Abstract:
Some embodiments of the invention are directed toward a robotic head that includes a head enclosure; a translucent face mask coupled with the head enclosure, having a front side and a rear side; a neck system coupled with the head enclosure and configured to move the head enclosure; and a projector coupled with the head enclosure and disposed to project images of a face onto the rear side of the face mask.

Description:
SPONSORED RESEARCH AND DEVELOPMENT 
     This invention was made with government support under Grant Numbers IIP1449747 and IIS1111568 awarded by The National Science Foundation. The government has certain rights in the invention. 
    
    
     BACKGROUND 
     Current robot technologies have yet to reach the full emotional and social capabilities necessary for rich and robust interaction with human beings. Robots with emotional and social capabilities may be useful for interacting with people in home situations, such as the elderly, Alzheimer&#39;s patients, children with autism, or others who may benefit from an interactive robot. Robotic heads that can model natural face-to-face communication with individuals in different social, learning, and therapeutic contexts may be desired. Such robotic heads may help overcome the “Uncanny Valley” effect, where the effect of an aesthetic design of a robot may influence the user&#39;s experience, perception, and acceptance of the robot. 
     SUMMARY 
     Some embodiments of the invention are directed toward a robotic head that includes a head enclosure; a translucent face mask coupled with the head enclosure, having a front side and a rear side; a neck system coupled with the head enclosure and configured to move the head enclosure; and a projector coupled with the head enclosure and disposed to project images of a face onto the rear side of the face mask. 
     In some embodiments, the robotic head includes a lens with a wide-projection angle through which the projector projects images of a face onto the rear side of the face mask. 
     In some embodiments, the face mask is removably coupled with the head enclosure. 
     In some embodiments, the face mask includes a plurality of facial features. 
     In some embodiments, the projector is coupled with an external rear portion of the head enclosure, and the head enclosure includes a hole through which the projector projects images of a face onto the rear side of the face mask. 
     In some embodiments, the neck system includes a pan-tilt unit that moves the head enclosure with two or three degrees of freedom. In some embodiments, the neck moves the head enclosure with one-hundred to one-hundred fifty degrees of yaw, fifteen to thirty degrees of pitch, and fifteen to thirty degrees of roll. In some embodiments, the neck comprises at least one of a servomotor and a gear. 
     In some embodiments, the head enclosure has a shape that is substantially half ovoid. 
     In some embodiments, the robotic head includes a wig. 
     In some embodiments, the projector is configured to project changes in facial expression onto the rear side of the face mask. 
     Some embodiments include a robotic head projection calibration method that includes projecting a two-dimensional image of a face with a plurality of fiducial marker points onto a rear surface of a face mask; recording an image of the face mask with the plurality of fiducial marker points projected onto the rear surface of the face mask; determining a plurality of distances between the location of each of the plurality of fiducial marker points on the face mask relative to an expected location of each of the plurality of fiducial marker points on the face mask; calculating a transformation based on the plurality of distances; and applying the transformation to two-dimensional images of a face. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       These and other features, aspects, and advantages of the present disclosure are better understood when the following Disclosure is read with reference to the accompanying drawings. The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. 
         FIG. 1A  is a perspective view of an example robotic head. 
         FIG. 1B  is another perspective view of the robotic head illustrated in  FIG. 1A . 
         FIG. 2A  is a perspective view of another example robotic head, with a face mask removed. 
         FIG. 2B  is a transparent side view of an example neck system of the robotic head illustrated in  FIG. 2A . 
         FIG. 2C  is a perspective view of the neck system illustrated in  FIG. 2B . 
         FIG. 2D  is a perspective view of the robotic head illustrated in  FIG. 2A , with an example facial image. 
         FIG. 2E  is a side view of the robotic head illustrated in  FIG. 2A . 
         FIG. 2F  is a front view of the robotic head illustrated in  FIG. 2A . 
         FIG. 3A  is a perspective view of an example pan-tilt unit with two degrees of freedom. 
         FIG. 3B  is a side view of the pan-tilt unit illustrated in  FIG. 3A . 
         FIGS. 4A, 4B, 4C, and 4D  illustrate an example calibration method. 
     
    
    
     DETAILED DESCRIPTION 
     In some embodiments described herein, two-dimensional (2D) and three-dimensional (3D) facial images may be rear-projected onto a human-like face of a robotic head. In some embodiments, the face of the robotic head may include a face mask that is removable and/or interchangeable. In some embodiments, the face mask may be a translucent face mask onto which the facial images may be projected. In some embodiments, the face mask may be constructed or molded from a clear plastic and/or coated with rear projection paint. In some embodiments, the face mask of the robotic head may be 3D, which may reduce the Mona Lisa Effect that may result when 3D objects are displayed on 2D surfaces. In some embodiments, the facial images may be created using a character animation application and may include natural speech and facial expressions. The facial images may, for example, be cartoon-like, animated, and/or photorealistic. In some embodiments, the character animation application may calibrate the facial images for a particular face mask. 
     In some embodiments described herein, the robotic head may include a neck system that may allow the robotic head to move in a manner that resembles movement of a human head. In some embodiments, the robotic head may include enclosures, such as, for example, an enclosure for the neck system, which may make the robotic head more realistic and also may prevent projected light from being scattered from the sides of the robotic head so the facial image may look brighter. 
     An example robotic head  100  is shown in  FIG. 1A  and  FIG. 1B . In some embodiments, the robotic head  100  may include a display system. The display system may include a projector  102  that projects a facial image on a face mask  104  of the robotic head  100 . In some embodiments, the projector  102  may use rear-projection to project the facial image on the face mask  104 . In some embodiments, the projector  102  may include a lens  106  with a wide-projection angle, such as, for example, a fish eye lens. In some embodiments, the projector  102  may be portable. In some embodiments, the projector  102  may be high-resolution and/or high-luminosity. In some embodiments, the projector  102  may be able to display a resolution of approximately 1200 by 800 pixels and may have a contrast ratio of approximately 10,000 to one. The projector  102  may be capable of up to, for example, 300 ANSI Lumens under normal indoor illumination conditions. The projector  102  may, for example, be a Dell DLP M110 portable projector (e.g., a DLP projector) or other similar DLP projector. 
     In some embodiments, the projector  102  may include or be attached to an optical lens converter. The converter may reduce the focal length of the projector  102  and increase the viewing angle of the projector  102 . For example, the projector  102  may be attached to a Nikon Fisheye Converter FC-E8 or similar converter. The converter may, for example, allow the projector  102  to display the facial image on the entire face mask  104  of the robotic head  100  from a relatively close distance. In some embodiments, various optical element such as, for example, a prism or a mirror, may be used to project images to the face mask  104  such as, for example, to make the distance between the projector and the mask shorter and the head more compact. 
     In some embodiments, the robotic head  100  may include a neck system. In some embodiments, the neck system may control the projector  102  and/or position of the face mask  104 . In some embodiments, a character animation application may control the neck system to rotate the face mask  104  to track user faces (hereinafter referred to as “face tracking”) and user hand gestures (hereinafter referred to as “hand gesture tracking”). In some embodiments, a user face and/or user hand gesture tracking device may be included as part of the robotic head  100 . 
     In some embodiments, the neck system may include a pan-tilt unit  108 . In some embodiments, the pan-tilt unit  108  may move the head in three degrees of freedom that may provide, for example, one-hundred to one-hundred fifty degrees of yaw (x-y), fifteen to thirty degrees of pitch (x-z plane), and/or fifteen to thirty degrees of roll (y-z plane). In some embodiments, the neck system may include the pan-tilt unit later described in  FIGS. 3A and 3B . In some embodiments, the pan-tilt unit  108  may include one or more gears and/or servomotors  110 . The gears may, for example, be low friction and/or constructed from plastic or similar material. The servomotors  110  may, for example, be brushless. In some embodiments, the gears may include any suitable gear ratio. In some embodiments, a first and a second gear may have a ratio of about 7:6. Also, the servomotors  110  may have any suitable speed, such as, for example, 0.15 sec/60° and/or 0.20 sec/60°. In some embodiments the suitable speed may be, for example, 0.05 sec/60°, 0.10 sec/60°, 0.15 sec/60°, 0.20 sec/60°, 0.30 sec/60°, 0.35 sec/60°, 0.40 sec/60°, etc. In some embodiments, the servomotors  110  may include one or more Hitec 7594SH servomotors, which may have a speed of 0.15 sec/60° and/or a torque of 333 oz-in, or other similar servomotor. The servomotors may have any other torque from about 20 oz-in to 500 oz-in or more. In some embodiments, the servomotors  110  may include one or more Futaba S3010 servomotors, which may have a speed of 0.20 sec/60° and/or a torque of 72 oz-in, or other similar servomotor. In some embodiments, a first servomotor may include a Hitec 7594SH servomotor, a Dynamixel servo motor, or other similar servomotor, and a second servomotor may include a Futaba S3010 servomotor or other similar servomotor. The design of the components of the neck system, including the pan-tilt unit  108 , may allow it to be light, compact, and quiet. In some embodiments, the neck system and/or the projector  102  may be sized to be covered by the face mask  104 . In some embodiments, the user may control the distance from the face mask  104  to the lens  106  in order to project the clearest possible image. 
     In some embodiments, the face mask  104  may be created using a mold of a 3D model. In some embodiments, the 3D model may include a neutral face. The mold may be, for example, created using a 3D printer and used to vacuum form a sheet of plastic or other material with similar properties. In some embodiments, the sheet may have a variety of thicknesses, such as, for example, approximately one-sixteenth, one-eighth, one-quarter, etc. of an inch thick. In some embodiments, the plastic may be translucent, clear, white, and/or acrylic plastic. The plastic may be coated by rear project paint. 
     In some embodiments, the face mask  104  may include various facial features. For example, the face mask  104  may include a nose-shaped portion that extends outwardly from the face mask  104 . As another example, the face mask  104  may include two eye-shaped portions above the nose shaped portion. As another example, the face mask  104  may include a mouth-shaped portion that is positioned below the nose-shaped portion. Various other facial features may also be included such as, for example, cheeks, a forehead, a bridge, a chin, etc. The facial features of the face mask  104  may only be geometrically similar to real facial features and/or may not include any color. 
     In some embodiments, a wig  112  may be mounted on the robotic head  100 . The wig  112  may be mounted to the robotic head  100  using any number of means; for example, a bar or band extending from a top of the face mask  104  to the projector  102 . The wig  112  may cover any stray light coming from the sides of the face mask  104  and/or any joints between the face mask  104  and the head enclosure  206 . 
     In some embodiments, the character animation application of the robotic head may create the facial image based on a multi-target morphing method. In some embodiments, the character animation application may process recorded utterances using a speech recognizer, such as, for example, Bavieca, an open source speech recognizer. In some embodiments, the speech recognizer may receive a sequence of words and a speech waveform as input and may provide a time-aligned phonetic transcription of the spoken utterance to the character animation application and/or produce a visual representation of the speech through the projector onto the face mask. 
     Any type of visual speech algorithm may be used to modify the image of the face in conjunction with speech or produce character animation images. One example, is a visual speech algorithm from Boulder Language Technologies. In some embodiments, the speech recognizer may represent aligned phonemes using, for example, the International Phonetic Alphabet (IPA). In some embodiments, the speech recognizer may group visually similar phonemes into units called visemes. For example, the consonants /b/, /p/, and /m/ in the words “buy,” “pie,” and “my” may form a single viseme class. English phonemes may be, for example, categorized into one or more classes, such as, for example, twenty viseme classes. In some embodiments, the viseme classes may represent articulation targets that lips and tongue move to during speech production. 
     In some embodiments, facial images may be designed for one or more viseme classes. In some embodiments, during speech production by the robotic head  100 , the character animation application may receive the time-aligned phonetic transcription from the speech recognizer and convert the phonetic symbols into corresponding visemes. In some embodiments, the visemes may specify movements of the mouth and tongue, which may be synchronized with recorded or synthesized speech. 
     In some embodiments, the facial images may include one or more portions. For example, facial images may include three portions, including eyes, face, and hair. In some embodiments, the character animation application may interchange corresponding portions of the facial images. For example, an eye portion of a first facial image may be interchanged with an eye portion of a second facial image or, for example, a face portion of a first facial image may be interchanged with a face portion of a second facial image. In some embodiments, the character animation application may control the eye portion independently of the other portions of the facial image. In some embodiments, eye gaze may be controlled independently of facial expression. In some embodiments, the eye portion may be controlled in concert with, for example, face tracking and/or hand gesture tracking. 
       FIG. 1B  is another perspective view of the robotic head  100  illustrated in  FIG. 1A . 
       FIG. 2A  is a perspective view of another example robotic head  200 , with a face mask removed. Various or some aspects of the robotic head  200  may be similar and/or include aspects from robotic head  100 . In some embodiments, the robotic head  200  may include a display system. In some embodiments, the display system may include a projector  202  that projects the facial image on a face mask of the robotic head  200 . The projector  202  may include or correspond to the projector  102  of  FIG. 1A  or  FIG. 1B . The projector  202  may include a lens  203  with a wide-projection angle, such as, for example, a fish eye lens. Specifically, in some embodiments, the lens  203  may include a  180  degree fish eye lens. In some embodiments, the lens  203  may allow a facial image to cover an entire face mask from a short baseline. Thus, in some embodiments, the robotic head  200  may have a small form factor. In some embodiments, the projector  202  may be located substantially close to the face mask and/or inside the robotic head  200 . One or all components of the robotic head  200  may fit inside the robotic head  200 . In some embodiments, the robotic head  200  may be portable. 
     In some embodiments, the robotic head  200  may include a neck system. The neck system may include a neck system  204 . In some embodiments, the neck system may control the rotation, orientation, position, yaw, tilt, pan, pitch, and/or roll of the projector  202  and/or the face mask  210 . The face mask  210  may include or correspond to the face mask  104  of  FIG. 1A  or  FIG. 1B . In some embodiments, the robotic head  200  may include the character animation application described with respect to  FIG. 1A  or  FIG. 1B . The character animation application, as described with respect to  FIG. 1A  or  FIG. 1B , may control the neck system to rotate the face mask  210  for face tracking and/or hand gesture tracking. 
     In some embodiments, the robotic head  200  may include a head enclosure  206 . In some embodiments, the head enclosure  206  may be shaped and sized to be human-like. The head enclosure  206 , for example, may have a half-ovoid shape. The head enclosure  206 , for example, may have a front side that has a concave shape and a back side that has a convex shape. 
     In some embodiments, the head enclosure may prevent any projected light from being scattered from the sides of the robotic head, which may make the projected facial image on the mask look brighter. For example, the head enclosure  206  may be substantially spherical to resemble the shape of a human head. In some embodiments, the projector  202  may be located within the head enclosure  206  or at the back of the head enclosure  206 . Alternatively or additionally, the head enclosure  206  may include an opening through which the projector  202  may display a facial image. The projector  202  and/or lens  203  may fit through the opening on the rear side of the head enclosure  206 . For example, the projector  202  may extend through the opening such that the lens  203  of the projector  202  may be located inside the head enclosure  206  while a portion of the projector  202  may be located outside and behind the head enclosure  206 . 
       FIG. 2B  is a transparent side view of an example neck system of the robotic head  200  illustrated in  FIG. 2A . In some embodiments, the neck system may include a pan-tilt unit  208 . In some embodiments, the pan-tilt unit  208  may include or correspond to the pan-tilt unit  108  of  FIG. 1A  and/or  FIG. 1B . In some embodiments, the pan-tilt unit  208  may move the face mask  104  in two degrees of freedom. The pan-tilt unit  208 , for example, may have a foot print of less than about thirty-six square inches. 
     As illustrated in  FIG. 2C , in some embodiments, the neck system  204  may include a lower portion that may act as a base and provide support for the robotic head  200 . In some embodiments, the lower portion may be substantially in a shape of a box. In some embodiments, the lower portion may be square, rectangular, or in another shape such as the shape of a human body torso that may provide support to the robotic head  200  and/or cover the pan-tilt unit  208 . The neck system  204  may be shaped and sized to be human-like. A middle portion of the neck system  204  may be substantially in a form of a human neck. The middle portion may be cylindrical and may provide support for the robotic head  200 . An upper portion of the neck system  204  may be substantially in a form of a human neck and/or human shoulders. The upper portion may be wider than the middle portion of the neck system  204 . The neck system  204  may hide one or more wires and/or electrical components, and may also include locations to, for example, mount a USB and/or insert a power input. 
       FIG. 2D  is a perspective view of the robotic head  200  illustrated in  FIG. 2A , with an example facial image. In some embodiments, a face mask  210  may be a translucent face mask onto which a 2D or 3D facial image may be light-projected. In some embodiments, the face mask  210  may act as a rear-projection screen to which the projector  202  may project. The face mask  210  may include or correspond to the face mask  104  of  FIG. 1A  or  FIG. 1B . In some embodiments described, the face mask  210  may be removable and/or interchangeable. The face mask  210  may be attached to the head enclosure  206  using, for example, a clip, snap, tie, buckle, hook or another fastener. The face mask  210  may be created using a mold of a 3D model in the same or similar way as described with respect to face mask  104  of  FIG. 1A  or  FIG. 1B , and may be easily and quickly customized. The face mask  210  may be constructed from plastic or similar material. The material may be translucent, white, and/or acrylic. An image may be calibrated to a new mask using the calibration method described in further detail in  FIG. 4 . 
     In some embodiments, the face mask  210  and/or head enclosure  206  may be sized to be covered by the face mask  210 . In some embodiments, using the character animation application, the user may control the distance from the face mask  210  to the lens  203  in order to project the clearest possible image. 
     As illustrated in  FIGS. 2E and 2F , in some embodiments, the face mask  210  may include a neutral face capable of accommodating many different types of facial images and many facial expressions. In some embodiments, the face mask  210  may include smoothed features that resemble of a human face. 
       FIG. 3A  is a perspective view of an example pan-tilt unit  300  with two degrees of freedom. In some embodiments, the pan-tilt unit  300  may be included in the neck system of robotic head  100  and/or robotic head  200 . In some embodiments, the pan-tilt unit  300  may move the robotic head  100  and/or robotic head  200  with two degrees of freedom, such as, for example, pitch and yaw. In some embodiments, the pan-tilt unit  300  may include one or more gears  302  and/or servomotors  304 . In some embodiments, the gears  302  may, for example, be low friction and/or constructed from plastic or a similar material. In some embodiments, the servomotors  304  may, for example, be brushless. In some embodiments, the servomotors  304  may support the weight of the projector  202  and/or the head enclosure  206 . The lens  203  may be located at a distance above the servomotors  304 , such as, for example, approximately six to eight inches. In some embodiments, the pan-tilt unit  300  may include one or more bearings  306 . In some embodiments, the bearings  306  may provide points of support for the pan-tilt unit  300 . In some embodiments, the bearings  306  may be located on a vertical rod  308 . In some embodiments, a gear hub  312  attached to the one or more gears  302  may be connected to the vertical rod  308  by a fastener, such as, for example, a pin. In some embodiments, the a first end of the vertical rod  308  may located proximate to the base  309  of the pan-tilt unit  300 , and a second end of the vertical rod  308  may be attached to a platform  310 . In some embodiments, the first end of the vertical rod  308  may not touch the base  309 . In some embodiments, a tilt system of the pan-tilt unit  300  may be located on top of the platform  310 , which may be supported by the vertical rod  308 . In some embodiments, the bearings  306  and vertical rod  308  may allow the robotic head  200  to turn or swivel around a stable central axis through the use of the gears  302 . 
     The pan-tilt unit  300  may include, for example, two or more bearings  306  on the vertical rod  308 , which may be located a distance away from each other on the vertical rod  308 . In some embodiments, the two bearings  306  may be located, for example, approximately two inches away from each other on the vertical rod  308 . In some embodiments, a first of the two bearings  306  may be attached or embedded to the base  309  and may reduce bending moment to prevent wobbling. In some embodiments, a second of the two bearings  306  may be located above the first of the two bearings  306  on the vertical rod  308  and may support a vertical load. In some embodiments, the second of the two bearings  306  may be located towards the middle of the vertical rod  308 . In some embodiments, the second of the two bearings  306  may be attached to a platform  314 , which may be supported by one or more legs to provide additional support for the vertical rod  308 . In some embodiments, the second of the two bearings  306  may be located approximately two inches above the first of the two bearings  306 . In some embodiments, the bearings  306  may include a flange mount and/or one or more screw to attach to the vertical rod  308  to support a vertical load. In some embodiments, the vertical rod  308  may be constructed of aluminum or a similar material capable of providing support. 
     In some embodiments, a facial image may correspond to a facial expression, such as, for example, neutral, anger, disgust, fear, joy, sadness, or surprise. In some circumstances, an emotion and a viseme may conflict when combined in a facial expression. Conflicting facial expressions and visemes may be blended by the character animation application according to various models in order to avoid any unnatural appearance resulting from combining an emotion with a viseme. For example, in order to avoid any unnatural appearance resulting from combining an emotion with a viseme, a viseme and an emotion that are to be combined may be assigned a weight factor and a maximum emotion weight, respectively. 
     In Some embodiments, the facial expression morph targets may be split into upper and lower face morph targets. The upper face targets, for example, may include everything from the tip of the nose upwards. The lower face targets, for example, may include the region below the nose; mainly the lips, lower cheeks and chin. This partitioning of the face may enable us to adjust the weight of just the lower face morph target weights so that the upper face may remain consistent with the morph targets of desired expressions. For labial and labiodental visemes (those for the letters m, b, p, f and v) that require the avatar&#39;s lips to be closed or nearly closed to look natural, visemes pre-blended with the open mouthed emotions may be used. These may be used to replace the viseme and lower face expression when they come up in combination. 
     Some embodiments include a robotic head projection calibration method. The calibration method, for example, may be used to determine any image distortion caused by the optical system, lens, mirrors, projector, and/or the face mask. The method may include projecting a two-dimensional image of a face with a plurality of fiducial marker points onto a rear surface of a face mask. The plurality of fiducial marker points may include, for example, a plurality of grid lines. The plurality of fiducial marker points may include, for example, points that correspond to facial features such as, for example, corners of one or more eyes, corners of the mouth, points of the noise, points on the chin, points on the eyebrows, etc. 
     In some embodiments, an image of the face mask may be recorded with the plurality of fiducial marker points projected onto the rear surface of the face mask. The image may be recorded, for example, using a camera disposed within the robotic head. 
     In some embodiments, a plurality of distances between the location of each of the plurality of fiducial marker points on the face mask relative to an expected location of each of the plurality of fiducial marker points on the face mask may be determine. For example, if one of the fiducial marker points is the corner of the left eye. The distance between the corner of the left eye and the actual position of the fiducial marker point on the face mask may be determined or estimated based on the recorded image of the facemask. The distance, for example, may be determined as the number of pixels between the fiducial marker point and the corner of the left eye. 
     In some embodiments, a transformation based on the plurality of distances between the fiducial marker points and the actual positions on the face mask may be calculated. In some embodiments, the transformation may be applied to two-dimensional images of a face prior to projecting the images on the face mask. In some embodiments, the inverse of the transformation may be applied. 
     In some embodiments, a character animation application may be used to calibrate the facial image to reduce any distortion of the facial image on the face mask  104  and/or the face mask  210  that may be caused by a projector and/or a lens. In some embodiments, the character animation application may calibrate the facial image one time prior to run-time, or it may calibrate the facial image at run time in each frame. In some embodiments, in order to achieve a smooth animation displaying at, for example, thirty frames-per-second (fps), the original facial image may be calibrated instead of rectifying the facial image at run time in each frame. 
     In some embodiments, in order to calibrate the facial image, a flat screen may be placed approximately in front of or behind the face mask  104  and/or the face mask  210 . A neutral 3D facial image may be mapped, for example, to screen coordinates according to the following expression:
 
 S=NWVP  
 
In the above-expression, N represents a model of the neutral 3D facial image in virtual 3D coordinates, as illustrated in  FIG. 4A . W, V, and P represent world (W), view (V), and projection (P) matrices, respectively. S may represent a model of the neutral 3D facial image mapped to screen coordinates, as illustrated in  FIG. 4B .
 
     M may represent a model of S projected to the face mask, as illustrated in  FIG. 4C , or in other words, M=project(S). M′ may represent a distorted model of S that appears undistorted when projected to the face mask. In some embodiments, the character animation application may find N′, where N′ may represent a distorted model of the neutral 3D facial image in virtual 3D coordinates, such that M′=project(S′) looks undistorted on the face mask, where
 
 S′=N′WVP.  
 
     In some embodiments, the character animation application may create a checkerboard in the screen coordinates, as illustrated in  FIG. 4B , which may be projected on the face mask, as illustrated in  FIG. 4C . In some embodiments, the character animation application may define a piecewise homography or other geometry transformations mapping between rectangles projected on the face mask and triangles on an image of the face mask displayed on the screen, as illustrated in  FIG. 4D . In some embodiments, in order to find M′, the character animation application may apply an affine transformation to place a mold, used to create the face mask, on an image of the face mask, as illustrated in  FIG. 4D . Further, in some embodiments, the character animation application may apply the piecewise homography or other geometry transformations on the mold model and replace the corresponding vertices of the model of the neutral facial image in the screen coordinates, S, with a distorted mold model to estimate S′. N′ may be determined according to the expression:
 
 N′=S ′( WVP ) −1 ,
 
where N′, S′, W, V, and P are defined as above. The character animation application use the above described calibration method to display a wide variety of facial images on the face mask  104  and/or the face mask  210 , such as, for example, cartoon-like, animated, and/or photorealistic facial images.
 
     In some embodiments, the robotic head  100  and/or the robotic head  200  may include one or more speakers that are used to produce audio speech. In some embodiments, the robotic head  100  and/or the robotic head  200  may include a proximity detector that may recognize facial expressions and/or body language of a user. The visual speech and/or animation provided by the robotic head may be in response to the facial expressions and/or the body language of the user. In some embodiments, the robotic head  100  and/or the robotic head  200  may include a computer system that may be used to run calibration processes, speech recognition, speech responses, visual animation, etc. 
     The term “substantially” means within 5% or 10% of the value referred to or within manufacturing tolerances. 
     Various embodiments are disclosed. The various embodiments may be partially or completely combined to produce other embodiments. 
     Numerous specific details are set forth herein to provide a thorough understanding of the claimed subject matter. However, those skilled in the art will understand that the claimed subject matter may be practiced without these specific details. In other instances, methods, apparatuses, or systems that would be known by one of ordinary skill have not been described in detail so as not to obscure claimed subject matter. 
     The use of “adapted to” or “configured to” herein is meant as open and inclusive language that does not foreclose devices adapted to or configured to perform additional tasks or steps. Additionally, the use of “based on” is meant to be open and inclusive, in that a process, step, calculation, or other action “based on” one or more recited conditions or values may, in practice, be based on additional conditions or values beyond those recited. Headings, lists, and numbering included herein are for ease of explanation only and are not meant to be limiting. 
     While the present subject matter has been described in detail with respect to specific embodiments thereof, it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing, may readily produce alterations to, variations of, and equivalents to such embodiments. Accordingly, it should be understood that the present disclosure has been presented for-purposes of example rather than limitation, and does not preclude inclusion of such modifications, variations, and/or additions to the present subject matter as would be readily apparent to one of ordinary skill in the art.