Patent Publication Number: US-2023140737-A1

Title: Drift cancelation for portable object detection and tracking

Description:
RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 17/409,675 filed on Aug. 23, 2021, issued as U.S. Pat. No. 11,537,196 on Dec. 27, 2022, entitled “DRIFT CANCELATION FOR PORTABLE OBJECT DETECTION AND TRACKING” (Docket No. ULTI 1037-7); which is a continuation of U.S. application Ser. No. 16/600,175 filed on Oct. 11, 2019, issued as U.S. Pat. No. 11,099,630 on Aug. 24, 2021, entitled “DRIFT CANCELATION FOR PORTABLE OBJECT DETECTION AND TRACKING” (Docket No. ULTI 1037-6); which is a continuation of U.S. application Ser. No. 16/016,292, filed on Jun. 22, 2018, issued as U.S. Pat. No. 10,444,825 on Oct. 15, 2019, entitled “DRIFT CANCELATION FOR PORTABLE OBJECT DETECTION AND TRACKING” (Docket No. ULTI 1037-5); which is a continuation of U.S. application Ser. No. 14/620,093, filed on Feb. 11, 2015, issued as U.S. Pat. No. 10,007,329 on Jun. 26, 2018, entitled “DRIFT CANCELATION FOR PORTABLE OBJECT DETECTION AND TRACKING” (Docket No. LEAP 1037-2/LPM-1037US1); which claims the benefit of U.S. Provisional Application No. 61/938,635 filed on Feb. 11, 2014, entitled “DRIFT CANCELATION FOR PORTABLE OBJECT DETECTION AND TRACKING” (Docket No. LEAP 1037-1/LPM-1037PR). The provisional and non-provisional applications are hereby incorporated by reference for all purposes. 
     This application is related to U.S. patent application Ser. No. 14/620,182 filed on Feb. 11, 2015, entitled “SYSTEMS AND METHODS OF INTEGRATING THREE-DIMENSIONAL (3D) SPACE SENSING WITH VIRTUAL REALITY/AUGMENTED REALITY HEAD MOUNTED DEVICES” (Docket No. LEAP 1037-3/LPM-1037US2). 
    
    
     FIELD OF THE TECHNOLOGY DISCLOSED 
     The present disclosure relates generally to human machine interface and in particular to drift cancellation techniques enabling portable object detection and tracking. 
     BACKGROUND 
     The subject matter discussed in this section should not be assumed to be prior art merely as a result of its mention in this section. Similarly, a problem mentioned in this section or associated with the subject matter provided as background should not be assumed to have been previously recognized in the prior art. The subject matter in this section merely represents different approaches, which in and of themselves can also correspond to implementations of the claimed technology. 
     Conventional motion capture approaches rely on markers or sensors worn by the subject while executing activities and/or on the strategic placement of numerous bulky and/or complex equipment in specialized and rigid environments to capture subject movements. Unfortunately, such systems tend to be expensive to construct. In addition, markers or sensors worn by the subject can be cumbersome and interfere with the subject&#39;s natural movement. Further, systems involving large numbers of cameras tend not to operate in real time, due to the volume of data that needs to be analyzed and correlated. Such considerations have limited the deployment and use of motion capture technology. 
     Consequently, there is a need for improved devices with greater portability and techniques for capturing the motion of objects in real time without fixed or difficult to configure sensors or markers. 
     SUMMARY 
     Implementations of the technology disclosed address these and other problems by providing methods and systems for capturing motion and/or determining the path of an object traveling in relation to a movable or moving frame of reference associated with one or more optical, acoustic or vibrational sensors. Implementations can enable use of portable devices, e.g., head mounted displays (HMDs), wearable goggles, watch computers, smartphones, and so forth, and/or mobile devices, e.g., autonomous and semi-autonomous robots, factory floor material handling systems, autonomous mass-transit vehicles, automobiles (human or machine driven), and so forth that comprise sensors and processors employing optical, audio or vibrational detection mechanisms suitable for providing gesture detection, personal virtual device experiences, autonomous vehicle control, and other machine control and/or machine communications applications. 
     In one implementation, motion sensors and/or other types of sensors are coupled to a motion-capture system to monitor motion of at least the sensor of the motion-capture system resulting from, for example, users&#39; touch. Information from the motion sensors can be used to determine first and second positional information of the sensor with respect to a fixed point at first and second times. Difference information between the first and second positional information is determined. Movement information for the sensor with respect to the fixed point is computed based upon the difference information. The movement information for the sensor is applied to apparent environment information sensed by the sensor to remove motion of the sensor therefrom to yield actual environment information; which can be communicated. Control information can be communicated to a system configured to provide a virtual reality or augmented reality experience via a portable device and/or to systems controlling machinery or the like based upon motion capture information for an object moving in space derived from the sensor and adjusted to remove motion of the sensor itself. In some applications, a virtual device experience can be augmented by the addition of haptic, audio and/or visual projectors. 
     In an implementation, apparent environmental information is captured from positional information of an object portion at the first time and the second time using a sensor of the motion-capture system. Object portion movement information relative to the fixed point at the first time and the second time is computed based upon the difference information and the movement information for the sensor. 
     In further implementations, a path of the object is calculated by repeatedly determining movement information for the sensor, using the motion sensors, and the object portion, using the sensor, at successive times and analyzing a sequence of movement information to determine a path of the object portion with respect to the fixed point. Paths can be compared to templates to identify trajectories. Trajectories of body parts can be identified as gestures. Gestures can indicate command information to be communicated to a system. Some gestures communicate commands to change operational modes of a system (e.g., zoom in, zoom out, pan, show more detail, next display page, and so forth). 
     Advantageously, some implementations can enable gesture recognition for use in wearable or other personal devices. This capability allows the user to execute intuitive gestures involving virtualized contact with a virtual object. For example, a device can be provided a capability to distinguish motion of objects from motions of the device itself in order to facilitate proper gesture recognition. Some implementations can provide improved interfacing with a variety of portable or wearable machines (e.g., smart telephones, portable computing systems, including laptop, tablet computing devices, personal data assistants, special purpose visualization computing machinery, including heads up displays (HUD) for use in aircraft or automobiles for example, wearable virtual and/or augmented reality systems, including Google Glass, and others, graphics processors, embedded microcontrollers, gaming consoles, or the like; wired or wirelessly coupled networks of one or more of the foregoing, and/or combinations thereof), obviating or reducing the need for contact-based input devices such as a mouse, joystick, touch pad, or touch screen. Some implementations can provide for improved interface with computing and/or other machinery than would be possible with heretofore known techniques. In some implementations, a richer human—machine interface experience can be provided. 
     Other aspects and advantages of the present technology can be seen on review of the drawings, the detailed description and the claims, which follow. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the drawings, like reference characters generally refer to like parts throughout the different views. Also, the drawings are not necessarily to scale, with an emphasis instead generally being placed upon illustrating the principles of the disclosed technology. In the following description, various implementations of the technology disclosed are described with reference to the following drawings, in which: 
         FIG.  1    illustrates a system for capturing image and other sensory data according to an implementation of the technology disclosed. 
         FIG.  2    is a simplified block diagram of a computer system implementing image analysis suitable for supporting a virtual environment enabled apparatus according to an implementation of the technology disclosed. 
         FIG.  3 A  is a perspective view from the top of a sensor in accordance with the technology disclosed, with motion sensors along an edge surface thereof. 
         FIG.  3 B  is a perspective view from the bottom of a sensor in accordance with the technology disclosed, with motion sensors along the bottom surface thereof. 
         FIG.  3 C  is a perspective view from the top of a sensor in accordance with the technology disclosed, with detachable motion sensors configured for placement on a surface. 
         FIG.  4    illustrates apparent movement of objects from the perspective of the user of a virtual environment enabled apparatus in accordance with the technology disclosed. 
         FIG.  5    illustrates apparent movement of objects from the perspective of the user of a virtual environment enabled apparatus in accordance with the technology disclosed. 
         FIG.  6    shows a flowchart of one implementation of determining motion information in a movable sensor apparatus. 
         FIG.  7    shows a flowchart of one implementation of applying movement information to apparent environment information sensed by the sensor to yield actual environment information in a movable sensor apparatus. 
         FIG.  8    illustrates one implementation of a system for providing a virtual device experience. 
         FIG.  9    shows a flowchart of one implementation of providing a virtual device experience. 
         FIG.  10    shows a flowchart of one implementation of cancelling drift in a head mounted device (HMD). 
     
    
    
     DETAILED DESCRIPTION 
     Among other aspects, the technology described herein with reference to example implementations can provide for automatically (e.g., programmatically) cancelling out motions of a movable sensor configured to capture motion and/or determining the path of an object based on imaging, acoustic or vibrational waves. Implementations can enable gesture detection, virtual reality and augmented reality, and other machine control and/or machine communications applications using portable devices, e.g., head mounted displays (HMDs), wearable goggles, watch computers, smartphones, and so forth, or mobile devices, e.g., autonomous and semi-autonomous robots, factory floor material handling systems, autonomous mass-transit vehicles, automobiles (human or machine driven), and so forth, equipped with suitable sensors and processors employing optical, audio or vibrational detection. In some implementations, projection techniques can supplement the sensory based tracking with presentation of virtual (or virtualized real) objects (visual, audio, haptic, and so forth) created by applications loadable to, or in cooperative implementation with, the HMD or other device to provide a user of the device with a personal virtual experience (e.g., a functional equivalent to a real experience). 
     Some implementations include optical image sensing. For example, a sequence of images can be correlated to construct a 3-D model of the object, including its position and shape. A succession of images can be analyzed using the same technique to model motion of the object such as free-form gestures. In low-light or other situations not conducive to optical imaging, where free-form gestures cannot be recognized optically with a sufficient degree of reliability, audio signals or vibrational waves can be detected and used to supply the direction and location of the object as further described herein. 
     Refer first to  FIG.  1   , which illustrates a system  100  for capturing image data according to one implementation of the technology disclosed. System  100  is preferably coupled to a wearable device  101  that can be a personal head mounted display (HMD) having a goggle form factor such as shown in  FIG.  1   , a helmet form factor, or can be incorporated into or coupled with a watch, smartphone, or other type of portable device or any number of cameras  102 ,  104  coupled to sensory processing system  106 . Cameras  102 ,  104  can be any type of camera, including cameras sensitive across the visible spectrum or with enhanced sensitivity to a confined wavelength band (e.g., the infrared (IR) or ultraviolet bands); more generally, the term “camera” herein refers to any device (or combination of devices) capable of capturing an image of an object and representing that image in the form of digital data. For example, line sensors or line cameras rather than conventional devices that capture a two-dimensional (2D) image can be employed. The term “light” is used generally to connote any electromagnetic radiation, which may or may not be within the visible spectrum, and may be broadband (e.g., white light) or narrowband (e.g., a single wavelength or narrow band of wavelengths). 
     Cameras  102 ,  104  are preferably capable of capturing video images (i.e., successive image frames at a constant rate of at least 15 frames per second), although no particular frame rate is required. The capabilities of cameras  102 ,  104  are not critical to the technology disclosed, and the cameras can vary as to frame rate, image resolution (e.g., pixels per image), color or intensity resolution (e.g., number of bits of intensity data per pixel), focal length of lenses, depth of field, etc. In general, for a particular application, any cameras capable of focusing on objects within a spatial volume of interest can be used. For instance, to capture motion of the hand of an otherwise stationary person, the volume of interest might be defined as a cube approximately one meter on a side. 
     As shown, cameras  102 ,  104  can be oriented toward portions of a region of interest  112  by motion of the device  101 , in order to view a virtually rendered or virtually augmented view of the region of interest  112  that can include a variety of virtual objects  116  as well as contain an object of interest  114  (in this example, one or more hands) that moves within the region of interest  112 . One or more sensors  108 ,  110  capture motions of the device  101 . In some implementations, one or more light sources  115 ,  117  are arranged to illuminate the region of interest  112 . In some implementations, one or more of the cameras  102 ,  104  are disposed opposite the motion to be detected, e.g., where the hand  114  is expected to move. This is an optimal location because the amount of information recorded about the hand is proportional to the number of pixels it occupies in the camera images, and the hand will occupy more pixels when the camera&#39;s angle with respect to the hand&#39;s “pointing direction” is as close to perpendicular as possible. Sensory processing system  106 , which can be, e.g., a computer system, can control the operation of cameras  102 ,  104  to capture images of the region of interest  112  and sensors  108 ,  110  to capture motions of the device  101 . Information from sensors  108 ,  110  can be applied to models of images taken by cameras  102 ,  104  to cancel out the effects of motions of the device  101 , providing greater accuracy to the virtual experience rendered by device  101 . Based on the captured images and motions of the device  101 , sensory processing system  106  determines the position and/or motion of object  114 . 
     For example, as an action in determining the motion of object  114 , sensory processing system  106  can determine which pixels of various images captured by cameras  102 ,  104  contain portions of object  114 . In some implementations, any pixel in an image can be classified as an “object” pixel or a “background” pixel depending on whether that pixel contains a portion of object  114  or not. Object pixels can thus be readily distinguished from background pixels based on brightness. Further, edges of the object can also be readily detected based on differences in brightness between adjacent pixels, allowing the position of the object within each image to be determined. In some implementations, the silhouettes of an object are extracted from one or more images of the object that reveal information about the object as seen from different vantage points. While silhouettes can be obtained using a number of different techniques, in some implementations, the silhouettes are obtained by using cameras to capture images of the object and analyzing the images to detect object edges. Correlating object positions between images from cameras  102 ,  104  and cancelling out captured motions of the device  101  from sensors  108 ,  110  allows sensory processing system  106  to determine the location in 3D space of object  114 , and analyzing sequences of images allows sensory processing system  106  to reconstruct 3D motion of object  114  using conventional motion algorithms or other techniques. See, e.g., U.S. patent application Ser. No. 13/414,485 (filed on Mar. 7, 2012) and U.S. Provisional Patent Application Nos. 61/724,091 (filed on Nov. 8, 2012) and 61/587,554 (filed on Jan. 7, 2012), the entire disclosures of which are hereby incorporated by reference. 
     Presentation interface  120  employs projection techniques in conjunction with the sensory based tracking in order to present virtual (or virtualized real) objects (visual, audio, haptic, and so forth) created by applications loadable to, or in cooperative implementation with, the device  101  to provide a user of the device with a personal virtual experience. Projection can include an image or other visual representation of an object. 
     One implementation uses motion sensors and/or other types of sensors coupled to a motion-capture system to monitor motions within a real environment. A virtual object integrated into an augmented rendering of a real environment can be projected to a user of a portable device  101 . Motion information of a user body portion can be determined based at least in part upon sensory information received from cameras  102 ,  104  or acoustic or other sensory devices. Control information is communicated to a system based in part on a combination of the motion of the portable device  101  and the detected motion of the user determined from the sensory information received from cameras  102 ,  104  or acoustic or other sensory devices. The virtual device experience can be augmented in some implementations by the addition of haptic, audio and/or other sensory information projectors. For example, with reference to  FIG.  8   , optional video projection mechanism  804  can project an image of a page (e.g., virtual device  801 ) from a virtual book object superimposed upon a desk (e.g., surface portion  116 ) of a user; thereby creating a virtual device experience of reading an actual book, or an electronic book on a physical e-reader, even though no book or e-reader is present. Optional haptic projector  806  can project the feeling of the texture of the “virtual paper” of the book to the reader&#39;s finger. Optional audio projector  802  can project the sound of a page turning in response to detecting the reader making a swipe to turn the page. 
     A plurality of sensors  108 ,  110  can coupled to the sensory processing system  106  to capture motions of the device  101 . Sensors  108 ,  110  can be any type of sensor useful for obtaining signals from various parameters of motion (acceleration, velocity, angular acceleration, angular velocity, position/locations); more generally, the term “motion detector” herein refers to any device (or combination of devices) capable of converting mechanical motion into an electrical signal. Such devices can include, alone or in various combinations, accelerometers, gyroscopes, and magnetometers, and are designed to sense motions through changes in orientation, magnetism or gravity. Many types of motion sensors exist and implementation alternatives vary widely. 
     The illustrated system  100  can include any of various other sensors not shown in  FIG.  1    for clarity, alone or in various combinations, to enhance the virtual experience provided to the user of device  101 . For example, in low-light situations where free-form gestures cannot be recognized optically with a sufficient degree of reliability, system  106  may switch to a touch mode in which touch gestures are recognized based on acoustic or vibrational sensors. Alternatively, system  106  may switch to the touch mode, or supplement image capture and processing with touch sensing, when signals from acoustic or vibrational sensors are sensed. In still another operational mode, a tap or touch gesture may act as a “wake up” signal to bring the image and audio analysis system  106  from a standby mode to an operational mode. For example, the system  106  may enter the standby mode if optical signals from the cameras  102 ,  104  are absent for longer than a threshold interval. 
     It will be appreciated that the figures shown in  FIG.  1    are illustrative. In some implementations, it may be desirable to house the system  100  in a differently shaped enclosure or integrated within a larger component or assembly. Furthermore, the number and type of image sensors, motion detectors, illumination sources, and so forth are shown schematically for the clarity, but neither the size nor the number is the same in all implementations. 
     Refer now to  FIG.  2   , which shows a simplified block diagram of a computer system  200  for implementing sensory processing system  106 . Computer system  200  includes a processor  202 , a memory  204 , a motion detector and camera interface  206 , a presentation interface  120 , speaker(s)  209 , a microphone(s)  210 , and a wireless interface  211 . Memory  204  can be used to store instructions to be executed by processor  202  as well as input and/or output data associated with execution of the instructions. In particular, memory  204  contains instructions, conceptually illustrated as a group of modules described in greater detail below, that control the operation of processor  202  and its interaction with the other hardware components. An operating system directs the execution of low-level, basic system functions such as memory allocation, file management and operation of mass storage devices. The operating system may include a variety of operating systems such as Microsoft WINDOWS operating system, the Unix operating system, the Linux operating system, the Xenix operating system, the IBM AIX operating system, the Hewlett Packard UX operating system, the Novell NETWARE operating system, the Sun Microsystems SOLARIS operating system, the OS/2 operating system, the BeOS operating system, the MACINTOSH operating system, the APACHE operating system, an OPENACTION operating system, iOS, Android or other mobile operating systems, or another operating system of platform. 
     The computing environment may also include other removable/non-removable, volatile/nonvolatile computer storage media. For example, a hard disk drive may read or write to non-removable, nonvolatile magnetic media. A magnetic disk drive may read from or writes to a removable, nonvolatile magnetic disk, and an optical disk drive may read from or write to a removable, nonvolatile optical disk such as a CD-ROM or other optical media. Other removable/non-removable, volatile/nonvolatile computer storage media that can be used in the exemplary operating environment include, but are not limited to, magnetic tape cassettes, flash memory cards, digital versatile disks, digital video tape, solid state RAM, solid state ROM, and the like. The storage media are typically connected to the system bus through a removable or non-removable memory interface. 
     Processor  202  may be a general-purpose microprocessor, but depending on implementation can alternatively be a microcontroller, peripheral integrated circuit element, a CSIC (customer-specific integrated circuit), an ASIC (application-specific integrated circuit), a logic circuit, a digital signal processor, a programmable logic device such as an FPGA (field-programmable gate array), a PLD (programmable logic device), a PLA (programmable logic array), an RFID processor, smart chip, or any other device or arrangement of devices that is capable of implementing the actions of the processes of the technology disclosed. 
     Motion detector and camera interface  206  can include hardware and/or software that enables communication between computer system  200  and cameras  102 ,  104 , as well as sensors  108 ,  110  (see  FIG.  1   ). Thus, for example, motion detector and camera interface  206  can include one or more camera data ports  216 ,  218  and motion detector ports  217 ,  219  to which the cameras and motion detectors can be connected (via conventional plugs and jacks), as well as hardware and/or software signal processors to modify data signals received from the cameras and motion detectors (e.g., to reduce noise or reformat data) prior to providing the signals as inputs to a motion-capture (“mocap”) program  214  executing on processor  202 . In some implementations, motion detector and camera interface  206  can also transmit signals to the cameras and sensors, e.g., to activate or deactivate them, to control camera settings (frame rate, image quality, sensitivity, etc.), to control sensor settings (calibration, sensitivity levels, etc.), or the like. Such signals can be transmitted, e.g., in response to control signals from processor  202 , which may in turn be generated in response to user input or other detected events. 
     Instructions defining mocap program  214  are stored in memory  204 , and these instructions, when executed, perform motion-capture analysis on images supplied from cameras and audio signals from sensors connected to motion detector and camera interface  206 . In one implementation, mocap program  214  includes various modules, such as an object analysis module  222  and a path analysis module  224 . Object analysis module  222  can analyze images (e.g., images captured via interface  206 ) to detect edges of an object therein and/or other information about the object&#39;s location. In some implementations, object analysis module  222  can also analyze audio signals (e.g., audio signals captured via interface  206 ) to localize the object by, for example, time distance of arrival, multilateration or the like. (“Multilateration is a navigation technique based on the measurement of the difference in distance to two or more stations at known locations that broadcast signals at known times. See Wikipedia, at http://en.wikipedia.org/w/index.php?title=Multilateration&amp;oldid=523281858, on Nov. 16, 2012, 06:07 UTC). Path analysis module  224  can track and predict object movements in 3D based on information obtained via the cameras. Some implementations will include a Virtual Reality/Augmented Reality environment manager  226  that provides integration of virtual objects reflecting real objects (e.g., hand  114 ) as well as synthesized objects  116  for presentation to user of device  101  via presentation interface  120  to provide a personal virtual experience. One or more applications  228  can be loaded into memory  204  (or otherwise made available to processor  202 ) to augment or customize functioning of device  101  thereby enabling the system  200  to function as a platform. Successive camera images are analyzed at the pixel level to extract object movements and velocities. Audio signals place the object on a known surface, and the strength and variation of the signals can be used to detect object&#39;s presence. If both audio and image information is simultaneously available, both types of information can be analyzed and reconciled to produce a more detailed and/or accurate path analysis. 
     Presentation interface  120 , speakers  209 , microphones  210 , and wireless network interface  211  can be used to facilitate user interaction via device  101  with computer system  200 . These components can be of generally conventional design or modified as desired to provide any type of user interaction. In some implementations, results of motion capture using motion detector and camera interface  206  and mocap program  214  can be interpreted as user input. For example, a user can perform hand gestures or motions across a surface that are analyzed using mocap program  214 , and the results of this analysis can be interpreted as an instruction to some other program executing on processor  200  (e.g., a web browser, word processor, or other application). Thus, by way of illustration, a user might use upward or downward swiping gestures to “scroll” a webpage currently displayed to the user of device  101  via presentation interface  120 , to use rotating gestures to increase or decrease the volume of audio output from speakers  209 , and so on. Path analysis module  224  may represent the detected path as a vector and extrapolate to predict the path, e.g., to improve rendering of action on device  101  by presentation interface  120  by anticipating movement. 
     It will be appreciated that computer system  200  is illustrative and that variations and modifications are possible. Computer systems can be implemented in a variety of form factors, including server systems, desktop systems, laptop systems, tablets, smart phones or personal digital assistants, and so on. A particular implementation may include other functionality not described herein, e.g., wired and/or wireless network interfaces, media playing and/or recording capability, etc. In some implementations, one or more cameras and two or more microphones may be built into the computer rather than being supplied as separate components. Further, an image or audio analyzer can be implemented using only a subset of computer system components (e.g., as a processor executing program code, an ASIC, or a fixed-function digital signal processor, with suitable I/O interfaces to receive image data and output analysis results). 
     While computer system  200  is described herein with reference to particular blocks, it is to be understood that the blocks are defined for convenience of description and are not intended to imply a particular physical arrangement of component parts. Further, the blocks need not correspond to physically distinct components. To the extent that physically distinct components are used, connections between components (e.g., for data communication) can be wired and/or wireless as desired. Thus, for example, execution of object analysis module  222  by processor  202  can cause processor  202  to operate motion detector and camera interface  206  to capture images and/or audio signals of an object traveling across and in contact with a surface to detect its entrance by analyzing the image and/or audio data. 
       FIGS.  3 A- 3 C  illustrate three different configurations of a movable sensor system  300 A-C, with reference to example implementations packaged within a single housing as an integrated sensor. In all cases, sensor  300 A,  300 B,  300 C includes a top surface  305 , a bottom surface  307 , and a side wall  310  spanning the top and bottom surfaces  305 ,  307 . With reference also to  FIG.  3 A , the top surface  305  of sensor  300 A contains a pair of windows  315  for admitting light to the cameras  102 ,  104 , one of which is optically aligned with each of the windows  315 . If the system includes light sources  115 ,  117 , surface  305  may contain additional windows for passing light to the object(s) being tracked. In sensor  300 A, motion sensors  108 ,  110  are located on the side wall  310 . Desirably, the motion sensors are flush with the surface of side wall  310  so that, the motion sensors are disposed to sense motions about a longitudinal axis of sensor  300 A. Of course, the motion sensors can be recessed from side wall  310  internal to the device in order to accommodate sensor operation and placement within available packaging space so long as coupling with the external housing of sensor  300 A remains adequate. In sensor  300 B, motion sensors  108 ,  110  are located proximate to the bottom surface  307 , once again in a flush or recessed configuration. The top surface of the sensor  300 B (not shown in the figure for clarity sake) contains camera windows  315  as shown in  FIG.  3 A . In  FIG.  3 C , motion sensors  108 ,  110  are external contact transducers that connect to sensor  300 C via jacks  320 . This configuration permits the motion sensors to be located away from the sensor  300 C, e.g., if the motion sensors are desirably spaced further apart than the packaging of sensor  300 C allows. In other implementations, movable sensor components of  FIG.  2    can be imbedded in portable (e.g., head mounted displays (HMDs), wearable goggles, watch computers, smartphones, and so forth) or movable (e.g., autonomous robots, material transports, automobiles (human or machine driven)) devices. 
       FIG.  4    illustrates apparent movement of objects from the perspective of the user of a virtual environment enabled apparatus  400  in accordance with the technology.  FIG.  4    shows two views of a user of a device  101  viewing a field of view  113  at two different times. As shown in block  401 , at an initial time t 0 , user is viewing field of view  113   a  using device  101  in a particular initial position to view an area  113   a . As shown in block  402 , device  101  presents to user a display of the device field of view  113   a  that includes objects  114  (hands) in a particular pose. As shown in block  403 , subsequently at time t 1 , the user has repositioned device  101 . Accordingly, the apparent position of objects  114  in the field of view  113   b  shown in block  404  has changed from the apparent position of the objects  114  in field of view  113   a . Even in the case where the hands  114  did not move in space, the user sees an apparent movement of the hands  114  due to the change in position of the device. 
     Now with reference to  FIG.  5   , an apparent movement of one or more moving objects from the perspective of the user of a virtual environment enabled apparatus  500  is illustrated. As shown by block  502 , field of view  113   a  presented by device  101  at time t 0  includes an object  114 . At time t 0 , the position and orientation of tracked object  114  is known with respect to device reference frame  120   a , again at time t 0 . As shown by block  404 , at time t 1 , the position and orientation of both device reference frame  120   b  and tracked object  114  have changed. As shown by block  504 , field of view  113   b  presented by device  101  at time t 1  includes object  114  in a new apparent position. Because the device  101  has moved, the device reference frame  120  has moved from an original or starting device reference frame  120   a  to a current or final reference frame  120   b  as indicated by transformation T. It is noteworthy that the device  101  can rotate as well as translate. Implementations can provide sensing the position and rotation of reference frame  120   b  with respect to reference frame  120   a  and sensing the position and rotation of tracked object  114  with respect to  120   b , at time t 1 . Implementations can determine the position and rotation of tracked object  114  with respect to  120   a  from the sensed position and rotation of reference frame  120   b  with respect to reference frame  120   a  and the sensed position and rotation of tracked object  114  with respect to  120   b.    
     In an implementation, a transformation R T  is determined that moves dashed line reference frame  120   a  to dotted line reference frame  120   b . Applying the reverse transformation −R T  makes the dotted line reference frame  120   b  lie on top of dashed line reference frame  120   a . Then the tracked object  114  will be in the right place from the point of view of dashed line reference frame  120   a . In determining the motion of object  114 , sensory processing system  106  can determine its location and direction by computationally analyzing images captured by cameras  102 ,  104  and motion information captured by sensors  108 ,  110 . For example, an apparent position of any point on the object (in 3D space) at time 
     
       
         
           
             
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                 ⁢ 
                 
                   : 
                   [ 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       x 
                                       ′ 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       ′ 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 z 
                                 ′ 
                               
                             
                           
                         
                       
                     
                     
                       
                         1 
                       
                     
                   
                   ] 
                 
               
             
             , 
           
         
       
     
     using an affine transform 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       R 
                       ref 
                     
                   
                   
                     
                       T 
                       ref 
                     
                   
                 
                 
                   
                     0 
                   
                   
                     1 
                   
                 
               
               ] 
             
             . 
           
         
       
     
     The correct location at time t=t 1  of a point on the tracked object with respect to device reference frame  120   a  is given by equation (1): 
     
       
         
           
             
               
                 
                   
                     
                       [ 
                       
                         
                           
                             
                               R 
                               ref 
                               T 
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   - 
                                   
                                     R 
                                     ref 
                                     T 
                                   
                                 
                                 ) 
                               
                               ⋆ 
                               
                                 T 
                                 ref 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                     ⋆ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         x 
                                       
                                     
                                     
                                       
                                         y 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   z 
                                 
                               
                             
                           
                         
                         
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         x 
                                         ′ 
                                       
                                     
                                   
                                   
                                     
                                       
                                         y 
                                         ′ 
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   z 
                                   ′ 
                                 
                               
                             
                           
                         
                       
                       
                         
                           1 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
         
         
           
             Where: 
             R ref —Represents an affine transform describing the transformation from the device reference frame  120   a  to the device reference frame  120   b.    
             T ref —Represents translation of the device reference frame  120   a  to the device reference frame  120   b.    
           
         
       
    
     One conventional approach to obtaining the Affine transform R (from axis unit vector u=(u x , u y , u z ), rotation angle θ) method. Wikipedia, at http://en.wikipedia.org/wiki/Rotation_matrix, Rotation matrix from axis and angle, on Jan. 30, 2014, 20:12 UTC, upon which the computations equation (2) are at least in part inspired: 
     
       
         
           
             
               
                 
                   R 
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               θ 
                             
                             + 
                             
                               
                                 u 
                                 x 
                                 2 
                               
                               ( 
                               
                                 1 
                                 - 
                                 
                                   cos 
                                   ⁢ 
                                   θ 
                                 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 u 
                                 x 
                               
                               ⁢ 
                               
                                 
                                   u 
                                   y 
                                 
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     cos 
                                     ⁢ 
                                     θ 
                                   
                                 
                                 ) 
                               
                             
                             - 
                             
                               
                                 u 
                                 z 
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               θ 
                             
                           
                         
                         
                           
                             
                               
                                 u 
                                 x 
                               
                               ⁢ 
                               
                                 
                                   u 
                                   z 
                                 
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     cos 
                                     ⁢ 
                                     θ 
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 u 
                                 y 
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               θ 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 u 
                                 y 
                               
                               ⁢ 
                               
                                 u 
                                 x 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     cos 
                                     ⁢ 
                                     θ 
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 u 
                                 z 
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               θ 
                             
                           
                         
                         
                           
                             
                               cos 
                               ⁢ 
                               θ 
                             
                             + 
                             
                               
                                 u 
                                 y 
                                 2 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     cos 
                                     ⁢ 
                                     θ 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 u 
                                 y 
                               
                               ⁢ 
                               
                                 u 
                                 z 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     cos 
                                     ⁢ 
                                     θ 
                                   
                                 
                                 ) 
                               
                             
                             - 
                             
                               
                                 u 
                                 y 
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               θ 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 u 
                                 z 
                               
                               ⁢ 
                               
                                 u 
                                 x 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     cos 
                                     ⁢ 
                                     θ 
                                   
                                 
                                 ) 
                               
                             
                             - 
                             
                               
                                 u 
                                 y 
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               θ 
                             
                           
                         
                         
                           
                             
                               
                                 u 
                                 z 
                               
                               ⁢ 
                               
                                 u 
                                 y 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     cos 
                                     ⁢ 
                                     θ 
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 u 
                                 x 
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               θ 
                             
                           
                         
                         
                           
                             
                               cos 
                               ⁢ 
                               θ 
                             
                             + 
                             
                               
                                 u 
                                 z 
                                 2 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     cos 
                                     ⁢ 
                                     θ 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               R 
               T 
             
             = 
             
               [ 
               
                 
                   
                     
                       
                         cos 
                         ⁢ 
                         θ 
                       
                       + 
                       
                         
                           u 
                           x 
                           2 
                         
                         ( 
                         
                           1 
                           - 
                           
                             cos 
                             ⁢ 
                             θ 
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       
                         
                           u 
                           y 
                         
                         ⁢ 
                         
                           
                             u 
                             x 
                           
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         
                           u 
                           z 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         θ 
                       
                     
                   
                   
                     
                       
                         
                           u 
                           z 
                         
                         ⁢ 
                         
                           
                             u 
                             x 
                           
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           u 
                           y 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         θ 
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           u 
                           x 
                         
                         ⁢ 
                         
                           u 
                           y 
                         
                         ⁢ 
                         
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           u 
                           z 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         θ 
                       
                     
                   
                   
                     
                       
                         cos 
                         ⁢ 
                         θ 
                       
                       + 
                       
                         
                           u 
                           y 
                           2 
                         
                         ⁢ 
                         
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         
                           u 
                           z 
                         
                         ⁢ 
                         
                           u 
                           y 
                         
                         ⁢ 
                         
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         
                           u 
                           x 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         θ 
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           u 
                           x 
                         
                         ⁢ 
                         
                           u 
                           z 
                         
                         ⁢ 
                         
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         
                           u 
                           y 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         θ 
                       
                     
                   
                   
                     
                       
                         
                           u 
                           y 
                         
                         ⁢ 
                         
                           u 
                           z 
                         
                         ⁢ 
                         
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           u 
                           x 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         θ 
                       
                     
                   
                   
                     
                       
                         cos 
                         ⁢ 
                         θ 
                       
                       + 
                       
                         
                           u 
                           z 
                           2 
                         
                         ⁢ 
                         
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ] 
             
           
         
       
       
         
           
             
               - 
               
                 R 
                 T 
               
             
             = 
             
               [ 
               
                 
                   
                     
                       
                         
                           - 
                           cos 
                         
                         ⁢ 
                         θ 
                       
                       - 
                       
                         
                           u 
                           x 
                           2 
                         
                         ( 
                         
                           1 
                           - 
                           
                             cos 
                             ⁢ 
                             θ 
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       
                         
                           - 
                           
                             u 
                             y 
                           
                         
                         ⁢ 
                         
                           
                             u 
                             x 
                           
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           u 
                           z 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         θ 
                       
                     
                   
                   
                     
                       
                         
                           - 
                           
                             u 
                             z 
                           
                         
                         ⁢ 
                         
                           
                             u 
                             x 
                           
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         
                           u 
                           y 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         θ 
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           - 
                           
                             u 
                             x 
                           
                         
                         ⁢ 
                         
                           
                             u 
                             y 
                           
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         
                           u 
                           z 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         θ 
                       
                     
                   
                   
                     
                       
                         
                           - 
                           cos 
                         
                         ⁢ 
                         θ 
                       
                       - 
                       
                         
                           u 
                           y 
                           2 
                         
                         ( 
                         
                           1 
                           - 
                           
                             cos 
                             ⁢ 
                             θ 
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       
                         
                           - 
                           
                             u 
                             z 
                           
                         
                         ⁢ 
                         
                           
                             u 
                             y 
                           
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           u 
                           x 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         θ 
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           - 
                           
                             u 
                             x 
                           
                         
                         ⁢ 
                         
                           
                             u 
                             z 
                           
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           u 
                           y 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         θ 
                       
                     
                   
                   
                     
                       
                         
                           - 
                           
                             u 
                             y 
                           
                         
                         ⁢ 
                         
                           
                             u 
                             z 
                           
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         
                           u 
                           x 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         θ 
                       
                     
                   
                   
                     
                       
                         
                           - 
                           cos 
                         
                         ⁢ 
                         θ 
                       
                       - 
                       
                         
                           u 
                           z 
                           2 
                         
                         ( 
                         
                           1 
                           - 
                           
                             cos 
                             ⁢ 
                             θ 
                           
                         
                         ) 
                       
                     
                   
                 
               
               ] 
             
           
         
       
     
     is a vector representing a translation of the object with respect to origin of the coordinate system of the translated frame 
     
       
         
           
             
               
                 - 
                 
                   R 
                   T 
                 
               
               ⋆ 
               T 
             
             = 
               
             
               [ 
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             - 
                                             cos 
                                           
                                           ⁢ 
                                           θ 
                                         
                                         - 
                                         
                                           
                                             u 
                                             x 
                                             2 
                                           
                                           ⁢ 
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               
                                                 cos 
                                                 ⁢ 
                                                 θ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       a 
                                       ) 
                                     
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             - 
                                             cos 
                                           
                                           ⁢ 
                                           θ 
                                         
                                         - 
                                         
                                           
                                             u 
                                             y 
                                             2 
                                           
                                           ⁢ 
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               
                                                 cos 
                                                 ⁢ 
                                                 θ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       b 
                                       ) 
                                     
                                   
                                   + 
                                 
                               
                             
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           - 
                                           
                                             u 
                                             z 
                                           
                                         
                                         ⁢ 
                                         
                                           u 
                                           x 
                                         
                                         ⁢ 
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             
                                               cos 
                                               ⁢ 
                                               θ 
                                             
                                           
                                           ) 
                                         
                                       
                                       + 
                                       
                                         
                                           u 
                                           y 
                                         
                                         ⁢ 
                                         sin 
                                         ⁢ 
                                         θ 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     c 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             - 
                                             
                                               u 
                                               x 
                                             
                                           
                                           ⁢ 
                                           
                                             u 
                                             y 
                                           
                                           ⁢ 
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               
                                                 cos 
                                                 ⁢ 
                                                 θ 
                                               
                                             
                                             ) 
                                           
                                         
                                         + 
                                         
                                           
                                             u 
                                             z 
                                           
                                           ⁢ 
                                           sin 
                                           ⁢ 
                                           θ 
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       a 
                                       ) 
                                     
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             - 
                                             cos 
                                           
                                           ⁢ 
                                           θ 
                                         
                                         - 
                                         
                                           
                                             u 
                                             y 
                                             2 
                                           
                                           ⁢ 
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               
                                                 cos 
                                                 ⁢ 
                                                 θ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       b 
                                       ) 
                                     
                                   
                                   + 
                                 
                               
                             
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           - 
                                           
                                             u 
                                             z 
                                           
                                         
                                         ⁢ 
                                         
                                           u 
                                           y 
                                         
                                         ⁢ 
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             
                                               cos 
                                               ⁢ 
                                               θ 
                                             
                                           
                                           ) 
                                         
                                       
                                       - 
                                       
                                         
                                           u 
                                           x 
                                         
                                         ⁢ 
                                         sin 
                                         ⁢ 
                                         θ 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     c 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       - 
                                       
                                         u 
                                         x 
                                       
                                     
                                     ⁢ 
                                     
                                       u 
                                       z 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           cos 
                                           ⁢ 
                                           θ 
                                         
                                       
                                       ) 
                                     
                                   
                                   - 
                                   
                                     
                                       u 
                                       y 
                                     
                                     ⁢ 
                                     sin 
                                     ⁢ 
                                     θ 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 ( 
                                 a 
                                 ) 
                               
                             
                             + 
                             
                               
                                 ( 
                                 
                                   
                                     
                                       - 
                                       
                                         u 
                                         y 
                                       
                                     
                                     ⁢ 
                                     
                                       u 
                                       z 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           cos 
                                           ⁢ 
                                           θ 
                                         
                                       
                                       ) 
                                     
                                   
                                   + 
                                   
                                     
                                       u 
                                       x 
                                     
                                     ⁢ 
                                     sin 
                                     ⁢ 
                                     θ 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 ( 
                                 b 
                                 ) 
                               
                             
                             + 
                           
                         
                       
                       
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     - 
                                     cos 
                                   
                                   ⁢ 
                                   θ 
                                 
                                 - 
                                 
                                   
                                     u 
                                     z 
                                     2 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       1 
                                       - 
                                       
                                         cos 
                                         ⁢ 
                                         θ 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               c 
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               ] 
             
           
         
       
     
     In another example, an apparent orientation and position of the object at time t=t 1 : affine transform 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       R 
                       obj 
                     
                   
                   
                     
                       T 
                       obj 
                     
                   
                 
                 
                   
                     0 
                   
                   
                     1 
                   
                 
               
               ] 
             
             , 
           
         
       
     
     can be converted to a real orientation and position of the object at time 
     
       
         
           
             t 
             = 
             
               
                 t 
                 1 
               
               ⁢ 
               
                 : 
                 [ 
                 
                   
                     
                       
                         R 
                         obj 
                         ′ 
                       
                     
                     
                       
                         T 
                         obj 
                         ′ 
                       
                     
                   
                   
                     
                       0 
                     
                     
                       1 
                     
                   
                 
                 ] 
               
             
           
         
       
     
     using a affine transform 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       R 
                       ref 
                     
                   
                   
                     
                       T 
                       ref 
                     
                   
                 
                 
                   
                     0 
                   
                   
                     1 
                   
                 
               
               ] 
             
             . 
           
         
       
     
     The correct orientation and position of the tracked object with respect to device reference frame at time t=t 0  ( 120   a ) is given by equation (3): 
     
       
         
           
             
               
                 
                   
                     
                       [ 
                       
                         
                           
                             
                               R 
                               ref 
                               T 
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   - 
                                   
                                     R 
                                     ref 
                                     T 
                                   
                                 
                                 ) 
                               
                               ⋆ 
                               
                                 T 
                                 ref 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                     ⋆ 
                     
                       [ 
                       
                         
                           
                             
                               R 
                               obj 
                             
                           
                           
                             
                               T 
                               obj 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             R 
                             obj 
                             ′ 
                           
                         
                         
                           
                             T 
                             obj 
                             ′ 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           1 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
         
         
           
             Where: 
             R ref —Represents an affine transform describing the transformation from the device reference frame  120   a  to the device reference frame  120   b.    
             R obj —Represents an affine transform describing the rotation of the object with respect to the device reference frame  120   b.    
             R obj ′—Represents an affine transform describing the rotation of the object with respect to the device reference frame  120   a.    
             T ref —Represents translation of the device reference frame  120   a  to the device reference frame  120   b.    
             T obj —Represents translation of the object with respect to the device reference frame  120   b.    
             T obj ′—Represents translation of the object with respect to the device reference frame  120   a.    
           
         
       
    
     In a yet further example, an apparent orientation and position of the object at time t=t 1 : affine transform 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       R 
                       obj 
                     
                   
                   
                     
                       T 
                       obj 
                     
                   
                 
                 
                   
                     0 
                   
                   
                     1 
                   
                 
               
               ] 
             
             , 
           
         
       
     
     can be converted to a real orientation and position of the object at time 
     
       
         
           
             t 
             = 
             
               
                 t 
                 1 
               
               ⁢ 
               
                 : 
                 [ 
                 
                   
                     
                       
                         R 
                         obj 
                         ′ 
                       
                     
                     
                       
                         T 
                         obj 
                         ′ 
                       
                     
                   
                   
                     
                       0 
                     
                     
                       1 
                     
                   
                 
                 ] 
               
             
           
         
       
     
     using an affine transform 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       R 
                       ref 
                     
                   
                   
                     
                       T 
                       ref 
                     
                   
                 
                 
                   
                     0 
                   
                   
                     1 
                   
                 
               
               ] 
             
             . 
           
         
       
     
     Furthermore, the position and orientation of the initial reference frame with respect to a (typically) fixed reference point in space can be determined using an affine transform 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       R 
                       init 
                     
                   
                   
                     
                       T 
                       init 
                     
                   
                 
                 
                   
                     0 
                   
                   
                     1 
                   
                 
               
               ] 
             
             . 
           
         
       
     
     The correct orientation and position of the tracked object with respect to device reference frame at time t=t 0  ( 120   a ) is given by equation (4): 
     
       
         
           
             
               
                 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 R 
                                 init 
                                 T 
                               
                             
                             
                               
                                 
                                   ( 
                                   
                                     - 
                                     
                                       R 
                                       init 
                                       T 
                                     
                                   
                                   ) 
                                 
                                 ⋆ 
                                 
                                   T 
                                   init 
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               1 
                             
                           
                         
                         ] 
                       
                       [ 
                       
                         
                           
                             
                               R 
                               ref 
                               T 
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   - 
                                   
                                     R 
                                     ref 
                                     T 
                                   
                                 
                                 ) 
                               
                               ⋆ 
                               
                                 T 
                                 ref 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                     ⋆ 
                     
                       [ 
                       
                         
                           
                             
                               R 
                               obj 
                             
                           
                           
                             
                               T 
                               obj 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                   = 
                     
                   
                     [ 
                     
                       
                         
                           
                             R 
                             obj 
                             ′ 
                           
                         
                         
                           
                             T 
                             obj 
                             ′ 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           1 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
         
         
           
             Where: 
             R init —Represents an affine transform describing the transformation from the world reference frame  119  to the device reference frame  120   a.    
             R ref —Represents an affine transform describing the transformation from the device reference frame  120   a  to the device reference frame  120   b.    
             R obj —Represents an affine transform describing the rotation of the object with respect to the device reference frame  120   b.    
             R obj ′—Represents an affine transform describing the rotation of the object with respect to the device reference frame  120   a.    
             T init —Represents translation of the world reference frame  119  to the device reference frame  120   a.    
             T ref  Represents translation of the device reference frame  120   a  to the device reference frame  120   b.    
             T obj —Represents translation of the object with respect to the device reference frame  120   b.    
             T obj ′—Represents translation of the object with respect to the device reference frame  120   a.    
           
         
       
    
       FIG.  6    shows a flowchart  600  of one implementation of determining motion information in a movable sensor apparatus. Flowchart  600  can be implemented at least partially with a computer or other data processing system, e.g., by one or more processors configured to receive or retrieve information, process the information, store results, and transmit the results. Other implementations may perform the actions in different orders and/or with different, fewer or additional actions than those illustrated in  FIG.  6   . Multiple actions can be combined in some implementations. For convenience, this flowchart is described with reference to the system that carries out a method. The system is not necessarily part of the method. 
     At action  610 , a first positional information of a portable or movable sensor is determined with respect to a fixed point at a first time. In one implementation, first positional information with respect to a fixed point at a first time t=t 0  is determined from one or motion sensors integrated with, or coupled to, a device including the portable or movable sensor. For example, an accelerometer can be affixed to device  101  of  FIG.  1    or sensor  300  of  FIG.  3   , to provide acceleration information over time for the portable or movable device or sensor. Acceleration as a function of time can be integrated with respect to time (e.g., by sensory processing system  106 ) to provide velocity information over time, which can be integrated again to provide positional information with respect to time. In another example, gyroscopes, magnetometers or the like can provide information at various times from which positional information can be derived. These items are well known in the art and their function can be readily implemented by those possessing ordinary skill. In another implementation, a second motion-capture sensor (e.g., such as sensor  300 A-C of  FIG.  3    for example) is disposed to capture position information of the first sensor (e.g., affixed to  101  of  FIG.  1    or sensor  300  of  FIG.  3   ) to provide positional information for the first sensor. 
     At action  620 , a second positional information of the sensor is determined with respect to the fixed point at a second time t=t 1 . 
     At action  630 , difference information between the first positional information and the second positional information is determined. 
     At action  640 , movement information for the sensor with respect to the fixed point is computed based upon the difference information. Movement information for the sensor with respect to the fixed point is can be determined using techniques such as discussed above with reference to equations (2). 
     At action  650 , movement information for the sensor is applied to apparent environment information sensed by the sensor to remove motion of the sensor therefrom to yield actual environment information. Motion of the sensor can be removed using techniques such as discussed above with reference to  FIGS.  4 - 5   . 
     At action  660 , actual environment information is communicated. 
       FIG.  7    shows a flowchart  700  of one implementation of applying movement information for the sensor to apparent environment information (e.g., apparent motions of objects in the environment  112  as sensed by the sensor) to remove motion of the sensor therefrom to yield actual environment information (e.g., actual motions of objects in the environment  112  relative to the reference frame  120   a ). Flowchart  700  can be implemented at least partially with a computer or other data processing system, e.g., by one or more processors configured to receive or retrieve information, process the information, store results, and transmit the results. Other implementations may perform the actions in different orders and/or with different, fewer or additional actions than those illustrated in  FIG.  7   . Multiple actions can be combined in some implementations. For convenience, this flowchart is described with reference to the system that carries out a method. The system is not necessarily part of the method. 
     At action  710 , positional information of an object portion at the first time and the second time are captured. 
     At action  720 , object portion movement information relative to the fixed point at the first time and the second time is computed based upon the difference information and the movement information for the sensor. 
     At action  730 , object portion movement information is communicated to a system. 
     Some implementations will be applied to virtual reality or augmented reality applications. For example, and with reference to  FIG.  8   , which illustrates a system  800  for projecting a virtual device experience  801  onto a surface medium  116  according to one implementation of the technology disclosed. System  800  includes a sensory processing system  106  controlling a variety of sensors and projectors, such as for example one or more cameras  102 ,  104  (or other image sensors) and optionally some illumination sources  115 ,  117  comprising an imaging system. Optionally, a plurality of vibrational (or acoustical) sensors  808 ,  810  positioned for sensing contacts with surface  116  can be included. Optionally projectors under control of system  106  can augment the virtual device experience  801 , such as an optional audio projector  802  to provide for example audio feedback, optional video projector  804 , an optional haptic projector  806  to provide for example haptic feedback to a user of virtual device experience  801 . For further information on projectors, reference may be had to “Visio-Tactile Projector” YouTube (https://www.youtube.com/watch?v=Bb0hNMxxewg) (accessed Jan. 15, 2014). In operation, sensors and projectors are oriented toward a region of interest  112 , that can include at least a portion of a surface  116 , or free space  112  in which an object of interest  114  (in this example, a hand) moves along the indicated path  118 . 
       FIG.  9    shows a flowchart  900  of one implementation of providing a virtual device experience. Flowchart  900  can be implemented at least partially with a computer or other data processing system, e.g., by one or more processors configured to receive or retrieve information, process the information, store results, and transmit the results. Other implementations may perform the actions in different orders and/or with different, fewer or additional actions than those illustrated in  FIG.  9   . Multiple actions can be combined in some implementations. For convenience, this flowchart is described with reference to the system that carries out a method. The system is not necessarily part of the method. 
     At action  910 , a virtual device is projected to a user. Projection can include an image or other visual representation of an object. For example, visual projection mechanism  804  of  FIG.  8    can project a page (e.g., virtual device  801 ) from a book into a virtual environment  801  (e.g., surface portion  116  or in space  112 ) of a reader; thereby creating a virtual device experience of reading an actual book, or an electronic book on a physical e-reader, even though no book nor e-reader is present. In some implementations, optional haptic projector  806  can project the feeling of the texture of the “virtual paper” of the book to the reader&#39;s finger. In some implementations, optional audio projector  802  can project the sound of a page turning in response to detecting the reader making a swipe to turn the page. 
     At action  920 , using an accelerometer, moving reference frame information of a head mounted display (or hand-held mobile device) relative to a fixed point on a human body is determined. 
     At action  930 , body portion movement information is captured. Motion of the body portion can be detected via sensors  108 ,  110  using techniques such as discussed above with reference to  FIG.  6   . 
     At action  940 , control information is extracted based partly on the body portion movement information with respect to the moving reference frame information. For example, repeatedly determining movement information for the sensor and the object portion at successive times and analyzing a sequence of movement information can be used to determine a path of the object portion with respect to the fixed point. For example, a 3D model of the object portion can be constructed from image sensor output and used to track movement of the object over a region of space. The path can be compared to a plurality of path templates and identifying a template that best matches the path. The template that best matches the path control information to a system can be used to provide the control information to the system. For example, paths recognized from an image sequence (or audio signal, or both) can indicate a trajectory of the object portion such as a gesture of a body portion. 
     At action  950 , control information can be communicated to a system. For example, a control information such as a command to turn the page of a virtual book can be sent based upon detecting a swipe along the desk surface of the reader&#39;s finger. Many other physical or electronic objects, impressions, feelings, sensations and so forth can be projected onto surface  116  (or in proximity thereto) to augment the virtual device experience and applications are limited only by the imagination of the user. 
       FIG.  10    shows a flowchart  1000  of one implementation of cancelling drift in a head mounted device (HMD). Flowchart  1000  can be implemented at least partially with a computer or other data processing system, e.g., by one or more processors configured to receive or retrieve information, process the information, store results, and transmit the results. Other implementations may perform the actions in different orders and/or with different, fewer or additional actions than those illustrated in  FIG.  10   . Multiple actions can be combined in some implementations. For convenience, this flowchart is described with reference to the system that carries out a method. The system is not necessarily part of the method. 
     At action  1010 , using an accelerometer, moving reference frame information of a head mounted display (or hand-held mobile device) relative to a fixed point on a human body is determined. 
     At action  1020 , body portion movement information is captured. 
     At action  1030 , control information is extracted based partly on the body portion movement information with respect to the moving reference frame information. 
     At action  1040 , the control information is communicated to a system. 
     In some implementations, motion capture is achieved using an optical motion-capture system. In some implementations, object position tracking is supplemented by measuring a time difference of arrival (TDOA) of audio signals at the contact vibrational sensors and mapping surface locations that satisfy the TDOA, analyzing at least one image, captured by a camera of the optical motion-capture system, of the object in contact with the surface, and using the image analysis to select among the mapped TDOA surface locations as a surface location of the contact. 
     Reference may be had to the following sources, incorporated herein by reference, for further information regarding computational techniques:
     1. Wikipedia, at http://en.wikipedia.org/wiki/Euclidean_group, on Nov. 4, 2013, 04:08 UTC;   2. Wikipedia, at http://en.wikipedia.org/wiki/Affine_transformation, on Nov. 25, 2013, 11:01 UTC;   3. Wikipedia, at http://en.wikipedia.org/wiki/Rotation_matrix, Rotation matrix from axis and angle, on Jan. 30, 2014, 20:12 UTC;   4. Wikipedia, at http://en.wikipedia.org/wiki/Rotation_group_SO(3), Axis of rotation, on Jan. 21, 2014, 21:21 UTC;   5. Wikipedia, at http://en.wikipedia.org/wiki/Transformation_matrix, Affine Transformations, on Jan. 28, 2014, 13:51 UTC; and   6. Wikipedia, at http://en.wikipedia.org/wiki/Axis % E2%80%93angle_representation, on Jan. 25, 2014, 03:26 UTC.   

     While the disclosed technology has been described with respect to specific implementations, one skilled in the art will recognize that numerous modifications are possible. The number, types and arrangement of cameras and sensors can be varied. The cameras&#39; capabilities, including frame rate, spatial resolution, and intensity resolution, can also be varied as desired. The sensors&#39; capabilities, including sensitively levels and calibration, can also be varied as desired. Light sources are optional and can be operated in continuous or pulsed mode. The systems described herein provide images and audio signals to facilitate tracking movement of an object, and this information can be used for numerous purposes, of which position and/or motion detection is just one among many possibilities. 
     Threshold cutoffs and other specific criteria for distinguishing object from background can be adapted for particular hardware and particular environments. Frequency filters and other specific criteria for distinguishing visual or audio signals from background noise can be adapted for particular cameras or sensors and particular devices. In some implementations, the system can be calibrated for a particular environment or application, e.g., by adjusting frequency filters, threshold criteria, and so on. 
     Any type of object can be the subject of motion capture using these techniques, and various aspects of the implementation can be optimized for a particular object. For example, the type and positions of cameras and/or other sensors can be selected based on the size of the object whose motion is to be captured, the space in which motion is to be captured, and/or the medium of the surface through which audio signals propagate. Analysis techniques in accordance with implementations of the technology disclosed can be implemented as algorithms in any suitable computer language and executed on programmable processors. Alternatively, some or all of the algorithms can be implemented in fixed-function logic circuits, and such circuits can be designed and fabricated using conventional or other tools. 
     Computer programs incorporating various features of the technology disclosed may be encoded on various computer readable storage media; suitable media include magnetic disk or tape, optical storage media such as compact disk (CD) or DVD (digital versatile disk), flash memory, and any other non-transitory medium capable of holding data in a computer-readable form. Computer-readable storage media encoded with the program code may be packaged with a compatible device or provided separately from other devices. In addition program code may be encoded and transmitted via wired optical, and/or wireless networks conforming to a variety of protocols, including the Internet, thereby allowing distribution, e.g., via Internet download. 
     Thus, although the disclosed technology has been described with respect to specific implementations, it will be appreciated that the disclosed technology is intended to cover all modifications and equivalents within the scope of the following claims.