Patent Publication Number: US-11025959-B2

Title: Probabilistic model to compress images for three-dimensional video

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 15/617,878, entitled “Probabilistic Model to Compress Images for Three-Dimensional Video,” filed Jun. 8, 2017, which is a continuation-in-part of U.S. patent application Ser. No. 15/269,734, entitled “Behavioral Directional Encoding of Three-Dimensional Video,” filed Sep. 19, 2016 (now U.S. Pat. No. 9,774,887). This application is a continuation-in-part of U.S. patent application Ser. No. 14/842,465, entitled “Virtual Reality System Including Social Graph,” filed Sep. 21, 2015, which claims priority under 35 USC § 119(e) to U.S. Provisional Application No. 62/142,909, entitled “Image Stitching,” filed Apr. 3, 2015 and U.S. Provisional Application No. 62/055,259, entitled “Virtual Reality System Including Social Graph,” filed Sep. 25, 2014, is a continuation-in-part of U.S. patent application Ser. No. 14/726,118, entitled “Camera Array Including Camera Modules,” filed May 29, 2015 (now U.S. Pat. No. 9,911,454), and is a continuation-in-part of U.S. application Ser. No. 14/444,938, entitled “Camera Array Including Camera Modules,” filed Jul. 28, 2014 (now U.S. Pat. No. 9,451,162), each of which is incorporated by reference. 
    
    
     FIELD 
     The embodiments discussed herein are related to behavioral directional encoding of three-dimensional video. More particularly, the embodiments discussed herein relate to using a probabilistic model, such as a heat map, to determine optimal segment parameters and portions of a three-dimensional video to blur. 
     BACKGROUND 
     Generating virtual reality content for a 360° environment may be analogized to generating content that is displayed in a sphere that surrounds a user. Because the user may look anywhere in the sphere, current virtual reality systems generate high-quality content for every pixel in the sphere. As a result, virtual reality content is data rich. Because the user may only look in one direction, most of the pixels in the view are not seen by the user. For example, it is frequently a waste of bandwidth to include data rich content that is located behind the user because the user is unlikely to turn 180 degrees to view that content. 
     When the virtual reality content is for a video, the data requirements are massive because the video is generated for each pixel in the sphere. As a result, it may be difficult to stream the virtual reality content to the user because of bandwidth constraints. 
     One solution to the problem of current virtual reality systems may be to provide a viewing device with virtual reality content that corresponds to the direction of the user&#39;s gaze. However, because the user may move and look in a different direction, the movement may result in the user perceiving a lag in the virtual reality content as the virtual reality system updates the direction and transmits virtual reality content for the different direction. 
     Another solution may be to predict the direction of the user&#39;s gaze. However, if the prediction is wrong, the resulting virtual reality content may have both lower quality and less stability than traditional virtual reality content. 
     SUMMARY 
     According to one innovative aspect of the subject matter described in this disclosure, a method includes receiving head-tracking data that describe one or more positions of people while the people are viewing a three-dimensional video, generating a probabilistic model of the one or more positions of the people based on the head-tracking data, wherein the probabilistic model identifies a probability of a viewer looking in a particular direction as a function of time, generating video segments from the three-dimensional video, and for each of the video segments: determining a directional encoding format that projects latitudes and longitudes of locations of a surface of a sphere onto locations on a plane, determining a cost function that identifies a region of interest on the plane based on the probabilistic model, and generating optimal segment parameters that minimize a sum-over position for the region of interest. 
     In some embodiments, the probabilistic model is a heat map. In some embodiments, the method may also include re-encoding the three-dimensional video to include the optimal segment parameters for each of the video segments and to blur portions of each of the video segments based on the probability, wherein an intensity of a level of blur increases as the probability of the viewer looking in the particular direction decreases and providing a re-encoded video and the optimal segment parameters for each of the video segments to a viewing device, wherein the viewing device uses the optimal segment parameters for each of the video segments to un-distort the re-encoded video and texture the re-encoded video to the sphere to display the re-encoded video with the region of interest for each of the video segments displayed at a higher resolution than other regions in each of the video segments. In some embodiments, the three-dimensional video may be re-encoded to include the optimal segment parameters for each of the video segments and blurring portions of each of the video segments occurs responsive to a threshold number of the people viewing the three-dimensional video. In some embodiments, the method includes for each of the video segments, identifying a region of low interest, re-encoding the three-dimensional video to include the optimal segment parameters for each of the video segments and blurring of the region of low interest, and providing a re-encoded video and the optimal segment parameters for each of the video segments to a viewing device, wherein the viewing device uses the optimal segment parameters for each of the video segments to un-distort the re-encoded video and texture the re-encoded video to the sphere to display the re-encoded video with the region of interest for each of the video segments displayed at a higher resolution than other regions in each of the video segments and the region of low interest displayed at a lower resolution than other regions in each of the video segments. In some embodiments, the method includes re-encoding the three-dimensional video to include the optimal segment parameters for each of the video segments and blurring portions of each of the video segments based on the probability, wherein an intensity of a level of blur increases as the probability of the viewer looking in the particular direction decreases and providing a re-encoded video and the optimal segment parameters for each of the video segments to a client device, wherein the client device uses the re-encoded video and the optimal segment parameters for each of the video segments to generate a two-dimensional video that automates head movement. The method may further include providing a user with an option to modify the two-dimensional video by at least one of selecting different optimal segment parameters and selecting a different region of interest for one or more of the video segments. In some embodiments, the method further includes cropping the region of interest for one or more video segments based on the optimal segment parameters to form one or more thumbnails of one or more cropped regions of interest and generating a timeline of the three-dimensional video with the one or more thumbnails. In some embodiments, generating the video segments from the three-dimensional video includes generating equal-length video segments of a predetermined length. 
     In some embodiments, a system comprises one or more processors coupled to a memory, a head tracking module stored in the memory and executable by the one or more processors, the head tracking module operable to receive head-tracking data that describe one or more positions of people while the people are viewing a set of three-dimensional videos, generate a set of probabilistic models of the one or more positions of the people based on the head-tracking data, and estimate a first probabilistic model for a first three-dimensional video, wherein the first probabilistic model identifies a probability of a viewer looking in a particular direction as a function of time and the first three-dimensional video is not part of the set of three-dimensional videos, a segmentation module stored in the memory and executable by the one or more processors, the segmentation module operable to generate video segments from the three-dimensional video, and a parameterization module stored in the memory and executable by the one or more processors, the parameterization module operable to, for each of the video segments: determine a directional encoding format that projects latitudes and longitudes of locations of a surface of a sphere onto locations on a plane, determine a cost function that identifies a region of interest on the plane based on the first probabilistic model, and generate optimal segment parameters that minimize a sum-over position for the region of interest. 
     Other aspects include corresponding methods, systems, apparatus, and computer program products for these and other innovative aspects. 
     The disclosure is particularly advantageous in a number of respects. First, the virtual reality application generates a probabilistic model, such as a heat map, that describes a probability of a viewer looking in a particular direction as a function of time. The virtual reality application may re-encode a three-dimensional video based on the probabilistic model to blur portions of the three-dimensional video and to optimize regions of interest in the three-dimensional video based on the probability. As a result, the re-encoded three-dimensional video may be transmitted to a client device with a lower bitrate and may be perceived by a viewer as having higher visual quality than other examples of three-dimensional video. In addition, less bandwidth is spent by the client device to un-distort and re-encode the three-dimensional video with blurred portions. 
     The client device includes a codec that is advantageously compatible with the methods described in this application. As a result, no additional software is needed for the client device to render the three-dimensional video. In addition, because the blurring occurs locally and reduces the entropy of that region of the three-dimensional video, it makes the three-dimensional video more compressive. As a result, the codec on the client device spends less bandwidth on the blurred portions relative to the rest of the three-dimensional video and more bandwidth on the regions of interest in the three-dimensional video. 
     In some embodiments, the virtual reality application generates probabilistic models for a set of three-dimensional videos and uses artificial intelligence, such as a neural network, to estimate a probabilistic model for a particular three-dimensional video. This advantageously avoids the need to find people to view every three-dimensional video in order to generate head-tracking data. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates an example virtual reality system that generates optimal segment parameters for a three-dimensional video according to some embodiments. 
         FIG. 2  illustrates an example computing device that generates optimal segment parameters for a three-dimensional video according to some embodiments. 
         FIG. 3  illustrates an example user interface that includes a timeline of a video with thumbnails according to some embodiments. 
         FIG. 4  illustrates an example flow diagram for generating optimal segment parameters for a three-dimensional video according to some embodiments. 
         FIG. 5  illustrates an example flow diagram for re-encoding a three-dimensional video with blurred portions. 
         FIG. 6  illustrates an example flow diagram for generating optimal segment parameters and a probabilistic model from a training set. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     The disclosure relates to generating virtual reality content. A virtual reality application receives head-tracking data that describe positions of people&#39;s heads while the people are viewing a three-dimensional video. For example, the head-tracking data measures the yaw, pitch, and roll associated with people that are using a viewing device to view the three-dimensional video. 
     The virtual reality application generates probabilistic model of the one or more positions of the people based on the head-tracking data. The probabilistic model identifies a probability of a viewer looking in a particular direction as a function of time. For example, if most people that view the video look straight ahead at a particular object, the direction that is directly behind most people is unlikely to be a direction that people look in. 
     The virtual reality application generates video segments from the three-dimensional video. For example, the video segments may be a fixed length of time, such as two seconds (or three, four, etc.) or the video segments may be based on scene boundaries in the three-dimensional video. 
     For each of the video segments, the virtual reality application determines a directional encoding format that projects latitudes and longitudes of locations of a surface of sphere onto locations on a plane. For example, the virtual reality application may use a map projection to take three-dimensional video content that is designed for a sphere and map it onto a plane. For each of the video segments, the virtual reality application determines a cost function that identifies a region of interest on the plane based on the probabilistic model. For example, the virtual reality application may determine that most people look in a particular direction during the video segment. For each of the video segments, the virtual reality application generates optimal segment parameters that minimize a sum-over position for the region of interest. For example, the virtual reality application generates yaw, pitch, and roll values for the segment to identify the region of interest. 
     The optimal segment parameters may be used in a variety of applications. For example, the virtual reality application may re-encode the three-dimensional video to include the optimal segment parameters for each of the video segments, blur portions of each of the video segments based on the probability, and provide the re-encoded video and the optimal segment parameters to a viewing device. The viewing device may use the optimal segment parameters to un-distort the re-encoded video and texture the re-encoded video to the sphere. As a result, a user using the viewing the three-dimensional video may view the regions of interest at a higher resolution than the other regions in the three-dimensional video and the blurred portions of the three-dimensional video at a lower resolution than other regions in the three-dimensional video. 
     Example System 
       FIG. 1  illustrates an example virtual reality system  100  that determines optimal segment parameters for virtual reality content. The virtual reality system  100  comprises a camera array  101 , a client device  105 , a viewing device  115 , a server  120 , and a network  125 . 
     While  FIG. 1  illustrates one camera array  101 , one client device  105 , one viewing device  115 , and one server  120 , the disclosure applies to a system architecture having one or more camera arrays  101 , one or more client devices  105 , one or more viewing devices  115 , and one or more servers  120 . Furthermore, although  FIG. 1  illustrates one network  125  coupled to the entities of the system  100 , in practice one or more networks  125  may be connected to these entities and the one or more networks  125  may be of various and different types. 
     The camera array  101  may comprise camera modules that capture video data. The camera array  101  may communicate with the client device  105  and/or the server  120  by accessing the network  125  via signal line  102 . Signal line  102  may represent a wireless or a wired connection. For example, the camera array  101  may wirelessly transmit video data over the network  125  to the server  120 . In some embodiments, the camera array  101  may be directly connected to the client device  105 . For example, the camera array  101  may be connected to the client device  105  via a universal serial bus (USB) cable. 
     The network  125  may be a conventional type, wired or wireless, and may have numerous different configurations including a star configuration, token ring configuration, or other configurations. Furthermore, the network  125  may include a local area network (LAN), a wide area network (WAN) (e.g., the Internet), or other interconnected data paths across which multiple devices may communicate. In some embodiments, the network  125  may be a peer-to-peer network. The network  125  may also be coupled to or include portions of a telecommunications network for sending data in a variety of different communication protocols. In some embodiments, the network  125  may include Bluetooth™ communication networks or a cellular communication network for sending and receiving data including via short messaging service (SMS), multimedia messaging service (MMS), hypertext transfer protocol (HTTP), direct data connection, wireless access protocol (WAP), e-mail, etc. 
     The client device  105  may be a processor-based computing device. For example, the client device  105  may be a personal computer, laptop, tablet computing device, smartphone, set top box, network-enabled television, or any other processor based computing device. In some embodiments, the client device  105  includes network functionality and is communicatively coupled to the network  125  via a signal line  104 . The client device  105  may be configured to transmit data to the server  120  or to receive data from the server  120  via the network  125 . A user  110  may access the client device  105 . 
     The client device  105  may include a virtual reality (VR) application  103   a . The virtual reality application  103   a  may be configured to control the camera array  101  and/or aggregate video data and audio data to generate a stream of three-dimensional video data. In some embodiments, the virtual reality application  103   a  can be implemented using hardware including a field-programmable gate array (“FPGA”) or an application-specific integrated circuit (“ASIC”). In some other embodiments, the virtual reality application  103   a  may be implemented using a combination of hardware and software. 
     The server  120  may be a hardware server that includes a processor, a memory, a database  107 , and network communication capabilities. In the illustrated embodiment, the server  120  is coupled to the network  125  via signal line  108 . The server  120  sends and receives data to and from one or more of the other entities of the system  100  via the network  125 . For example, the server  120  receives virtual reality content including a stream of three-dimensional video data (or compressed three-dimensional video data) from the camera array  101  and/or the client device  105  and stores the virtual reality content on a storage device (e.g., the database  107 ) associated with the server  120 . The database  107  may store a set of three-dimensional videos that are used to generate head-tracking data. For example, the virtual reality application  103   b  may use the head-tracking data to estimate a probabilistic model for a three-dimensional video that is not part of the set of three-dimensional videos. 
     The server  120  may include a virtual reality application  103   b  that receives video data and audio data from the client device  105  and/or the camera array  101  and aggregates the video data to generate the virtual reality content. The virtual reality application  103   b  may generate the optimal segment parameters for the three-dimensional video. 
     The viewing device  115  may be operable to display virtual reality content. The viewing device  115  may include or use a computing device to decode and render a stream of three-dimensional video data on a virtual reality display device (e.g., Oculus Rift virtual reality display) or other suitable display devices that include, but are not limited to: augmented reality glasses; televisions, smartphones, tablets, or other devices with three-dimensional displays and/or position tracking sensors; and display devices with a viewing position control, etc. The viewing device  115  may also decode and render a stream of three-dimensional audio data on an audio reproduction device (e.g., a headphone or other suitable speaker devices). The viewing device  115  may include the virtual reality display configured to render the three-dimensional video data and the audio reproduction device configured to render the three-dimensional audio data. 
     The viewing device  115  may be coupled to the network  125  via signal line  106 . The viewing device  115  may communicate with the client device  105  and/or the server  120  via the network  125  or via a direct connection with the client device  105  (not shown). A user  113  may interact with the viewing device  115 . The user  113  may be the same or different from the user  110  that accesses the client device  105 . 
     In some embodiments, the viewing device  115  receives virtual reality content from the client device  105 . Alternatively or additionally, the viewing device  115  receives the virtual reality content from the server  120 . The virtual reality content may include one or more of a stream of three-dimensional video data, a stream of three-dimensional audio data, a compressed stream of three-dimensional video data, a compressed stream of three-dimensional audio data, and other suitable content. In some embodiments, the viewing device  115  and the client device  105  may be the same device. 
     The viewing device  115  may track a head orientation of a user  113  while the user  113  is viewing three-dimensional video. For example, the viewing device  115  may include one or more accelerometers or gyroscopes used to detect a change in the user&#39;s  113  head orientation. The viewing device  115  may decode and render the stream of three-dimensional video data on a virtual reality display device based on the head orientation of the user  113 . As the user  113  changes his or her head orientation, the viewing device  115  may adjust the rendering of the three-dimensional video data and three-dimensional audio data based on the changes of the user&#39;s  113  head orientation. The viewing device  115  may log head-tracking data and transmit the head-tracking data to the virtual reality application  103 . Although not illustrated, in some embodiments the viewing device  115  may include some or all of the components of the virtual reality application  103  described below. 
     The virtual reality application  103  may receive the head-tracking data corresponding to the three-dimensional video from the viewing device  115 . The virtual reality application  103  may generate video segments from the three-dimensional video and determine optimal segment parameters for each of the video segments based on the head-tracking data. For example, the virtual reality application  103  may receive head-tracking data for multiple users  113  and determine from the head-tracking data that most users  113  have particular head orientations during the viewing. The particular head orientations could include looking upwards as a bird is displayed as flying overhead, moving from left to right as a car is displayed as driving past the user  113 , etc. The virtual reality application  103  may transmit the optimal segment parameters to the viewing device  115 , which may use the optimal segment parameters to re-encode the three-dimensional video. For example, the viewing device  115  may re-encode the three-dimensional video to include regions of interest (i.e., one or more areas where users  113  were more likely to look) with a higher resolution than other regions of the three-dimensional video. 
     Example Computing Device 
       FIG. 2  illustrates an example computing device  200  that generates three-dimensional video according to some embodiments. The computing device  200  may be the server  120  or the client device  105 . In some embodiments, the computing device  200  may include a special-purpose computing device configured to provide some or all of the functionality described below with reference to  FIG. 2 . 
       FIG. 2  may include a processor  222 , a memory  224 , a communication unit  226 , and a display  228 . The processor  222 , the memory  224 , the communication unit  226 , and the display  228  are communicatively coupled to the bus  220 . Other hardware components may be part of the computing device  200 , such as sensors (e.g., a gyroscope, accelerometer), etc. 
     The processor  222  may include an arithmetic logic unit, a microprocessor, a general-purpose controller, or some other processor array to perform computations and provide electronic display signals to a display device. The processor  222  processes data signals and may include various computing architectures including a complex instruction set computer (CISC) architecture, a reduced instruction set computer (RISC) architecture, or an architecture implementing a combination of instruction sets. Although  FIG. 2  includes a single processor  222 , multiple processors may be included. Other processors, operating systems, sensors, displays, and physical configurations may be possible. The processor  222  is coupled to the bus  220  for communication with the other components via signal line  203 . 
     The memory  224  stores instructions or data that may be executed by the processor  222 . The instructions or data may include code for performing the techniques described herein. For example, the memory  224  may store the virtual reality application  103 , which may be a series of modules that include instructions or data for generating three-dimensional videos. 
     The memory  224  may include a dynamic random access memory (DRAM) device, a static random access memory (SRAM) device, flash memory, or some other memory device. In some embodiments, the memory  224  also includes a non-volatile memory or similar permanent storage device and media including a hard disk drive, a CD-ROM device, a DVD-ROM device, a DVD-RAM device, a DVD-RW device, a flash memory device, or some other mass storage device for storing information on a more permanent basis. The memory  224  is coupled to the bus  220  for communication with the other components via signal line  205 . 
     The communication unit  226  may include hardware that transmits and receives data to and from the camera array  101 , the viewing device  115 , and the client device  105  or the server  120 , depending on whether the virtual reality application  103  is stored on the server  120  or the client device  105 , respectively. The communication unit  226  is coupled to the bus  220  via signal line  207 . In some embodiments, the communication unit  226  includes one or more ports for direct physical connection to the network  125  or another communication channel. For example, the communication unit  226  includes a USB, SD, CAT-5, or similar port for wired communication with the computing device  200 . In some embodiments, the communication unit  226  includes a wireless transceiver for exchanging data with the computing device  200  or other communication channels using one or more wireless communication methods, including IEEE 802.11, IEEE 802.16, Bluetooth®, or another suitable wireless communication method. 
     In some embodiments, the communication unit  226  includes a cellular communications transceiver for sending and receiving data over a cellular communications network including via short messaging service (SMS), multimedia messaging service (MMS), hypertext transfer protocol (HTTP), direct data connection, WAP, e-mail, or another suitable type of electronic communication. In some embodiments, the communication unit  226  includes a wired port and a wireless transceiver. The communication unit  226  also provides other conventional connections to the network  125  for distribution of files or media objects using standard network protocols including TCP/IP, HTTP, HTTPS, and SMTP, etc. 
     The display  228  may include hardware for displaying graphical data from the virtual reality application  103 . For example, the display  228  renders graphics for displaying a user interface where a user may view a two-dimensional video that was generated from a three-dimensional video. The display  228  is coupled to the bus  220  via signal line  209 . The display  228  is optional hardware that may not be included in the computing device  200 , for example, if the computing device  200  is a server. 
     The virtual reality application  103  may include an aggregation module  202 , a head tracking module  204 , a segmentation module  206 , a parameterization module  208 , an encoder module  210 , and a user interface module  212 . Although the modules are illustrated as being part of the same computing device  200 , in some embodiments some of the modules are stored on the server  120  and some of the modules are stored on the client device  105 . For example, the server  120  may include the head tracking module  204 , the segmentation module  206 , the parameterization module, and the encoder module  210  and the client device  105  may include the user interface module  212 . 
     The aggregation module  202  may include code and routines for aggregating video data. In some embodiments, the aggregation module  202  includes a set of instructions executable by the processor  222  to aggregate video data. In some embodiments, the aggregation module  202  is stored in the memory  224  of the computing device  200  and is accessible and executable by the processor  222 . In some embodiments, the aggregation module  202  may be part of a separate application. 
     The aggregation module  202  may receive video data from the camera array  101 . In some embodiments, the video data includes separate video recordings for each camera module included in the camera array  101  and a device identifier (ID) that identifies the camera module corresponding to each separate video recording. 
     A two-dimensional (2D) spherical panoramic image may be used to represent a panorama of an entire scene. The aggregation module  202  may generate two stereoscopic panorama images for two eyes to provide a stereoscopic view of the entire scene. For example, a left panoramic image may be generated for the left eye viewing and a right panoramic image may be generated for the right eye viewing. 
     A pixel in a panoramic image may be represented by a yaw value and a pitch value. Yaw represents rotation around the center and may be represented on the horizontal x-axis as: yaw=360°×x/width. Yaw has a value between 0° and 360°. Pitch represents up or down rotation and may be represented on the vertical y-axis as: pitch=90°×(height/2−y)/(height/2). Pitch has a value between −90° and 90°. 
     Typical stereoscopic systems (e.g., three-dimensional movies) may respectively show two different planar images to two eyes to create a sense of depth. In each planar image, all pixels in the image represent a single eye viewing position. For example, all pixels in the planar image may represent a view into the same viewing direction. However, in the panoramic image described herein (the left or right panoramic image), each pixel in the panoramic image may represent a view into a slightly different direction. For example, a pixel at an x position with pitch=0° in a left panoramic image may represent an eye viewing position of the left eye as the head is rotated by the yaw indicated by the x position. Similarly, a pixel at an x position with pitch=0° in a right panoramic image represents an eye viewing position of the right eye as the head is rotated by the yaw indicated by the x position. For pitch=0° (e.g., no up and down rotations), as the head is rotated from x=0 to x=width, a blended panorama for eye viewing positions with all 360-degree head rotations in the horizontal axis may be produced. 
     In some implementations, the blended panorama is effective for head rotations along the horizontal axis (e.g., yaw) but not for the vertical axis (e.g., pitch). For example, when a user looks upward, the quality of the stereo view may degrade. In order to correct this deficiency, the interocular distance may be adjusted based on the current pitch value. For example, if pitch≠0°, the interocular distance associated with the pitch may be adjusted as: interocular distance=max(interocular distance)×cos(pitch), where max(interocular distance) represents the maximum value of the interocular distance (e.g., the interocular distance is at its maximum when pitch=0°). In some examples, the maximum value of the interocular distance may be about 60 millimeters. In other examples, the maximum value of the interocular distance may have a value greater than 60 millimeters or less than 60 millimeters. 
     The aggregation module  202  may construct a left camera mapping map for each pixel in a left panoramic image. For example, for a pixel in a left panoramic image that represents a point in a panorama, the left camera mapping map may identify matching camera modules from a camera array with spherical modules that have each a better view for the point in the panorama than other camera modules. Thus, the left camera mapping map may map pixels in a left panoramic image to matching camera modules that have better views for the corresponding pixels. 
     For each pixel in a left panoramic image that represents a point in a panorama, the aggregation module  202  may determine a yaw, a pitch, and an interocular distance using the above mathematical expressions (1), (2), and (3), respectively. The aggregation module  202  may use the yaw and pitch to construct a vector representing a viewing direction of the left eye (e.g., a left viewing direction) to the corresponding point in the panorama. 
     Similarly, the aggregation module  202  may construct a right camera mapping map that identifies a corresponding matching camera module for each pixel in a right panoramic image. For example, for a pixel in a right panoramic image that represents a point in a panorama, the right camera mapping map may identify a matching camera module that has a better view for the point in the panorama than other camera modules. Thus, the right camera mapping map may map pixels in a right panoramic image to matching camera modules that have better views for the corresponding pixels. 
     For each pixel in a right panoramic image that represents a point in a panorama, the aggregation module  202  may determine a yaw, a pitch, and an interocular distance using the above mathematical expressions, respectively. The aggregation module  202  may use the yaw and pitch to construct a vector representing a viewing direction of the right eye (e.g., a right viewing direction) to the corresponding point in the panorama. 
     The aggregation module  202  may receive video recordings that describe image frames from the various camera modules in a camera array. The aggregation module  202  identifies a location and timing associated with each of the camera modules and synchronizes the image frames based on locations and timings of the camera modules. The aggregation module  202  synchronizes image frames captured by different camera modules at the same time frames. 
     For example, the aggregation module  202  receives a first video recording with first images from a first camera module and a second video recording with second images from a second camera module. The aggregation module  202  identifies that the first camera module is located at a position with yaw=0° and pitch=0° and the second camera module is located at a position with yaw=30° and pitch=0°. The aggregation module  202  synchronizes the first images with the second images by associating a first image frame from the first images at a time frame T=T 0  with a second image frame from the second images at the time frame T=T 0 , a third image frame from the first images at a time frame T=T 1  with a fourth image frame from the second images at the time frame T=T 1 , and so on and so forth. 
     The aggregation module  202  may construct a stream of left panoramic images from the image frames based on the left camera mapping map. For example, the aggregation module  202  identifies matching camera modules listed in the left camera mapping map. The aggregation module  202  constructs a first left panoramic image PI L,0  for a first time frame T=T 0  by stitching together image frames captured at the first time frame T=T 0  by the matching camera modules. The aggregation module  202  constructs a second left panoramic image PI L,1  at a second time frame T=T 1  using image frames captured at the second time frame T=T 1  by the matching camera modules, and so on and so forth. The aggregation module  202  constructs the stream of left panoramic images to include the first left panoramic image PI L,0  at the first time frame T=T 0 , the second left panoramic image PI L,1  at the second time frame T=T 1 , and other left panoramic images at other corresponding time frames. 
     Specifically, for a pixel in a left panoramic image PI L,i  at a particular time frame T=T 1  (i=0, 1, 2, . . . ), the aggregation module  202 : (1) identifies a matching camera module from the left camera mapping map; and (2) configures the pixel in the left panoramic image PI L,i  to be a corresponding pixel from an image frame captured by the matching camera module at the same time frame T=T 1 . The pixel in the left panoramic image PI L,i  and the corresponding pixel in the image frame of the matching camera module may correspond to the same point in the panorama. For example, for a pixel location in the left panoramic image PI L,i  that corresponds to a point in the panorama, the aggregation module  202 : (1) retrieves a pixel that also corresponds to the same point in the panorama from the image frame captured by the matching camera module at the same time frame T=T 1 ; and (2) places the pixel from the image frame of the matching camera module into the pixel location of the left panoramic image PI L,i . 
     Similarly, the aggregation module  202  constructs a stream of right panoramic images from the image frames based on the right camera mapping map by performing operations similar to those described above with reference to the construction of the stream of left panoramic images. For example, the aggregation module  202  identifies matching camera modules listed in the right camera mapping map. The aggregation module  202  constructs a first right panoramic image PI R,0  for a first time frame T=T 0  by stitching together image frames captured at the first time frame T=T 0  by the matching camera modules. The aggregation module  202  constructs a second right panoramic image PI R,1  at a second time frame T=T 1  using image frames captured at the second time frame T=T 1  by the matching camera modules, and so on and so forth. The aggregation module  202  constructs the stream of right panoramic images to include the first right panoramic image PI R,0  at the first time frame T=T 0 , the second right panoramic image PI R,1  at the second time frame T=T 1 , and other right panoramic images at other corresponding time frames. 
     Specifically, for a pixel in a right panoramic image PI R,i  at a particular time frame T=T 1  (i=0, 1, 2, . . . ), the aggregation module  202 : (1) identifies a matching camera module from the right camera mapping map; and (2) configures the pixel in the right panoramic image PI R,i  to be a corresponding pixel from an image frame captured by the matching camera module at the same time frame T=T 1 . The pixel in the right panoramic image PI R,i  and the corresponding pixel in the image frame of the matching camera module may correspond to the same point in the panorama. 
     The aggregation module  202  may obtain virtual reality content from the stream of left panoramic images, the stream of right panoramic images, and the audio data by sending one or more of the stream of left panoramic images, the stream of right panoramic images, and the audio data to the encoder module  210  for encoding. The encoder module  210  may compress the stream of left panoramic images and the stream of right panoramic images to generate a stream of compressed three-dimensional video data using video compression techniques. In some implementations, within each stream of the left or right panoramic images, the encoder module  210  may use redundant information from one frame to a next frame to reduce the size of the corresponding stream. For example, with reference to a first image frame (e.g., a reference frame), redundant information in the next image frames may be removed to reduce the size of the next image frames. This compression may be referred to as temporal or inter-frame compression within the same stream of left or right panoramic images. 
     Alternatively or additionally, the encoder module  210  may use one stream (either the stream of left panoramic images or the stream of right panoramic images) as a reference stream and may compress the other stream based on the reference stream. This compression may be referred to as inter-stream compression. For example, the encoder module  210  may use each left panoramic image as a reference frame for a corresponding right panoramic image and may compress the corresponding right panoramic image based on the referenced left panoramic image. The encoding process is discussed in greater detail below with reference to the encoder module  210 . Once the encoder module  210  completes the encoding process, the aggregation module  202  may transmit, via the communication unit  226 , the three-dimensional video to the viewing device  115 . 
     The head tracking module  204  may include code and routines for receiving head tracking data and generating a probabilistic model. In some embodiments, the head tracking module  204  includes a set of instructions executable by the processor  222  to receive head tracking data and generate the probabilistic model. In some embodiments, the head tracking module  204  is stored in the memory  224  of the computing device  200  and is accessible and executable by the processor  222 . 
     The head tracking module  204  may receive head tracking data from the viewing device  115  that corresponds to a three-dimensional video. The head tracking data may describe a person&#39;s head movement as the person watches the three-dimensional video. For example, the head tracking data may reflect that a person moved her head up and to the right to look at an image of a squirrel in a tree. In some embodiments, the head tracking data includes yaw (i.e., rotation around a vertical axis), pitch (i.e., rotation around a side-to-side axis), and roll (i.e., rotation around a front-to-back axis) for a person as a function of time that corresponds to the three-dimensional video. In some implementations, the head tracking module  204  determines a head-mounted display position for each person at a particular frequency, such as 10 Hz throughout the three-dimensional video. 
     In some embodiments, the head tracking module  204  generates user profiles based on the head tracking data. For example, the head tracking module  204  may aggregate head tracking data from multiple people and organize it according to a first most common region of interest in the three-dimensional video, a second most common region of interest in the three-dimensional video, and a third most common region of interest in the three-dimensional video. In some embodiments, the head tracking module  204  may generate user profiles based on demographic information corresponding to the people. For example, the head tracking module  204  may generate a user profile based on age, gender, etc. In some embodiments, the head tracking module  204  may generate a user profile based on physical characteristics. For example, the head tracking module  204  may identify people that move frequently while viewing the three-dimensional video and people that move very little. In some embodiments, the head tracking module  204  generates a user profile for a particular user. 
     The head tracking module  204  generates a probabilistic model of one or more positions of people that view a three-dimensional video. The probabilistic model identifies a probability of a viewer looking in a particular direction as a function of time. For example, the probabilistic model identifies that a viewer will likely look at a particular object as it moves in the three-dimensional video and that the viewer is unlikely to look direction behind the current location where the viewer is looking. 
     The head tracking module  204  may generate the probabilistic model on a pixel-by-pixel basis, based on regions in the view, such as a field-of-view, equal-sized divisions of the sphere, etc. 
     The probabilistic model may include a heat map. For example, the heat map may be rendered as a sequence of false-colored images. In some embodiments, the probabilistic model is displayed as an overlay on top of the three-dimensional video. In some embodiments, the probabilistic model is not displayed but is instead used by the encoder module  210  as described below. 
     In some embodiments, the parameterization module  208  uses the probabilistic model to determine where one or more people are looking. For example, analysis of one or more probabilistic models may indicate that people frequently look in particular direction when watching a given piece of virtual reality content. Subsequent people may benefit from this information since it may help them to know where they should be looking when watching the virtual reality content. The encoder module  210  may present recommendations to people about where they should be looking when viewing virtual reality content. The recommendations may be audio cues, visual cues or a combination of audio and visual cues. In some embodiments, the visual cues may include blurring every portion of the virtual reality content except for the recommended location where a viewer should be looking. 
     In some embodiments, the head tracking module  204  may use artificial intelligence to generate a set of probabilistic models from a set of three-dimensional videos. For example, the database  107  stored on the server  120  may include all three-dimensional videos offered by a company that generates virtual reality content. The head tracking module  204  may use head-tracking data from users that view those three-dimensional videos as a training set for generating the set of probabilistic models. The head tracking module  204  may include a neural network that is trained using the set of probabilistic models to determine a probabilistic distribution of viewer gaze. 
     In some embodiments, the artificial intelligence may be used iteratively, such that each time a new three-dimensional video is generated, the head tracking module  204  uses artificial intelligence (e.g., the neural network) to generate a probabilistic model for the new three-dimensional video. This advantageously results in the creation of probabilistic models for three-dimensional videos that have never been watched. 
     The segmentation module  206  may include code and routines for generating video segments from the three-dimensional video. In some embodiments, the segmentation module  206  includes a set of instructions executable by the processor  222  to generate the video segments. In some embodiments, the segmentation module  206  is stored in the memory  224  of the computing device  200  and is accessible and executable by the processor  222 . 
     The segmentation module  206  generates video segments from the three-dimensional video. In some embodiments, the segmentation module  206  generates equal-length video segments of a predetermined length. For example, the segmentation module  206  divides a three-minute three-dimensional video into 360 two-second segments. In some embodiments, the segmentation module  206  detects scene boundaries in the three-dimensional video and segments the three-dimensional video based on the scene boundaries. For example, the segmentation module  206  compares a first frame to a next frame to identify differences that indicate a transition between shots. When the segmentation module  206  detects the transition between shots, the segmentation module  206  generates a segment that includes the shot. In some embodiments, the segmentation module  206  may generate segments using a combination of detection of scene boundaries and timing. For example, the segmentation module  206  may first segment the three-dimensional video based on transitions between shots and further segment if any shots exceed a predetermined length of time, such as five seconds. 
     The parameterization module  208  may include code and routines for generating optimal segment parameters. In some embodiments, the parameterization module  208  includes a set of instructions executable by the processor  222  to generate the optimal segment parameters. In some embodiments, the parameterization module  208  is stored in the memory  224  of the computing device  200  and is accessible and executable by the processor  222 . 
     Three-dimensional video is viewable in all directions. Thus, the three-dimensional video may be modeled by a sphere where a user is in the center of the sphere and may view content from the three-dimensional video in any direction. In some embodiments, the parameterization module  208  converts the locations on the surface of the sphere into a plane. For example, the parameterization module  208  may use a map projection to transform the latitudes and longitudes of locations on the surface of the sphere into locations on a plane. In some embodiments, for each of the video segments, the parameterization module  208  determines a directional encoding format (i.e., a map projection) that projects latitudes and longitudes of locations of the surface of the sphere into locations on the plane. The directional encoding format, i.e., the projection of the latitudes and longitudes of locations of the surface of the sphere may be represented by the following equation:
 
 f (yaw,pitch,roll,parameters)→resolution  Eq. (1a)
 
     where the yaw, pitch, and roll values are obtained from the head-tracking data and/or the probabilistic model. Specifically, the yaw, pitch, and roll values describes a position of a person that is viewing the three-dimensional video as a function of time. The yaw, pitch, and roll values may include head-tracking data that is aggregated for multiple people that view the three-dimensional video. The parameters represent a location in the plane and the resolution is the resolution of the three-dimensional video at a region that corresponds to the yaw, pitch, and roll values. 
     In some embodiments, the directional encoding format may be represented by the following equation:
 
 f (parameters(pitch,yaw))→resolution  Eq. (1b)
 
     The parameterization module  208  may design a cost function that gives a measure of perceived resolution (e.g., a geometric mean of horizontal and vertical pixels per degree at a display center) for a user gazing in a particular direction at a particular timestamp for a particular set of parameters for the projection. For example, where the latitude/longitude is 0 on the sphere, the particular set of parameters may indicate how biased the encoding is towards its high-resolution region. In some embodiments, the total cost function may be defined as a sum of the individual costs as a function of optimal segment parameters at a particular point in the three-dimensional video. 
     The parameterization module  208  may set a resolution threshold, such as 10 pixels per degree, that is display and bandwidth-target dependent. If f(parameters) is greater than the resolution threshold, there is no benefit and a cost function that incorporates hinge loss from machine learning may be represented by the following equation:
 
cost(yaw,pitch,roll,params)=max(10− f (yaw,pitch,roll,params),0)  Eq. (2a)
 
     where params represents the optimal segment parameters. The parameterization module  208  uses the cost function to identify a region of interest on the plane based on the head-tracking data and/or the probabilistic model by minimizing a total cost for all users that viewed the three-dimensional video. Persons of ordinary skill in the art will recognize that other cost functions may be used. The parameterization module  208  may generate optimal segment parameters that minimize a sum-over position for the region of interest by applying the cost function. The optimal segment parameters may include a (yaw, pitch) tuple that encodes the region of interest in the video segment. In some embodiments, the parameterization module  208  determines one or more regions of low interest based on the probabilistic model. For example, a region of low interest may include a field-of-view or other division of a three-dimensional video based on the probabilistic model. 
     In some embodiments, the parameterization module  208  determines multiple directional encodings in each of the video segments for three-dimensional video to identify multiple regions of interest within the three-dimensional video. For example, the head tracking module  204  generates a first user profile and a second user profile and the parameterization module  208  generates first optimal segment parameters associated with the first user profile and second optimal segment parameters associated with the second user profile. 
     The parameterization module  208  may determine the multiple directional encodings using time-dependent clustering and/or a model that is similar to k-means clustering. The parameterization module  208  may determine n paths in the three-dimensional video where each path represents an independent set of parameters. If n&gt;1, the cost function may be defined as:
 
cost_multi(yaw,pitch,roll,parameter_sets)=max([cost(yaw,pitch,roll,param_set) for param_set in parameter_sets])  Eq. (2b)
 
     In some embodiments, a new directional encoding format may be designed with multiple potential regions of interest. The new directional encoding format may be converted into the above resolution and cost functions. 
     The encoder module  210  may include code and routines for re-encoding the three-dimensional video. In some embodiments, the encoder module  210  includes a set of instructions executable by the processor  222  to re-encode the three-dimensional video. In some embodiments, the encoder module  210  is stored in the memory  224  of the computing device  200  and is accessible and executable by the processor  222 . 
     The encoder module  210  may re-encode the three-dimensional video to include the optimal segment parameters for each of the video segments. For example, the encoder module  210  may re-encode the three-dimensional video by generating a re-encoded video that includes a high-resolution version of the region of interest and a lower resolution version of the other regions in the re-encoded video. The encoder module  210  may transmit, via the communication unit  226 , the re-encoded video and the optimal segment parameters for each of the video segments to the viewing device  115 . 
     In some embodiments, the encoder module  210  re-encodes the three-dimensional video by blurring portions of the three-dimensional video. The encoder module  210  may blur on a pixel-by-pixel basis according to a probability that the viewer is looking at a particular pixel based on the probabilistic model. Alternatively or additionally, the encoder module  210  may blur based on regions of interest or regions of low interest. 
     In some embodiments, the encoder module  210  blurs each of the video segments with varying intensity such that the intensity of a level of blur increases as the probability of a viewer looking in a particular direction decreases. For example, a video segment with a single moving object may include the region around the moving object optimized to include high resolution, the area surrounding the moving object including slightly lower resolution, the top and bottom of the video segment including significant blur etc. 
     In some embodiments, the encoder module  210  re-encodes the three-dimensional video to include optimal segment parameters for each of the video segments and/or blurs portions of each of the video segments responsive to a threshold number of people viewing the three-dimensional video. For example, if only two people viewed the three-dimensional video, the head-tracking data generated from those people viewing the three-dimensional video may be insufficient to reliably predict a probability of a viewer looking in a particular location. 
     The viewing device  115  may receive the re-encoded video and the optimal segment parameters for each of the video segments from the encoder module  210 . The viewing device  115  may use the optimal segment parameters for each of the video segments to un-distort the re-encoded video and texture the re-encoded video to the sphere to display the re-encoded video with the region of interest for each of the video segments displayed at a higher resolution that other regions in each of the video segments. 
     In some embodiments, the encoder module  210  re-encodes the three-dimensional video to include different sets of optimal segment parameters. For example, the head track module  204  may generate a first user profile that reflects a most common region in each of the video segments and a second user profile that reflects a second most common region in each of the video segments. The parameterization module  208  may generate first optimal segment parameters associated with the first user profile and second optimal segment parameters associated with the second user profile. The encoder module  210  may re-encode the three-dimensional video to include the first optimal segment parameters and the second optimal segment parameters for each of the video segments. The encoder module  210  may provide the re-encoded video, the first optimal segment parameters for each of the video segments, and the second optimal segment parameters for each of the video segments to the viewing device  115 . The viewing device  115  may un-distort the re-encoded video and texture the re-encoded video to the sphere to display the re-encoded video with two regions of interest for each of the video segments displayed at a higher resolution than other regions in each of the video segments. 
     In some embodiments, the head-track module  204  may generate multiple user profiles where different people were looking at the same region of interest for a particular video segment. For example, the head-track module  204  may generate different user profiles based on the age of the people that viewed the three-dimensional video. There may be instances where the people in the different age groups looked at the same object in the three-dimensional video because the object was moving fast, making a loud noise, etc. As a result, in some embodiments, the encoder module  210  may re-encode the three-dimensional video to include a single region of interest at a higher resolution than other regions of interest for a video segment even though the re-encoded video is based on multiple sets of segment parameters. In some embodiments where the head-track module  204  generates a user profile for a particular user, the encoder module  210  may re-encode the three-dimensional video for a user based on the user profile for the particular user. 
     In some embodiments, the encoder module  210  re-encodes the three-dimensional video for use as a two-dimensional video. For example, the encoder module  210  re-encodes the three-dimensional video to include the optimal segment parameters for each of the video segments and provides a re-encoded video and the optimal segment parameters for each of the video segments to the client device  105  or the viewing device  115 . The client device  105  may be used for browser-based players that display the two-dimensional video, for example, on a computer screen. The viewing device  115  may be used, for example, when a user wants to switch from an interactive three-dimensional video to an autopilot mode that displays a two-dimensional video that does all the work for the user. 
     The client device  105  or the viewing device  115  may use the re-encoded video and the optimal segment parameters for each of the video segments to generate a two-dimensional video that automates head movement. The optimal segment parameters for each video segment provide a model for how a user moves while watching the three-dimensional video. The two-dimensional video may automate pitch and yaw movements to simulate the model based on the optimal segment parameters. This may advantageously allow users to view an autopilot mode that automates the three-dimensional movement without having to control the two-dimensional video themselves by using, for example, a mouse, joystick, keys, etc. 
     In some embodiments, the encoder module  210  generates the two-dimensional video from the three-dimensional video based on the optimal segment parameters. Because the optimal segment parameters for a video segment indicate a region of interest in the video segment, the encoder module  210  may generate a two-dimensional video that depicts head tracking movement as automatic panning within the two-dimensional video. For example, the encoder module  210  may convert a three-dimensional video that includes a bird flying overhead to a two-dimensional video where it appears as if the camera moves overhead to look at the bird, the way a person viewing the three-dimensional video would move. This may advantageously allow a person viewing content on his desktop computer to have a simulated virtual-reality experience. 
     The encoder module  210  may generate a two-dimensional video from the three-dimensional video that includes multiple optimal segment parameters. For example, the encoder module  210  may generate the two-dimensional video based on multiple user profiles created based on a first most common region of interest and a second most common region of interest, demographics information, etc. 
     The encoder module  210  may compress the three-dimensional video to generate a stream of compressed three-dimensional video data using video compression techniques. Because portions of the three-dimensional video may include blurring, the three-dimensional video may be more compressible than traditional three-dimensional videos. In some implementations, the aggregation module  202  may encode the stream of three-dimensional video data (or compressed three-dimensional video data) and audio data to form a stream of three-dimensional video. For example, the encoder module  210  may compress the stream of three-dimensional video data using h.264 and the stream of three-dimensional audio data using advanced audio coding (AAC). In another example, the encoder module  210  may compress the stream of three-dimensional video data and the stream of three-dimensional audio data using a standard MPEG format. 
     The user interface module  212  may include code and routines for generating a user interface. In some embodiments, the user interface module  212  includes a set of instructions executable by the processor  222  to generate the user interface. In some embodiments, the user interface module  212  is stored in the memory  224  of the computing device  200  and is accessible and executable by the processor  222 . 
     In some embodiments, the user interface module  212  may generate a user interface that includes options for manipulating the camera array  101 . For example, the user interface may include options for determining whether the camera array  101  starts and stops recording. The user interface may also include an option for viewing a preview of the video data captured by the camera array  101 . 
     The user interface module  212  may generate a user interface that includes options for viewing the three-dimensional video or a two-dimensional video generated from the three-dimensional video. The options may include starting and stopping a video. In some embodiments, the user interface includes a timeline of the video and an option to view the video starting at a section on the timeline. 
     In some embodiments, the user interface module  212  crops the region of interest for one or more of the video segments based on the optimal segment parameters to form one or more thumbnails of one or more cropped regions of interest. For example, the user interface module  212  may select a predetermined number of regions of interest to crop in the video segments. In some embodiments, the user interface module  212  may determine based on the head-tracking data that regions of interest where a threshold percentage of people looked at the same region of interest that the region of interest qualifies for cropping. For example, if the three-dimensional video includes an explosion and 98% of the people looked at the explosion, the user interface module  212  may determine that the 98% exceeds the threshold percentage of 75% and crop the region of interest. The user interface module  212  may generate a timeline of the three-dimensional video that includes the thumbnails. 
     Turning to  FIG. 3 , an example user interface  300  is illustrated that includes a video screen  305  for displaying a video and a timeline  310 . The video may be a three-dimensional video or a two-dimensional video generated from the three-dimensional video. The video screen  305  includes a play button  315  for starting the video. The timeline  310  includes three thumbnails  320 : a first thumbnail  320   a  of a zebra, a second thumbnail  320   b  of a peacock, and a third thumbnail  320   c  of a killdeer. The thumbnails  320  ( 320   a ,  320   b ,  320   c ) include a cropped version of the regions of interest in the video. The user interface module  212  generated the three thumbnails based on a percentage of people viewing the region of interest in each of the video segments exceeding a threshold percentage. 
     In some embodiments, the user interface module  212  generates a user interface that include an option for the user to modify the two-dimensional video. In some embodiments where multiple user profiles are available (e.g., a first user profile and a second user profile), the user interface may include an option to switch from the first user profile to the second user profile. In this example, the client device  105  may switch from using the re-encoded video and first optimal segment parameters to using the re-encoded video and second optimal segment parameters to generate the two-dimensional video. In some embodiments, the user interface may provide descriptions for different user profiles, such as most common for the most common regions of interest, second most common, slow movement for head-tracking data associated with people that move slowly while viewing the three-dimensional video, fast movement for head-tracking data associated with people that move quickly while viewing the three-dimensional video, etc. 
     In some embodiments, the user interface may include an option for the user to modify the two-dimensional video by directly inputting a pitch and yaw. For example, where the user is viewing the two-dimensional video on a client device  105 , the user may use a pointing device, such as a mouse, to select a region of interest in the two-dimensional video. The client device  105  may identify the pitch and yaw associated with the region of interest that the user selected. The client device  105  may use the pitch and yaw as optimal segment parameters to modify the two-dimensional video, for example, by displaying more detail for the selected region of interest. In some embodiments, the client device  105  may identify movement associated with the selection. For example, the client device  105  may identify mouse movement in an upward direction. The client device  105  may, as a result, display the two-dimensional video as panning upwards. 
     In another example, the user may directly input the pitch and yaw based on gyroscopic input. For example, if a user is viewing the two-dimensional video on a viewing device  115 , the user&#39;s head may move upwards. A gyroscope associated with the viewing device  115  may detect the upward movement and modify the two-dimensional view to display the two-dimensional video as panning upwards. In yet another embodiment, the client device  105  may be a mobile device, such as a smartphone, that includes a gyroscope that detects a user rotating the client device  105  to simulate upward movement. The client device  105  may modify the two-dimensional view to display the two-dimensional video as panning upwards based on the user rotating the client device  105 . 
     Example Flow Diagrams 
       FIG. 4  illustrates an example flow diagram  400  for generating three-dimensional video according to some embodiments. The steps in  FIG. 4  may be performed by the virtual reality application  103   a  stored on the client device  105 , the virtual reality application  103   b  stored on the server  120 , or a combination of the virtual reality application  103   a  stored on the client device  105  and the virtual reality application  103   b  the server  120 . 
     At step  402 , head-tracking data is received that describes one or more positions of one or more people while the one or more people are viewing a three-dimensional video (3D) on one or more viewing devices  115 . At step  404 , video segments are generated for the three-dimensional video. For example, the three-dimensional video may be divided into video segments that are each two seconds long. At step  406 , for each of the video segments, a directional encoding format is determined that projects latitudes and longitudes of locations of a surface of a sphere into locations on a plane, a cost function is determined that identifies a region of interest on the plane based on the head-tracking data, and optimal segment parameters are generated that minimize a sum-over position for the region of interest. 
     The separation of various components and servers in the embodiments described herein should not be understood as requiring such separation in all embodiments, and it should be understood that the described components and servers may generally be integrated together in a single component or server. Additions, modifications, or omissions may be made to the illustrated embodiment without departing from the scope of the present disclosure, as will be appreciated in view of the disclosure. 
       FIG. 5  illustrates an example flow diagram  500  for re-encoding a three-dimensional video with blurred portions. The steps in  FIG. 5  may be performed by the virtual reality application  103   a  stored on the client device  105 , the virtual reality application  103   b  stored on the server  120 , or a combination of the virtual reality application  103   a  stored on the client device  105  and the virtual reality application  103   b  the server  120 . 
     At step  502 , head-tracking data is received that describes one or more positions of people while the people are viewing a three-dimensional video on viewing devices  115 . At step  504 , a probabilistic model of the one or more positions of the people is generated based on the head-tracking data, where the probabilistic model identifies a probability of a viewer looking in a particular direction as a function of time. For example, the probabilistic model may include a heat map that includes a visual representation of the probability that a viewer is looking in a particular direction as a function of time. 
     At step  506 , video segments are generated from the three-dimensional video. At step  508 , for each of the video segments: determine a directional encoding format that projects latitudes and longitudes of locations of a surface of a sphere onto locations on a plane, determine a cost function that identifies a region of interest on the plane based on the probabilistic model, generate optimal segment parameters that minimize a sum-over position for the region of interest, and identify a probability of a viewer looking in a particular direction as a function of time based on the probabilistic model. 
     At step  510 , the three-dimensional video is re-encoded to include the optimal segment parameters for each of the video segments and to blur portions of each of the video segments based on the probability, where an intensity of a level of blur increases as the probability of the viewer looking in the particular direction decreases. 
       FIG. 6  illustrates an example flow diagram  600  for generating optimal segment parameters and a probabilistic model from a training set. The steps in  FIG. 6  may be performed by the virtual reality application  103   a  stored on the client device  105 , the virtual reality application  103   b  stored on the server  120 , or a combination of the virtual reality application  103   a  stored on the client device  105  and the virtual reality application  103   b  the server  120 . 
     At step  602 , head-tracking data is received that describes one or more positions of people while the people are viewing a set of three-dimensional videos. For example, the set of three-dimensional videos may include all the three-dimensional videos associated with a company that produces virtual-reality content. The company may provide the set of three-dimensional videos to users and receive, after receiving user consent, the head-track data after the users watch the virtual reality content. 
     At step  604 , a set of probabilistic models is generated of the one or more positions of the people based on the head-tracking data. For example, the set of probabilistic models describe the probability of a viewer looking in a particular direction for a corresponding three-dimensional video. 
     At step  606 , a first probabilistic model for a first three-dimensional video is estimated, where the first three-dimensional video is not part of the set of three-dimensional videos. For example, the set of three-dimensional videos serve as a training set for a neural network that can estimate the probability of a viewer looking in a particular direction in the first three-dimensional video. This advantageously allows the first probabilistic model to be generated without the expense associated with having people view the first three-dimensional video to generate the first probabilistic model. 
     At step  608 , for each of the video segments: a directional encoding format is determined that projects latitudes and longitudes of locations of a surface of a sphere onto locations on a plane, a cost function is determined that identifies a region of interest on the plane based on the first probabilistic model, optimal segment parameters are generated that minimize a sum-over position for the region of interest, and a probability is identified of a viewer looking in a particular direction as a function of time based on the first probabilistic model. 
     Embodiments described herein contemplate various additions, modifications, and/or omissions to the above-described panoptic virtual presence system, which has been described by way of example only. Accordingly, the above-described camera system should not be construed as limiting. For example, the camera system described with respect to  FIG. 1  below may include additional and/or different components or functionality than described above without departing from the scope of the disclosure. 
     Embodiments described herein may be implemented using computer-readable media for carrying or having computer-executable instructions or data structures stored thereon. Such computer-readable media may be any available media that may be accessed by a general purpose or special purpose computer. By way of example, and not limitation, such computer-readable media may include tangible computer-readable storage media including Random Access Memory (RAM), Read-Only Memory (ROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Compact Disc Read-Only Memory (CD-ROM) or other optical disk storage, magnetic disk storage or other magnetic storage devices, flash memory devices (e.g., solid state memory devices), or any other storage medium which may be used to carry or store desired program code in the form of computer-executable instructions or data structures and which may be accessed by a general purpose or special purpose computer. Combinations of the above may also be included within the scope of computer-readable media. 
     Computer-executable instructions comprise, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing device (e.g., one or more processors) to perform a certain function or group of functions. Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims. 
     As used herein, the terms “module” or “component” may refer to specific hardware embodiments configured to perform the operations of the module or component and/or software objects or software routines that may be stored on and/or executed by general purpose hardware (e.g., computer-readable media, processing devices, etc.) of the computing system. In some embodiments, the different components, modules, engines, and services described herein may be implemented as objects or processes that execute on the computing system (e.g., as separate threads). While some of the system and methods described herein are generally described as being implemented in software (stored on and/or executed by general purpose hardware), specific hardware embodiments or a combination of software and specific hardware embodiments are also possible and contemplated. In this description, a “computing entity” may be any computing system as previously defined herein, or any module or combination of modulates running on a computing system. 
     All examples and conditional language recited herein are intended for pedagogical objects to aid the reader in understanding the invention and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Although embodiments of the inventions have been described in detail, it may be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.