another exemplary tool for use with the system of  FIG. 1A ; 
         FIG. 2A  is a diagram depicting capturing the feel of a surface using the system of  FIG. 1A ; 
         FIG. 2B  is a diagram depicting recreating the feel of a surface using the system of  FIG. 1A ; 
         FIG. 3  is a flowchart depicting an exemplary method for capturing and recreating the feel of the surface of an object in accordance with an aspect of the present invention; 
         FIG. 4  is a block diagram illustrating a process for generating a texture model in accordance with aspects of the present invention; 
         FIG. 5  is a sample plot of a recorded signal, a predicted signal, and a residual signal for an exemplary texture model derived using the process of  FIG. 4 ; 
         FIG. 6  is a flowchart depicting an exemplary method for recreating the feel of a surface in accordance with an aspect of the present invention; 
         FIG. 7  is an image of an exemplary tool and tablet computer screen for use in recreating the feel of a surface in accordance with an aspect of the present invention; 
         FIG. 8  is a block diagram illustrating a process for generating a vibration waveform in accordance with aspects of the present invention; and 
         FIG. 9  is a sample plot of a recorded acceleration (top) and an exemplary vibration waveform (bottom) derived using the process of  FIG. 8 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The exemplary systems and methods disclosed herein are suitable for providing a haptic interface for a user. For example, the disclosed systems and methods may capture the haptic feedback from contact with a real surface. The disclosed systems and methods may then reproduce haptic feedback to simulate virtual contact with the real surface. As set forth in further detail below, the exemplary systems and methods capture and recreate haptic feedback by mathematically characterizing the vibrational feel of real and virtual surfaces. They further employ computer-generated vibrations to duplicate the feel of a real surface. 
     The exemplary systems and methods are described herein as relating to the capture and recreation of the “feel” of surfaces. One factor that contributes to the feel of a surface is the roughness and/or texture of the surface. The disclosed systems and methods are particularly suitable for capturing and recreating a surface&#39;s roughness or texture. 
     While aspects of the present invention are related to capturing and recreating all forms of haptic interaction, the systems and methods described herein may be particularly suitable for providing haptic interfaces that rely on “tool-mediated contact,” i.e., where a human touches a surface through an intermediate object or tool such as a plastic stylus, metal implement, or paintbrush. It has been determined that humans are surprisingly good at discerning haptic surface properties such as stiffness and texture through an intermediate tool; this acuity may stem in part from the human capability for distal attribution, in which a hand-held tool comes to feel like an extension of one&#39;s own body because its dynamics are simple to understand. As such, employing the disclosed systems and methods disclosed herein may be useful for simulating many activities of interest that are commonly conducted with an implement in hand, rather than with the bare fingertip or hand. 
     The exemplary systems and methods disclosed herein may also be used to perform haptography. Like photography is for visual sensations, haptography may enable an individual to 1) quickly and easily record all aspects of the haptic interaction between a tool tip and a real surface and 2) accurately reproduce it later for others to interactively experience in a wide variety of useful contexts. 
     For example, a haptographer may begin by identifying an object with a unique feel: a museum curator might select an interesting archaeological artifact, an engineer could pick a beautifully manufactured mechanical component, or a doctor might target an in vivo sample of tissue, tooth, or bone. Working in his or her standard surroundings, the haptographer may choose a suitable tool tip and attach it to a highly sensorized hand-held instrument. He or she then uses this combined tool to explore the object&#39;s surface via natural motions, which may include segments of tapping, stroking, and pressing, as well as repositioning movements in free space. A haptographic processor may collect multiple data streams throughout this brief interaction, including quantities such as the translation and rotation of the stylus and the object, the forces and torques applied to the object&#39;s surface, and the three-dimensional high-frequency accelerations of the tool tip. Tip acceleration may be particularly important because tool-mediated interaction with hard and textured surfaces can create vibrations that are particularly useful for recreating a realistic textural feel. 
     The haptographic processor may use the recorded data to construct a faithful geometric and haptic model of the object. This characterization process may take place in real time so that the state of the derived model could be conveyed to the haptographer instantaneously, just as the preview screen on a digital camera helps a photographer decide how to adjust the lighting and framing of the visual scene being captured. An acquired haptographic model (a “haptograph”) may desirably be renderable at a remote haptic interface. Rendering of the haptograph may be performed in real time or at a later time determined by a user. The systems and methods described herein provide new high-fidelity methods for creating and rendering haptographs. 
     Referring now to the drawings,  FIGS. 1A-2B  illustrate an exemplary system  100  for capturing and recreating the feel of the surface of an object in accordance with an aspect of the present invention. As an overview, system  100  includes a handheld tool  102 , a storage device  104 , and a processor  106 . Additional details of system  100  are described below. 
     Tool  102  is used by the user to touch the surface to be captured, or to recreate the surface to be recreated. Tool  102  is a handheld implement that can be grasped and manipulated by the user. Tool  102  may include a handle portion  112  for grasping by the user, and one or more tip portions  114  for contacting the surface to be captured. Tip portions  114  may be constructed in a wide variety of shapes and materials, and they may be interchangeable. In an exemplary embodiment, tool  102  may be shaped like a stylus or wand, as shown in  FIGS. 1B ,  1 C, and  2 A- 2 B. 
     Tool  102  may be used for capturing a surface, for recreating a captured surface, or for both purposes. The following components of tool  102  may be selected based on the desired use of tool  102 . Additionally, system  100  may include one tool  102  for capturing a surface and a separate tool  102  for recreating a surface. 
     Where tool  102  is used for contacting the surface to be captured, tool  102  includes at least one accelerometer  116 . Accelerometer  116  may be integrally built into tool  102 , or may be attached to tool  102 . Accelerometer  116  is coupled to tool  102  in a location where accelerometer  116  can measure an acceleration experienced by tool  102 . In an exemplary embodiment, accelerometer  116  may preferably be coupled to the tip portion  114  of tool  102 , as shown in  FIG. 1A , in order to improve sensing of the vibrations of tool  102  caused by the surface. While one accelerometer  116  is illustrated, it will be understood that tool  102  may include any number of accelerometers  116 . 
     Accelerometer  116  may desirably have multiple (e.g., three) orthogonal measurement axes for measuring the acceleration of tool  102  in multiple dimensions; however, it is not necessary that accelerometer  116  be a multiple-axis accelerometer. 
     Accelerometer  116  may desirably measure only vibrations occurring within a predetermined range of frequencies (i.e. within a passband). In an exemplary embodiment, accelerometer  116  has a bandwidth from approximately 20 Hz to approximately 200 Hz, and more preferably, a bandwidth from 20 Hz to approximately 1000 Hz or higher. Thus, accelerometer  116  may only measure vibrations having a frequency up to approximately 200 Hz, or more preferably, up to 1000 Hz or higher. System  100  may optionally be reconfigurable so that a user can change the bandwidth of the vibrations measured to suit the user&#39;s preference. For example, the passband could be adjusted to start below or above the above-identified frequencies, and optionally remove selected frequency ranges. It may be desirable to restrict the accelerations measured above 1000 Hz, as this frequency range approximately corresponds to the bandwidth of the human sense of touch. 
     Suitable accelerometers for use as accelerometer  116  include, for example, MEMS-based high-bandwidth accelerometers, capacitive accelerometers, piezoelectric or piezoresistive accelerometers, Hall effect accelerometers, magnetoresistive accelerometers, heat transfer accelerometers, or other suitable accelerometers. Suitable accelerometers for use as accelerometer  116  will be known to one of ordinary skill in the art from the description herein. 
     Where tool  102  is used for recreating the surface, tool  102  includes at least one actuator  118 . Actuator  118  may be integrally built into tool  102 , or may be attached to tool  102 . Actuator  118  is coupled to tool  102  in a location where actuator  118  can provide an acceleration to tool  102 . In an exemplary embodiment, actuator  118  is coupled to the handle portion  112  of tool  102 , as shown in  FIG. 1A , in order to provide a vibration that can be felt by the tool&#39;s holder. Actuator  118  may preferably be coupled to the tip portion  114  of tool  102  so that the vibrations it creates emanate from a location close to the point of contact between the tool&#39;s tip portion  114  and a real or virtual surface. Actuator  118  may also preferably consist of two parts coupled together via a spring; one part may be coupled to tool  102  directly, and the other part may vibrate while staying centered due to the spring. While one actuator  118  is illustrated, it will be understood that tool  102  may include any number of actuators  118 . 
     Actuator  118  provides vibrations to tool  102  that correspond in frequency of the vibrations measured by accelerometer  116 . Actuator  118  may desirably only provide vibrations occurring within a predetermined range of frequencies (i.e. within the passband), as described with respect to accelerometer  116 . Actuator  118  may optionally be reconfigurable so that a user can change the bandwidth of the vibrations created to suit the user&#39;s preference. For example, the passband could be adjusted to start below or above the above-identified frequencies, and optionally remove selected frequency ranges. It may be desirable to restrict the vibrations created above 1000 Hz, as this frequency range approximately corresponds to the bandwidth of the human sense of touch. 
     Actuator  118  must be powerful enough to create tool vibrations that the user can detect. Preferably, actuator  118  should provide vibrations to the user that correspond in amplitude to the vibrations felt by tool  102 . It is preferable that actuator  118  be operable to provide vibration output that can have independently varying frequencies and amplitude. In an exemplary embodiment, actuator  118  is a linear voice coil actuator. The linear voice coil actuator includes a coil of wire configured to function as an electromagnet, and a permanent magnet. These two elements are connected to one another by a spring-like piece such as a flexure bearing or a coil spring. One of these two elements (wire coil or permanent magnet) is firmly affixed to tool  102 , while the other is allowed to move freely, within the limits permitted by the spring. Driving a current through the wire coil causes equal and opposite forces between the coil and the magnet, which causes movement of either the wire coil, the magnet, or the wire coil and the magnet. The moving component of the voice coil actuator may desirably be mounted on low friction linear bearings. Suitable voice coil actuators for use as actuator  118  include, for example, voice coil linear actuators provided by H2W Technologies, Inc. or BEI Kimco Magnetics. Other suitable actuators will be known to one of ordinary skill in the art from the description herein. 
     Tool  102  also includes at least one force sensor  120 . Force sensor  120  may be integrally built into tool  102 , or may be attached to tool  102 . Force sensor  120  is coupled to tool  102  in a location where it can measure a contact force experienced by tool  102 . Force sensor  120  may measure force on tool  102  in any direction, e.g., normal force from the surface, torque on the tool  102 , or other forces. In an exemplary embodiment, force sensor  120  is coupled to tool  102  in order to sense the force felt by the tool&#39;s tip  114  when it contacts the surface to be captured. While one force sensor  120  is illustrated, it will be understood that tool  102  may include any number of force sensors  120 . Suitable force sensors for use as force sensor  120  will be known to one of ordinary skill in the art from the description herein. 
     Tool  102  also includes at least one speed sensor  122 . Speed sensor  122  may be integrally built into tool  102 , or may be attached to tool  102 . Speed sensor  122  is coupled to tool  102  in a location where it can measure the speed of motion of tool  102 . In an exemplary embodiment, speed sensor  122  is coupled to tool  102  in order to sense the speed of tool tip  114  as it is moved along the surface to be captured. Speed sensor  122  may also preferably measure the direction of movement of tool  102 . While this discussion refers to a sensor that directly measures speed, it will be understood that speed sensor  122  may also be another basic type of sensor, such as a position and/or an acceleration sensor, combined with appropriate signal processing to produce a speed measurement. While one speed sensor  122  is illustrated, it will be understood that tool  102  may include any number of speed sensors  122 . Suitable speed sensors for use as speed sensor  122  will be known to one of ordinary skill in the art from the description herein. 
     The above sensors are illustrative of the data that can be recorded regarding tool  102 , and are not meant to be limiting. For example, the position and orientation of tool  102  may also be measured. Tool  102  may preferably include one or more motion tracking sensors, such as infrared, optical, or magnetic locators (as shown in  FIG. 1B ), to determine the position and orientation of tool  102 . Suitable locators for use with tool  102  will be known to one of ordinary skill in the art. For another example, tool  102  may include a grip force sensor coupled to the handle portion  112  of tool  102 , to measure the force of the user&#39;s grip on tool  102 . 
     As described above, it may be desirable to measure acceleration frequencies within a predetermined frequency band, e.g., from 20 Hz to approximately 1000 Hz. Accordingly, it will be desirable that the sensors used with tool  102  have sampling rates that are relatively high with respect to the bandwidth of accelerometer  116 . Additionally, it may be desirable that the sampling rates of all sensors of tool  102  be the same, to facilitate synchronizing data from tool  102  for a respective touching event. 
     Storage device  104  is in communication with tool  102 . Data from the sensors on tool  102  may be transmitted to the storage system  104  in a variety of ways, Storage device  104  may receive analog or digital signals from tool  102  by wired electrical connections. Alternatively, storage device  104  may receive analog or digital signals from tool  102  wirelessly via a wireless communication protocol. A wireless connection between storage device  104  and tool  102  may be desirable to allow free movement of tool  102  by the user. Suitable signal transmission methods will be know to one of ordinary skill in the art from the description herein. 
     Storage device  104  stores the signals measured by tool  102  over time. Specifically, storage device  104  stores the acceleration measured by accelerometer  116 , the force measured by force sensor  120 , and the speed measured by speed sensor  122 . In an exemplary embodiment, storage device  104  is a computer readable storage medium, such as a computer memory. Suitable memory for use as storage device  104  will be known to one of ordinary skill in the art from the description herein. 
     Processor  106  is in communication with storage device  104 . Processor  106  processes the data from tool  102  that is stored in storage device  104 . For example, when tool  102  is used for capturing the feel of a surface, processor  106  is programmed to analyze the acceleration, force, and speed measured by tool  102  to generate a texture model of the surface. The texture model may correspond to the feel of the surface at a specific average force and/or at a specific average speed. In an exemplary embodiment, processor  106  generates a texture model for the surface by linear predictive coding. Additional details regarding the generation of a texture model will be provided herein. 
     For another example, when tool  102  is used for recreating the feel of a surface, processor  106  is programmed to determine an estimated contact force and an estimated contact speed based on the acceleration, force, and/or speed measured by tool  102 . Processor  106  is further programmed to create or select at least one vibration waveform from a texture model of the surface based on the estimated contact force and estimated contact speed. Processor  106  then actuates the actuator  118  of tool  102  based on the selected vibration waveform. Additional details regarding the actuation of actuator  118  will be provided herein. 
       FIG. 3  is a flowchart illustrating an exemplary method  200  for capturing the feel of a surface in accordance with an aspect of the present invention. As an overview, method  200  includes touching a surface with a handheld tool, recording data from the tool while the tool touches the surface, and generating a texture model for the surface based on the recorded data. For the purposes of illustration, the steps of method  200  are described herein with respect to the components of system  100 . Additional details of method  200  are described below. 
     In step  202 , the surface to be captured is touched with a handheld tool. A user may select a surface to be captured for creating a haptograph. Once the surface is selected, the user touches the surface with the handheld tool. In an exemplary embodiment, a user touches the surface with tool  102 , as shown in FIG.  2 A. The user may hold tool  102  at the handle portion  112  and touch the surface with the tip portion  114 . The user may desirably touch the surface with tool  102  in a stroking motion, i.e., by moving tool  102  while tool  102  is in contact with the surface. It may further be preferable that the user maintain a relatively steady contact force and speed during contact with the surface. Alternatively, the user may touch the surface with tool  102  in a tapping motion. It may be preferable that the tool  102  not damage the selected surface during a touching event. 
     In order to enable recreation of a full feel of the surface, it may be desirable that the user touch the surface with tool  102  a plurality of times. In a preferred embodiment, a user taps and/or strokes the surface a plurality of times with tool  102 . The user may alter the force with which the tool  102  touches the surface during the plurality of times, and/or may alter the speed at which the tool  102  moves across the surface during the plurality of times. For example, it may be preferable to capture a plurality of touching events covering a range of force and speed combinations at regular intervals. This may be desirable in order to create a plurality of data sets showing the acceleration experienced by tool  102  for differing forces and speeds of contact with the surface. 
     During the touching of the surface with tool  102 , it may be desirable to provide the user with feedback to assist in capturing data about the surface. For example, system  100  may provide graphical feedback to a user via one or more displays. System  100  may further provide auditory feedback to a user via one or more speakers. System  100  may further provide haptic feedback, substantially as described herein. 
     While tool  102  is described as being manipulated directly by a human user, it is contemplated that tool  102  may be manipulated in other ways. For example, step  202  may be performed by an automatic or semiautomatic mechanism configured to touch a surface with tool  102 . Alternatively, step  202  may be performed by a non-human primate or by a robot that is controlled remotely by a human or a non-human primate. 
     In step  204 , the data measured by the tool sensors is recorded while the tool touches the surface. In an exemplary embodiment, storage device  104  stores the data measured by accelerometer  116 , force sensor  118 , and speed sensor  120  of tool  102 . Thereby, for each touching event (i.e., when the tool  102  is in contact with the surface), storage device  104  stores the acceleration experienced by the tool  102 , the force experienced by the tool  102 , and the speed of the tool  102 . Storage device  104  desirably stores the data from each of these sensors over the same span of time, such that the signals are synchronized with one another. When tool  102  touches the surface a plurality of times, storage device  104  may store data measured by tool  102  for each touching event separately. 
     As described above, accelerometer  116  may have multiple measurement axes for measuring the acceleration of tool  102  in multiple dimensions. Accordingly, storage device  104  may store the acceleration data for each axis of accelerometer  116 . Alternatively, the acceleration data for the multiple dimensions may be reduced to a single dimension. This may be done in a number of different ways. 
     One option for reducing multiple-axis acceleration data to a single value is to simply record only one axis of acceleration recorded by accelerometer  116 . Another option for reducing multiple-axis acceleration data to a single dimension is to sum the multiple axes into a single value. Still another option is by projecting the multi-dimensional acceleration data onto a single dimension, and relying on the principle component of the acceleration. 
     In one exemplary embodiment, processor  106  reduces multiple dimensions of acceleration data into a single dimension using a discrete Fourier transform (DFT) analysis. By expressing each component of the multi-dimensional, e.g., 3D signal as an orthogonal basis function expansion, the components can be summed without destructive interference. 
     Human perception of high-frequency vibrations relies at least in part on the spectral content of the signal. Thus, it may be desirable that a dimensionally reduced vibration feel like it has the same spectrum as the original recorded signal. In other words, a synthesized 1D vibration should have the same energy at each frequency as the sum of the energies present at that frequency in the original vibration&#39;s three component directions. Consequently, the transformation should preserve the total Energy Spectral Density (ESD) of the original 3D signal, where the ESD of each component a(t) is E s (f)=|A(f)|2, where A(f) is the Fourier transform of a(t). 
     Because raw spectral estimates are noisy, spectral similarity need not be judged directly from the energy spectral density at each frequency. Instead, a spectral metric has been designed that takes into account the limited frequency resolution of human vibration perception. Hence, the spectral perceptual comparisons may use a frequency smoothing resolution. The smoothed version of A(f) may be denoted as Ã(f). Using a s (t) to represent the 1D synthesized signal that results from the transformation and As(f) to represent its discrete Fourier transform, the spectral matching metric may be written as: 
               M   sm     =     1   -       1     n   f       ⁢       ∑     f   =     20   ⁢           ⁢   H   ⁢           ⁢   z         1000   ⁢           ⁢   H   ⁢           ⁢   z       ⁢     (                         A   ~     x     ⁡     (   f   )            2     +                A   ~     y     ⁡     (   f   )            2     +                A   ~     z     ⁡     (   f   )            2     -                A   ~     s     ⁡     (   f   )            2                           A   ~     x     ⁡     (   f   )            2     +                A   ~     y     ⁡     (   f   )            2     +                A   ~     z     ⁡     (   f   )            2         )                 
(Equation 1) where n f  signifies the number of discrete frequencies in the sum. Here, the extent to which the synthesized signal preserves the energy in the original 3D signal is quantified for frequencies from 20 Hz to 1000 Hz, chosen to match the sensitivity to vibration of human hands. This frequency range could be changed to suit user preference. Over the included frequency range, this calculation provides a strict measure of the average normalized deviation between the 1D signal&#39;s smoothed ESD and the 3D signal&#39;s smoothed ESD. If the two are identical, the spectral match metric will be one.
 
     In view of the spectral requirements on the synthesized signal, the DFT represents one feasible choice of such basis functions. Following (Equation 1):
 
|{tilde over ( A )} s ( f )| 2 =√{square root over (| Ã   x ( f )| 2   +|Ã   y ( f )| 2   +|Ã   z ( f )| 2 )}{square root over (| Ã   x ( f )| 2   +|Ã   y ( f )| 2   +|Ã   z ( f )| 2 )}{square root over (| Ã   x ( f )| 2   +|Ã   y ( f )| 2   +|Ã   z ( f )| 2 )}  (Equation 2).
 
     Having obtained the absolute value of Ã s (f) and by that set the local spectrum of a s , a phase θ f  must be assigned that ensures desirable temporal properties. To this end, the phase is optimized to neglect the absolute values for simplicity. In the frequency domain, the sum of cross-correlations at zero time shift can be expressed as: 
               ∑     i   =   1     3     ⁢       a   i     *     a   s             
It can be shown that this quantity is maximized when the phase of Ã s  is chosen as follows:
 
               θ   f     m   ⁢           ⁢   ax       =     ∠   ⁢       ∑     i   =   1     3     ⁢       A   ~     i               
(Equation 3)
 
     The synthesized time-domain signal a s  is then obtained by a square-root, multiplication by e jθ  where j=√−1, and inverse DFT. By Parseval&#39;s theorem the result will always have the same signal energy as the sum of energies of the components. This new dimensional reduction approach may be particularly suitable for reducing multi-dimensional acceleration data to a single acceleration value. 
     As described above, accelerometer  116  may desirably measure only vibrations occurring within a predetermined frequency range. Accordingly, storage device  104  may only store acceleration data having a frequency within a predetermined frequency range, e.g., from approximately 20 Hz to approximately 1000 Hz. As set forth above, storage device  104  may optionally be reconfigurable so that a user can change the bandwidth of the recorded vibrations measured to suit the user&#39;s preference. 
     In step  206 , a texture model of the surface is generated. In an exemplary embodiment, processor  106  generates a texture model for the surface based on the data recorded by storage device  104 . From the stored data from force sensor  120  and speed sensor  122 , processor  106  determines an average force experienced by tool  102  and an average speed of tool  102 . Processor  106  may determine the average force and average speed for a subset of a touching event, an entire touching event, or for a group of touching events. 
     The feel of the surface is captured electronically by generating a mathematical model of the surface&#39;s texture. This texture model may then be used at a later time to recreate the accelerations or vibrations that are felt when contacting the surface. However, it may be difficult or impractical to record the accelerations or vibrations felt on the surface for all possible combinations of force and speed. Thus, a texture model must be created that enable the prediction of the acceleration/vibratory response of the surface at substantially all possible combinations of force and speed. 
     To solve this problem, in one exemplary embodiment, a texture model is created by linear predictive coding. For linear predictive coding, the response of the tool/surface interaction is treated as a filter to be identified.  FIG. 4  illustrates a block diagram for use in explaining linear predictive coding. An input signal a(k) represents the original time series of accelerations measured by accelerometer  116 . The filter&#39;s output vector is defined as â(k), which represents a forward linear prediction. H(z) is assumed to be an IIR (infinite impulse response) filter of length n of the form H(z)=[−h 1 z −1 −h 2 z −2  . . . −h n z −n ]. The residual of these two signals is the error vector e(k), and the transfer function P(z) is: 
                 E   ⁡     (   z   )         A   ⁡     (   z   )         =       1   -     H   ⁡     (   z   )         =     P   ⁡     (   z   )               
(Equation 4).
 
     The vector of filter coefficients may be defined as h=[h 1 , h 2 , h 3  . . . h n ] T , and the n-length time history of the input signal as a(k−1)=[a(k−1) a(k−2) . . . a(k-n)]. The residual at each step in time can then be written with the following difference equation:
 
 e ( k )= a ( k )−{tilde over ( a )}( k )= a ( k )− h   T   a ( k− 1)  (Equation 5).
 
     Optimal filter values of h can be found by defining a suitable cost function. The standard choice of mean-square error can be used, J(h)=E{e 2 (k)}, where E{ } denotes mathematical expectation. When the gradient of J(h) is flat, H is at an optimal value, h 0 . By algebraic manipulation, the following result for the gradient can be derived: 
                 ∂     J   ⁡     (   h   )           ∂   h       =       -   2     ⁢   E   ⁢     {     (       e   ⁡     (   k   )       ⁢     a   ⁡     (     k   -   1     )         )     }             
(Equation 6). When the gradient is flat at h 0 , the error is at a minimum e 0 (k), and the problem can be simplified to:
 
 E{e   0 ( k ) a ( k− 1)}=0 nxl   (Equation 7).
 
     By substituting values for the cross-correlation matrix (R=a(k−1)a T (k−1)) and the cross-correlation vector (p=a(k−1)a(k)) into (Equation 7), one arrives at the Wiener-Hopf equation:
 
 R·h   0   =p   (Equation 8).
 
     Assuming a non-singular R, the optimal forward predictor coefficients can be found by simply inverting the cross-correlation matrix, such as h 0 =R −1 p. Alternatively, a recursive method can be used, such as the Levinson-Durbin algorithm, to solve for h 0  from (Equation 8).  FIG. 5  shows a sample plot of a(k) (Recorded Signal), ã(k) (Predicted Signal), and e(k) (Residual) for an optimal filter H(z) of order n=120. By solving for H(z), processor  106  can generate a texture model for use in recreating the feel of the selected surface based on the measured n acceleration values experienced by tool  102  in capturing the feel of the surface. The texture model consists of the variance of the residual signal and the vector of chosen filter coefficients. 
       FIG. 6  is a flowchart illustrating an exemplary method  300  for recreating the feel of a surface in accordance with an aspect of the present invention. It will be understood that method  300  can be performed at a later time, in combination with, or immediately following the capture of the feel of a surface, as set forth above in method  200 . As an overview, method  300  includes touching a virtual surface with a handheld tool, determining estimated contact data, generating a vibration waveform, and actuating an actuator of the tool. For the purposes of illustration, the steps of method  300  are described herein with respect to the components of system  100 . Additional details of method  300  are described below. 
     In step  302 , a virtual surface is touched with a handheld tool. A user may select a real surface to be recreated from a list of available haptographs, or this choice may be pre-selected by the computer processor. Once the surface is selected, the user touches the virtual surface with the handheld tool. The virtual surface may be of any type that can recreate the feel of the selected surface. For example, the virtual surface may be overlaid on a real surface, such that the texture of the selected surface will be rendered on top of the texture of the real surface. In this example, the real surface may be the screen of a tablet computer or the surface of a typical object such as a foam block. Preferably, the surface of this real object is smooth. For another example, the virtual surface may exist in an area of space lacking a real surface, as shown in  FIG. 2B . In this example, the presence of the virtual surface may be indicated to the user through visual cues (e.g., on a computer monitor), through auditory cues (e.g., via speakers), and/or through haptic cues (e.g., via actuators attached to tool  102 ). In particular, this type of virtual surface may be created with an impedance-type haptic interface with one or more translational or rotational degrees of freedom. A suitable impedance-type haptic interface is shown in  FIG. 1D . The motors of such a device can be used to exert synthetic contact forces on tool  102 , to give the user the impression that he or she is touching a real surface at the given location. It is common for such virtual surfaces to be programmed to respond as linear springs, such that the force delivered to the user is proportional to and in the opposite direction as the tool tip&#39;s penetration into the virtual surface. 
     In a particular embodiment, tool  102  may be shaped as a stylus, and the virtual surface may be a tablet computer screen  103 , as shown in  FIG. 7 . For purposes of illustration, a WACOM™ tablet computer screen is shown, such as those that can be used with pressure- and tilt-sensitive pens for editing digital images, applying effects and filters, sketching, painting and modeling. The right part of the WACOM tablet computer screen has been covered with a real textured surface to enable method  200  (capturing the feel of a real surface), and the left part of the WACOM tablet computer screen has been left bare to form tablet computer screen  103 . The real textured surface may also be augmented to feel like other surfaces via application of method  300 . 
     Tool  102  may be tapped or stroked across the surface of the tablet computer screen  103  to recreate the feel of the selected surface. In this embodiment, the tablet computer screen  103  may be used to detect the contact force and speed of tool  102  in addition to or in place of force sensor  120  and speed sensor  122 . 
     In an exemplary embodiment, a user touches the virtual surface with tool  102 , as described above with respect to method  200 . The user may hold tool  102  at the handle portion  112  and touch the surface with the tip portion  114 . The user may desirably touch the virtual surface with tool  102  in a stroking motion, i.e., by moving tool  102  while tool  102  is in contact with the surface. Alternatively, the user may touch the virtual surface with tool  102  in a tapping motion. 
     In step  304 , estimated contact data for the tool are determined. In an exemplary embodiment, processor  106  calculates an estimated contact force of tool  102  based on the measurements of force sensor  120 , and calculates an estimated speed of tool  102  based on the measurements of speed sensor  122 . When no actual surface is present, as in the second virtual surface example, processor  106  may also estimate the contact force of tool  102  based on the amount by which the user has penetrated the virtual surface with the tool tip. In the same situation, processor  106  may calculate the estimated speed of tool  102  by computing the speed at which the user is moving tool  102  across (parallel to) the virtual surface. 
     In step  306 , a vibration waveform is generated. In an exemplary embodiment, processor  106  generates at least one vibration waveform based on the texture model for the surface to be recreated. As described above with respect to method  200 , processor  106  is programmed to create a texture model for the surface during capture of the feel of the surface. The texture models may be created, for example, by forward linear predictive coding, where the filter H(z) is the texture model for the surface. 
     As the user touches the virtual surface with tool  102 , processor  106  generates the vibration waveform from the texture model using the estimated contact force and the estimated contact speed.  FIG. 8  illustrates a block diagram for use in explaining the generation of a vibration waveform. An input signal e g (l) is a white noise vector of a specific variance that may be generated in real time. This input signal is generated based on the estimated contact force and speed determined in step  304 . The output signal is a g (l), a synthesized acceleration signal corresponding to the vibration waveform to be used to drive actuators  118 . Output signal a g (l) is a signal with spectral properties that are very close to those of the acceleration signal a(k) measured by accelerometer  116  at the given contact force and contact speed. A higher order filter H(z) (or texture model) will generally result in a better spectral match between the output acceleration signal a g (l) and the original signal a(k). By rewriting (Equation 4), a new transfer function can be formulated: 
                   A   g     ⁡     (   z   )           E   g     ⁡     (   z   )         =       1     1   -     H   ⁡     (   z   )           =     1     P   ⁡     (   z   )                 
(Equation 9).
 
     The difference equation for the synthesized acceleration is:
 
 a   g ( l )= e   g ( l )+ h   T   a   g ( l− 1)  (Equation 10).
 
     It will be understood that the signal power of the input signal is important for generating a vibration waveform having an appropriate magnitude (corresponding to the acceleration experienced during the capture of the feel of the surface). For linear predictive coding, the white noise input signal should have a variance equal to the variance of the residual signal from the texture modeling step.  FIG. 9  shows an exemplary recorded acceleration (top) and an exemplary vibration waveform (bottom) derived using the above-described algorithm. 
     The vibration waveform generated by processor  106  substantially corresponds to the accelerations measured by accelerometer  116  for the corresponding texture model. Processor  106  may generate multiple vibration waveforms that differ in frequency, amplitude, or phase, for example, to accurately reproduce the measured accelerations. Preferably, processor  106  estimates the tool&#39;s contact force and contact speed at a high temporal rate and adjusts the texture model to match these changing contact variables. When the user is allowed to explore the virtual surface freely, there will commonly be no texture model available for the specific contact variables currently being measured. In this case, the processor may interpolate between models captured under conditions similar to the current conditions, using a method such as bilinear interpolation. In the case of linear predictive coding, both the variance of the residual and the frequency response of the model need to be interpolated. 
     In step  308 , an actuator of the tool is actuated. In an exemplary embodiment, processor  106  actuates at least one actuator  118  of tool  102  based on the vibration waveform generated. Processor  106  actuates actuator  118  to provide vibrations to tool  102  that correspond to the accelerations measured by accelerometer  116  when the selected surface was captured. 
     The vibrations desirably correspond in both amplitude and frequency to the originally measured accelerations. As described above, accelerometer  116  may only measure and record vibrations inside a predetermined frequency range, e.g., from approximately 20 Hz to approximately 1000 Hz. Accordingly, actuator  118  may desirably only provide vibrations occurring within the predetermined frequency range. 
     The vibration may be monitored across all frequencies provided by actuator  118 . If the amplitude of vibrations provided by actuator  118  is not constant across all frequencies, processor  106  may be programmed compensate for any deviations. This may enable actuator  118  to provide more realistic vibrations to the user. 
     Aspects of the invention illustrated in the above described systems and methods achieve the following advantages not found in the prior art. 
     The above-described systems and methods provide a novel way to generate synthetic texture signals via automated analysis of real recorded data. These systems and methods are capable of modulating the synthetic signal based on changes in two critical probe-surface interaction parameters, translational velocity and normal force, by using bilinear interpolation. These synthetic signals are both simple and fast to compute, as well as strongly matched to their real counterparts in the time- and frequency-domains. 
     The above-described systems and methods establish an approach of haptography that can enable novel avenues of human-computer interaction and make significant contributions to the progress of ongoing research in several fields. For example, the above-described systems and methods may be usable for keeping haptic records, touching virtual versions of valuable items, touching remote objects in real time, and understanding human and robot touch capabilities. 
     Additionally, by employing a human haptographer holding the handheld tool, quick and safe explorations can be performed for the surfaces of almost any physical object. A human will naturally gravitate toward object areas that are most interesting to touch, effortlessly moving the tool in ways that match the motions that will be employed by eventual users of the associated rendering of the virtual surface. These stereotypical hand movements are known as exploratory procedures, and they are widely observed when an individual seeks to ascertain a specific object property of a surface. For example, lateral motion yields good haptic information about texture, and pressure elucidates compliance. 
     Although the invention is illustrated and described herein with reference to specific embodiments, the invention is not intended to be limited to the details shown. Rather, various modifications may be made in the details within the scope and range of equivalents of the claims and without departing from the invention.