Patent Publication Number: US-10313818-B2

Title: HRTF personalization based on anthropometric features

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation application and claims priority to U.S. patent application Ser. No. 14/265,154, filed Apr. 29, 2014, entitled “HRTF PERSONALIZATION BASED ON ANTHROPOMETRIC FEATURES,” now issued U.S. Pat. No. 9,900,722, which application is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     Head-related transfer functions (HRTFs) are acoustic transfer functions that describe the transfer of sound from a sound source position to the entrance of the ear canal of a human subject. HRTFs may be used to process a non-spatial audio signal to generate a HRTF-modified audio signal. The HRTF-modified audio signal may be played back over a pair of headphones that are placed over the ears of the human subject to simulate sounds as coming from various arbitrary locations with respect to the ears of the human subject. Accordingly, HRTFs may be used for a variety of applications, such as 3-dimensional (3D) audio for games, live streaming of audio for events, music performances, audio for virtual reality, and/or other forms of audiovisual-based entertainment. 
     However, due to anthropometric variability in human subjects, each human subject is likely to have a unique set of HRTFs. For example, the set of HRTFs for a human subject may be affected by anthropometric features such as the circumference of the head, the distance between the ears, neck length, etc. of the human subject. Accordingly, the HRTFs for a human subject are generally measured under anechoic conditions using specialized acoustic measuring equipment, such that the complex interactions between direction, elevation, distance and frequency with respect to the sound source and the ears of the human subject may be captured in the functions. Such measurements may be time consuming to perform. Further, the use of specialized acoustic measuring equipment under anechoic conditions means that the measurement of personalized HRTFs for a large number of human subjects may be difficult or impractical. 
     SUMMARY 
     Described herein are techniques for generating personalized head-related transfer functions (HRTFs) for a human subject based on a relationship between the anthropometric features of the human subject and the HRTFs of the human subject. The techniques involve the generation of a training dataset that includes anthropometric feature parameters and measured HRTFs of multiple representative human subjects. The training dataset is then used as the basis for the synthesis of HRTFs for a human subject based on the anthropometric feature parameters obtained for the human subject. 
     The techniques may rely on the principle that the magnitudes and the phase delays of a set of HRTFs of a human subject may be described by the same sparse combination as the corresponding anthropometric data of the human subject. Accordingly, the HRTF synthesis problem may be formulated as finding a sparse representation of the anthropometric features of the human subject with respect to the anthropometric features in the training dataset. The synthesis problem may be used to derive a sparse vector that represents the anthropometric features of the human subject as a linear superposition of the anthropometric features belonging to a subset of the human subjects from the training dataset. The sparse vector is subsequently applied to HRTF tensor data and HRTF group delay data of the measured HRTFs in the training dataset to obtain the HRTFs for the human subject. 
     In alternative instances, the imposition of sparsity in the synthesis problem may be substituted with the application of ridge regression to derive a vector that is a minimum representation. In additional instances, the use of a non-negative sparse representation in the synthesis problem may eliminate the use of negative weights during the derivation of the sparse vector. 
     This Summary is provided to introduce a selection of concepts in a simplified form that is further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The detailed description is described with reference to the accompanying figures. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. The use of the same reference number in different figures indicates similar or identical items. 
         FIG. 1  is a block diagram that illustrates an example scheme for using the anthropometric feature parameters of a human subject to derive personalized HRTFs for a human subject. 
         FIG. 2  is an illustrative diagram that shows example actual and virtual sound source positions for the measurement of HRTFs. 
         FIG. 3  is an illustrative diagram that shows example components of a HRTF engine that provides personalized HRTFs for a human subject based on the anthropometric feature parameters of the human subject. 
         FIG. 4  is a flow diagram that illustrates an example process for using the anthropometric feature parameters of a human subject to derive personalized HRTFs for the human subject. 
         FIG. 5  is a flow diagram that illustrates an example process for obtaining anthropometric feature parameters and HRTFs of a training subject. 
         FIG. 6  is a flow diagram that illustrates an example process for generating a personalized HRTF for a test subject. 
     
    
    
     DETAILED DESCRIPTION 
     Described herein are techniques for generating personalized head-related transfer functions (HRTFs) for a human subject based on a relationship between the anthropometric features of the human subject and the HRTFs of the human subject. The techniques involve the generation of a training dataset that includes anthropometric feature parameters and measured HRTFs of multiple representative human subjects. The training dataset is then used as the basis for the synthesis of HRTFs for a human subject based on the anthropometric feature parameters obtained for the human subject. 
     The techniques may rely on the principle that the magnitudes and the phase delays of a set of HRTFs of a human subject may be described by the same sparse combination as the corresponding anthropometric data of the human subject. Accordingly, the HRTF synthesis problem may be formulated as finding a sparse representation of the anthropometric features of the human subject with respect to the anthropometric features in the training dataset. The synthesis problem may be used to derive a sparse vector that represents the anthropometric features of the human subject as a linear superposition of the anthropometric features of a subset of the human subjects from the training dataset. The sparse vector is subsequently applied to HRTF tensor data and HRTF group delay data of the measured HRTFs in the training dataset to obtain the HRTFs for the human subject. 
     In alternative instances, the imposition of sparsity in the synthesis problem may be substituted with the application of ridge regression to derive a vector that is a minimum representation. In additional instances, the use of a non-negative sparse representation in the synthesis problem may eliminate the use of negative weights during the derivation of the sparse vector. 
     In at least one embodiment, the derivation of personalized HRTFs for a human subject involves obtaining multiple anthropometric feature parameters and multiple HRTFs of multiple training subjects. Subsequently, multiple anthropometric feature parameters of a human subject are acquired. A representation of the statistical relationship between the plurality of anthropometric feature parameters of the human subject and a subset of the multiple anthropometric feature parameters belonging to the plurality of training subjects is determined. The representation of the statistical relationship is then applied to the multiple HRTFs of the plurality of training subjects to obtain a set of personalized HRTFs for the human subject. 
     Thus, in some embodiments, the statistical relationship may consist of a statistical model that jointly describes both the anthropometric features of the human subject and the HRTFs of the human subject. In other embodiments, the anthropometric features of the human subject and the HRTFs of the human subject may be described using other statistical relationships, such as Bayesian networks, dependency networks, and so forth. 
     The use of the techniques described herein may enable the rapid derivation of personalized HRTFs for a human subject based on the anthropometric feature parameters of the human subject. Accordingly, this means that personalized HRTFs for the human subject may be obtained without the use of specialized acoustic measuring equipment in an anechoic environment. The relative ease at which the personalized HRTFs are obtained for human subjects may lead to the widespread use of personalized HRTFs to develop personalized 3-dimensional audio experiences. Examples of techniques for generating personalized HRTFs in accordance with various embodiments are described below with reference to  FIGS. 1-6 . 
     Example Scheme 
       FIG. 1  is a block diagram that illustrates an example scheme  100  for using the anthropometric feature parameters of the human subject to derive personalized HRTFs for a human subject. The example scheme  100  may include HRTF measurement equipment  102  and HRTF engine  104 . The HRTF measurement equipment  102  may be used to obtain HRTFs from multiple training subjects  106 . For example, the training subjects  106  may include 36 human subjects of both genders with an age range from 16 to 61 years old. 
     In various embodiments, the HRTF measurement equipment  102  may include an array of loudspeakers (e.g., 16 speakers) that are distributed evenly in an arc so as to at least partially surround a seated human subject in a spherical arrangement that excludes a spherical wedge. In at least one embodiment, the spherical wedge may be a 90° spherical wedge, i.e., a wedge that is a quarter of a sphere. However, the spherical wedge may constitute other wedge portions of a sphere in additional embodiments. The array of loudspeakers may be moved to multiple measurement positions (e.g., 25 positions) at multiple steps around the human subject. For example, the array of loud speakers may be moved at steps 11.25° between −45° elevation in front of the human subject to −45° elevation behind the human subject. 
     The human subject may sit in a chair with his or her head fixed in the center of the arc. Chirp signals of multiple frequencies played by the loudspeakers may be recorded with omni-directional microphones that are placed in the ear canal entrances of the seated human subject. In this way, the HRTF measurement equipment  102  may measure HRTFs for sounds that emanate from multiple positions around the human subject. For example, in an instance in which the chirp signals are emanating from an array of 16 loudspeakers that are moved to 25 array positions, the HRTFs may be measured for a total of 400 positions. 
     Since the loudspeakers are arranged in a spherical arrangement that partially surrounds the human subject, the HRTF measurement equipment  102  does not directly measure HRTFs at positions underneath the human subject (i.e., within the spherical wedge). Instead, the HRTF measurement equipment  102  may employ a computing device and an interpolation algorithm to derive the HRTFs for virtual positions in the spherical wedge underneath the human subjects. In at least one embodiment, the HRTFs for the virtual t positions may be estimated based on the measured HRTFs using a lower-order non-regularized least-squares fit technique. 
       FIG. 2  is an illustrative diagram  202  that shows example actual and virtual sound source positions for the measurement of HRTFs. As shown, region  204  may correspond to a position of a training subject (e.g., a head of the training subject). Sound source positions at which loudspeakers may emanate sound for directly measured HRTFs are indicated with “x”s, such as the “x”  206 . Conversely, virtual sound positions within a spherical wedge for which HRTFs may be interpolated are indicated with “o”s, such as the “o”  208 . However, in other embodiments, the HRTF measurement equipment  102  may provide sounds from sound source positions that completely surround a training subject in a total spherical arrangement. In such embodiments, the HRTF measurement equipment  102  may obtain measured HRTFs for the training subject without the use of interpolation. 
     Accordingly, in one instance, the HRTF measurement equipment  102  may acquire HRTFs for 512 sound source locations that are each represented by multiple frequency bins for the left and right ears of the human subject. For example, the multiple frequency bins may include 512 frequency bins that range from zero Hertz (Hz) to 24 kilohertz (kHz). The HRTF measurement equipment  102  may be used to obtain measured HRTFs  108  for the multiple training subjects  106 . In various embodiments, the HRTFs of each training subject may be represented as a set of frequency domain filters in pairs, with one set of frequency domain filters for the left ear and one set of frequency domain filters for the right ear. The measured HRTFs  108  may be stored by the HRTF measurement equipment  102  as part of the training data  110 . 
     Returning to  FIG. 1 , the training data  110  may further include the anthropometric feature parameters  112  of the training subjects  106 . The anthropometric feature parameters  112  may be obtained using manual measuring tools (e.g., tape measures, rulers, etc.), questionnaires, and/or automated measurement tools. For example, a computer-vision based tool may include a camera system that captures images of the training subjects  106 , such that an image processing algorithm may extract anthropometric measurements from the images. In other examples, other automated measurement tools that employ other sensing technologies, such as ultrasound, infrared and/or so forth, may be used to obtain anthropometric measurements of the training subjects  106 . In some embodiments, the anthropometric feature parameters  112  may include one or more of the following parameters list below in Table I. 
     
       
         
           
               
             
               
                 TABLE I 
               
               
                   
               
               
                 Anthropometric Feature parameters 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Head-related features: 
               
               
                   
                 head height, width, depth, and circumference; 
               
               
                   
                 neck height, width, depth, and circumference; 
               
               
                   
                 distance between eyes/distance between ears; 
               
               
                   
                 maximum head width (including ears); 
               
               
                   
                 ear canals and eyes positions; 
               
               
                   
                 intertragal incisure width; inter-pupillary distance. 
               
               
                   
                 Ear-related features: 
               
               
                   
                 pinna: position offset (down/back); height; width; rotation angle; 
               
               
                   
                 cavum concha height and width; 
               
               
                   
                 cymba concha height; fossa height. 
               
               
                   
                 Limbs and full body features: 
               
               
                   
                 shoulder width, depth, and circumference; 
               
               
                   
                 torso height, width, depth, and circumference; 
               
               
                   
                 distances: foot- knee; knee- hip; elbow- wrist; wrist- fingertip; 
               
               
                   
                 height. 
               
               
                   
                 Other features: 
               
               
                   
                 gender; age range; age; race; 
               
               
                   
                 hair color; eye color; weight; shirt size; shoe size. 
               
               
                   
                   
               
            
           
         
       
     
     The HRTF engine  104  may leverage the training data  110  to synthesize HRTFs for a test subject  114  based on the anthropometric feature parameters  118  obtained for the test subject  114 . In various embodiments, the HRTF engine  104  may synthesize a set of personalized HRTFs for a left ear of the test subject  114  and/or a set of personalized HRTFs for the right ear of the test subject  114 . 
     The HRTF engine  104  may be executed on one or more computing devices  116 . The computing devices  116  may include general purpose computers, such as desktop computers, tablet computers, laptop computers, servers, and so forth. However, in other embodiments, the computing devices  116  may include smart phones, game consoles, or any other electronic devices. The anthropometrics feature parameters  118  may include one or more of the measurements listed in Table I. In various embodiments, the anthropometric feature parameters  118  may be obtained using manual measuring tools, questionnaires, and/or automated measurement tools. 
     The HRTF engine  104  may rely on the principle that the magnitudes and the phase delays of a particular set of HRTFs may be described by the same sparse combination as the corresponding anthropometric data. Accordingly, the HRTF engine  104  may derive a sparse vector that represents the anthropometric feature parameters  118  of the test subject  114 . The sparse vector may represent the anthropometric feature parameters  118  as a linear superposition of the anthropometric feature parameters of a subset of the human subjects from the training data  110 . Subsequently, the HRTF engine  104  may perform HRTF magnitude synthesis  120  by applying the sparse vector directly on the HRTF tensor data in the training data  110  to obtain a HRTF magnitude. Likewise, the HRTF engine  104  may perform HRTF phase synthesis  122  by applying the sparse vector directly on the HRTF group delay data in the training data  110  to obtain a HRTF phase. The HRTF engine  104  may further combine the HRTF magnitude and the HRTF phase to compute a personalized HRTF. The HRTF engine  104  may perform the synthesis process for each ear of the test subject  114 . Accordingly, personalized HRTFs  124  for the test subject  114  may include HRTFs for the left ear and/or the right ear of the test subject  114 . 
     Example Components 
       FIG. 3  is an illustrative diagram that shows example components of a HRTF engine  104  that provides personalized HRTFs for a human subject based on the anthropometric feature parameters of the human subject. The HRTF engine  104  may be implemented by the one or more computing devices  116 . The computing device  116  may include one or more processors  302 , a user interface  304 , a network interface  306 , and memory  308 . Each of the processors  302  may be a single-core processor or a multi-core processor. The user interface  304  may include a data output device (e.g., visual display, audio speakers), and one or more data input devices. The data input devices may include, but are not limited to, combinations of one or more of keypads, keyboards, mouse devices, touch screens that accept gestures, microphones, voice or speech recognition devices, and any other suitable devices or other electronic/software selection methods. 
     The network interface  306  may include wired and/or wireless communication interface components that enable the computing devices  116  to transmit and receive data via a network. In various embodiments, the wireless interface component may include, but is not limited to cellular, Wi-Fi, Ultra-wideband (UWB), personal area networks (e.g., Bluetooth), satellite transmissions, and/or so forth. The wired interface component may include a direct I/O interface, such as an Ethernet interface, a serial interface, a Universal Serial Bus (USB) interface, and/or so forth. As such, the computing devices  116  may have network capabilities. For example, the computing devices  116  may exchange data with other electronic devices (e.g., laptops computers, desktop computers, mobile phones servers, etc.) via one or more networks, such as the Internet, mobile networks, wide area networks, local area networks, and so forth. Such electronic devices may include computing devices of the HRTF measuring equipment  102  and/or automated measurement tools. 
     The memory  308  may be implemented using computer-readable media, such as computer storage media. Computer-readable media includes, at least, two types of computer-readable media, namely computer storage media and communication media. Computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules, or other data. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that may be used to store information for access by a computing device. In contrast, communication media may embody computer readable instructions, data structures, program modules, or other data in a modulated data signal, such as a carrier wave, or other transmission mechanism. As defined herein, computer storage media does not include communication media. 
     The memory  308  of the computing devices  116  may store an operating system  310  and modules that implement the HRTF engine  104 . The modules may include a training data module  312 , a measurement extraction module  314 , a HRTF magnitude module  316 , a HRTF phase module  318 , a vector generation module  320 , a HRTF synthesis module  322 , and a user interface module  324 . Each of the modules may include routines, programs instructions, objects, and/or data structures that perform particular tasks or implement particular abstract data types. Additionally, a data store  326  may reside in the memory  308 . 
     The operating system  310  may include components that enable the computing devices  116  to receive data via various inputs (e.g., user controls, network interfaces, and/or memory devices), and process the data using the processors  302  to generate output. The operating system  310  may further include one or more components that present the output (e.g., display an image on an electronic display, store data in memory, transmit data to another electronic device, etc.). The operating system  310  may enable a user to interact with modules of the HRTF engine  104  using the user interface  304 . Additionally, the operating system  310  may include other components that perform various other functions generally associated with an operating system. 
     The training data module  312  may obtain the measured HRTFs  108  from the HRTF measurement equipment  102 . In turn, the training data module  312  may store the measured HRTFs  108  in the data store  322  as part of the training data  110 . In various embodiments, given N training subjects  106 , the HRTFs for each of the training subjects  106  may be encapsulated by a tensor of size D×K, where D is the number of HRTF directions and K is the number of frequency bins. The training data module  312  may stack the HRTFs of the training subjects  106  in a tensor H∈   N×D×K , such that the value H n,d,k  corresponds to the k-th frequency bin for d-th HRTF direction of the n-th person. 
     The HRTF phase for each of the training subjects  106  may be described by a single interaural time delay (ITD) scaling factor for an average group delay. This is because HRTF phase response is mostly linear and listeners are generally insensitive to the details of the interaural phase spectrum as long as the ITD of the combined low-frequency part of a waveform is maintained. Accordingly, the phase response of HRTFs for a test subject may be modeled as a time delay that is dependent on the direction and the elevation of a sound source. 
     Additionally, ITD as a function of the direction and the elevation of a sound source may be assumed to be similar across multiple human subjects, with the scaling factor being the difference across the multiple human subjects. The scaling factor for a human subject may be dependent on the anthropometric features of the human subject, such as the size of the head and the positions of the ears. Thus, the individual feature of the HRTF phase response that varies for each human subject is a scaling factor. The scaling factor for a particular human subject may be a value that is multiplied with an average ITD of the multiple human subjects to derive an individual ITD for the particular human subject. As a result, the problem of personalizing HRTF phases to learn a single scaling factor for a human subject may be a function of the anthropometric features belonging to the human subject. 
     The training data module  312  may store the ITD scaling factors for the training subjects  106 . Given N training subjects  106 , The ITD scaling factors for the training subjects  106  may be stacked in a vector H∈   N , such that the value H n  corresponds to the ITD scaling factor of the n-th person. 
     The training data module  312  may convert the categorical features (e.g., hair color, race, eye color, etc.) of the anthropometric feature parameters  112  into binary indicator variables. Alternatively or concurrently, the training data module  312  may apply a min-max normalization to each of the rest of the feature parameters separately to make the feature parameters more uniform. Accordingly, each training subject may be described by A anthropometric features, such that each training subject is viewed as a point in the space [0,1] A . Additionally, the training data module  312  may arrange the anthropometric features in the training data  110  in a matrix X∈[0,1] N×A , in which one row of X represents all the features of one training subject. 
     The measurement extraction module  314  may obtain one or more of the anthropometric feature parameters  118  of the test subject  116  from an automated measurement tool  328 . For example, an automated measurement tool  328  in the form of a computer-vision tool may capture images of the test subject  116  and extract anthropometric measurements from the images. The automated measurement tool  328  may pass the anthropometric measurements to the HRTF engine  104 . 
     The HRTF magnitude module  316  may synthesize the HRTF magnitudes for an ear of the test subject  114  based on anthropometric features y∈[0,1] A  of the test subject  114 . The HRTF synthesis problem may be treated by the HRTF magnitude module  316  as finding a sparse representation of the anthropometric features of the test subject  114 , in which the anthropometric features of the test subject  114  and the synthesized HRTFs share the same relationship and the training data  110  is sufficient to cover the anthropometric features of the test subject  114 . 
     Accordingly, the HRTF magnitude module  316  may use the vector generation module  320  to learn a sparse vector=[β 1 , β 2 , . . . , β N ] T . The sparse vector may represent the anthropometric features of the test subject  114  as a linear superposition of the anthropometric features from the training data (ŷ=β T X). This task may be reformulated as a minimization problem for a non-negative shrinking parameter λ:
 
{circumflex over (β)}=argmin β (Σ a=1   A ( y   a −Σ n=1   N β n   X   n,a ) 2 +λΣ n=1   N |β n |).  (1)
 
     The first part of equation (1) minimizes the differences between values of y and the new representation of y. The sparse vector ∈   N  provides one weight value per each of the training subject  106 , and not per anthropometric feature. The second part of the equation (1) is the l 1  norm regularization term that imposes the sparsity constraints, which makes the vector β sparse. The shrinking parameter λ in the regularization term controls the sparsity level of the model and the amount of the regularization. In some embodiments, the vector generation module  320  may tune the parameter λ for the synthesis of HRTF magnitudes based on the training data  110 . The tuning may be performed using a leave-one-person-out cross-validation approach. Accordingly, the vector generation module  320  may select a parameter λ that provides the smallest cross-validation error. In at least one embodiment, the cross-validation error may be calculated as the root mean square error, using the following equation: 
                       LSD   ⁡     (     H   ,     H   ^       )       =           1   D     ⁢       ∑     d   =   1     D     ⁢       (       LSD   d     ⁡     (     H   ,     H   ^       )       )     2           ⁡     [   dB   ]         ,           (   2   )               
in which the log-spectral distortion (LSD) is a distance measure between two HRTFs for a given sound source direction d and all frequency bins from the range k 1  to k 2 , and D is the number of available HRTF directions.
 
     In various embodiments, the vector generation module  320  may solve the minimization problem using the Least Absolute Shrinkage and Selection Operator (LASSO), or using a similar technique. The HRTFs of the test subject  114  share the same relationship as the anthropometric features of the test subject  114 . Accordingly, once the vector generation module  320  learns the sparse vector β from the anthropometric features of the test subject  114 , the HRTF magnitude module  316  may apply the learned sparse vector β directly to the HRTF tensor data included in the training data  110  to synthesize HRTF values Ĥ for the test subject  114  as follows:
 
 Ĥ   d,k =Σ n=1   N β n   H   n,d,k ,  (3)
 
in which Ĥ d,k  corresponds to k-th frequency bin for d-th HRTF direction of a synthesized HRTF.
 
     In some embodiments, the minimization problem that represents that task may include a non-negative sparse representation. The non-negative sparse representation may ensure that the weight values provided by the sparse vector ∈   N  are non-negative. Accordingly, the minimization problem for the non-negative shrinking parameter λ may be redefined as:
 
{circumflex over (β)}=argmin β (Σ a=1   A ( y   a −Σ n=1   N β n   X   n,a ) 2 +λΣ n=1   N |β n |),
 
subject to ∀ n=1   N β n ≥0.  (4)
 
As such, the vector generation module  320  may solve this minimization problem in a similar manner as the minimization problem defined by equation (1) using the Least Absolute Shrinkage and Selection Operator (LASSO), with the optional tuning of the parameter λ on the training data  110  using a leave-one-person-out cross-validation approach.
 
     In alternative embodiments, the l 1  norm regularization term, i.e., sparse representation, that is in the minimization problem defined by equation (1) may be replaced with the l 2  norm regularization term, i.e., ridge regression. Such a replacement may remove the imposition of sparsity in the model. Accordingly, the minimization problem for the non-negative shrinking parameter λ may be redefined as:
 
{circumflex over (β)}=argmin β (Σ a=1   A ( y   a −Σ n=1   N β n   X   n,a ) 2 +λΣ n=1   N β n   2 ),  (5)
 
in which the shrinkage parameter λ controls the size of the coefficients and the amount of the regularization, with the tuning of the parameter λ on the training data  110  using a leave-one-person-out cross-validation approach. Since this minimization problem is convex, the vector generation module  320  may solve this minimization problem to generate a unique learned vector β as the solution.
 
     The HRTF phase module  318  may estimate an ITD scaling factor for an ear of the test subject  114  given the anthropometric features y∈[0,1] A  of the test subject  114 . The ITD scaling factor estimation problem may be treated by the HRTF phase module  318  as finding a sparse representation of the anthropometric features of the test subject  114 . Thus, the ITD scaling factor estimation problem may be solved with the assumptions that the anthropometric features of the test subject  114  and the ITD scaling factors of the test subject  114  share the same relationship and the training data  110  is sufficient to cover the anthropometric features of the test subject  114 . 
     Accordingly, the vector generation module  320  may provide the learned sparse vector β for the test subject  114  to the HRTF phase module  318 . The learned sparse vector β provided to the HRTF phase module  318  may be learned in a similar manner as the sparse vector β provided to the HRTF magnitude module  316 , i.e., solving a minimization problem for a non-negative shrinking parameter λ However, in some embodiments, the vector generation module  320  may tune the parameter λ for the estimation of ITD scaling values based on the training data  110 . The tuning may be performed using an implementation of the leave-one-person-out cross-validation approach. In the implementation, the vector generation module  320  may take out the data associated with a single training subject from the training data  110 , estimate the sparse weighting vector using equation (1), and then estimate the scaling factor. The vector generation module  320  may repeat this process for all training subjects and the optimal λ for the training data  110  may be selected from a series of λ values as the value of λ which gives minimal error according to the following root mean square error equation: 
                   ɛ   =           1   N     ⁢       ∑     n   =   1     N     ⁢       (         h   ^     n     -     h   n       )     2         ,               (   6   )               
in which ĥ n  is the estimated scaling factor for the n-th training subject and h n  is the measured scaling factor for the same training subject.
 
     Once the vector generation module  320  learns the sparse vector β, the HRTF phase module  318  may apply the learned sparse vector β directly to the ITD scaling factors data in the training data  110  to estimate the ITD scaling factor value ĥ for the test subject  114  as follows:
 
 ĥ=Σ   n=1   N β n   h   n .  (7)
 
In various embodiments, the HRTF phase module  318  may multiply the scaling factor value ĥ and the average ITD to estimate the time delay as a function of the direction and the elevation of the test subject  114 . Subsequently, the HRTF phase module  318  may convert the time delay into a phase response for an ear of the test subject  114 .
 
     The HRTF synthesis module  322  may combine each of the HRTF values Ĥ with a corresponding scaling factor value ĥ for an ear of the test subject  114  to obtain a personalized HRTF for the ear of the test subject  114 . In various embodiments, each of the HRTF values Ĥ and its corresponding scaling factor value ĥ may be complex numbers. The HRTF synthesis module  322  may repeat such synthesis with respect to additional HRTF values to generate multiple HRTF values for multiple frequencies. Further, the steps performed by the various modules of the HRTF engine  104  may be repeated to generate additional HRTF values for the other ear of the test subject  114 . In this way, the HRTF engine  104  may generate the personalized HRTFs  124  for the test subject  114 . 
     The user interface module  324  may enable a user to use the user interface  304  to interact with the modules of the HRTF engine  104 . For example, the user interface module  324  may enable the user to input anthropometric feature parameters of the training subjects  106  and the test subject  114  into the HRTF engine  104 . In another example, the HRTF engine  104  may cause the user interface module  324  to show one or more questionnaires regarding anthropometric features of a test subject, such that the test subject is prompted to input one or more anthropometric feature parameters into the HRTF engine  104 . In some embodiments, the user may also use the user interface module  324  to adjust the various parameters and/or models used by the modules of the HRTF engine  104 . 
     The data store  326  may store data that are used by the various modules. In various embodiments, the data store may store the training data  110 , the anthropometric measurements of test subjects, such as the test subject  114 . The data store may also store the personalized HRTFs that are generated for the test subjects, such as the personalized HRTFs  124 . 
     Example Processes 
       FIGS. 4-6  describe various example processes for generating personalized HRTFs for a human subject based on a statistical relationship between the anthropometric features of the human subject and the anthropometric features of multiple human subjects. The order in which the operations are described in each example process is not intended to be construed as a limitation, and any number of the described operations may be combined in any order and/or in parallel to implement each process. Moreover, the operations in each of the  FIGS. 4-6  may be implemented in hardware, software, and a combination thereof. In the context of software, the operations represent computer-executable instructions that, when executed by one or more processors, cause one or more processors to perform the recited operations. Generally, computer-executable instructions include routines, programs, objects, components, data structures, and so forth that cause the particular functions to be performed or particular abstract data types to be implemented. 
       FIG. 4  is a flow diagram that illustrates an example process  400  for using the anthropometric feature parameters of a human subject to derive personalized HRTFs for a human subject. At block  402 , the HRTF engine  104  may obtain multiple anthropometric feature parameters and multiple HRTFs of a plurality of training subjects. For example, the HRTF engine  104  may obtain the measured HRTFs  108  and the anthropometric feature parameters  112  of the training subjects  106 . In various embodiments, the HRTF engine  104  may store measured HRTFs  108  and the anthropometric feature parameters  112  as training data  110 . 
     At block  404 , the HRTF engine  104  may acquire a plurality of anthropometric feature parameters of a test subject. For example, the HRTF engine  104  may ascertain the anthropometric feature parameters  118  of the test subject  114 . In some embodiments, one or more anthropometric feature parameters may be manually inputted into the HRTF engine  104  by a user. Alternatively or concurrently, an automated measurement tool may automatically detect the one or more anthropometric feature parameters and provide them to the HRTF engine  104 . 
     At block  406 , the HRTF engine  104  may determine a statistical relationship between the plurality of anthropometric feature parameters of the test subject and the multiple anthropometric feature parameters of the plurality of training subjects. For example, the HRTF engine  104  may rely on the principle that the magnitudes and the phase delays of a particular set of HRTFs may be described by the same sparse combination as the corresponding anthropometric data. In various embodiments, the statistical relationship may be determined using sparse representation modeling or ridge regression modeling. 
     At block  408 , the HRTF engine  104  may apply the statistical relationship to the multiple HRTFs of the plurality of training subjects to obtain a set of personalized HRTFs for the test subject. The personalized HRTFs may be used to modify a non-spatial audio-signal to simulate 3-dimensional sound for the test subject using a pair of audio speakers. 
       FIG. 5  is a flow diagram that illustrates an example process  500  for obtaining anthropometric feature parameters and HRTFs of a training subject. The example process  500  further describes block  402  of the process  400 . At block  502 , the HRTF engine  104  may obtain multiple anthropometric feature parameters of a training subject, such as one of the training subjects  106 , via one or more assessment tools. The assessment tools may include an automated measurement tool that automatically detects the one or more anthropometric features of the test subject. The assessment tools may include a user interface that shows one or more questionnaires regarding anthropometric features of a training subject, such that the training subject is prompted to input one or more anthropometric feature parameters into the HRTF engine  104 . The assessment tools may also include a user interface that enables a user to input anthropometric feature parameters regarding the training subject after the user has measured or otherwise determined the anthropometric feature parameters. 
     At block  504 , the HRTF engine  104  may store the multiple anthropometric feature parameters of the training subject as a part of the training data  110 . In various embodiments, the HRTF engine  104  may convert the categorical features (e.g., hair color, race, eye color, etc.) of the anthropometric feature parameters  112  into binary indicator variables. Alternatively or concurrently, the HRTF engine  104  may apply a min-max normalization to each of the rest of the feature parameters separately to make the feature parameters more uniform. 
     At block  506 , the HRTF engine  104  may obtain a set of HRTFs for the training subject via measures of sounds that are transmitted to the ears of the training subject from positions in a spherical arrangement that partially surrounds the training subject. The partially surrounding spherical arrangement may exclude a spherical wedge. In some embodiments, the training subject may sit in a chair with his or her head fixed in the center of an arc array of loud speakers. Chirp signals of multiple frequencies played by the loudspeakers may be recorded with omni-directional microphones that are placed in the ear canal entrances of the seated training subject. For example, in an instance in which the chirp signals are emanating from an array of 16 loudspeakers that are moved to 25 array positions, the HRTFs may be measured at a total of 400 positions for the training subject. 
     At block  508 , the HRTF engine  104  may interpolate an additional set of HRTFs for the training subject with respect to virtual positions in the spherical wedge based on the set of HRTFs. In various embodiments, the interpolated set of HRTFs may be estimated based on the set of HRTFs using a lower-order non-regularized least-squares fit technique. The HRTFs of each training subject may be represented as a set of frequency domain filters in pairs. 
     At block  510 , the HRTF engine  104  may store the set of HRTFs and the additional set of HRTFs of the training subject as a part of the training data  110 . For example, the HRTFs of the training subject may be encapsulated by a tensor of size D×K, where D is the number of HRTF directions and K is the number of frequency bins. 
       FIG. 6  is a flow diagram that illustrates an example process  600  for generating a personalized HRTF for a test subject. The example process  600  further describes block  408  of the process  400 . At block  602 , the HRTF engine  104  may determine a HRTF magnitude for a test subject (e.g., test subject  114 ) based on a statistical relationship representation. In various embodiments, the statistical relationship may be a relationship between the plurality of anthropometric feature parameters of the test subject and one or more of the multiple anthropometric feature parameters of the plurality of training subjects. 
     Thus, in some embodiments, the statistical relationship may consist of a statistical model that jointly describes both the anthropometric features of the test subject and the HRTFs of the test subject. In other embodiments, the anthropometric features of the test subject and the HRTFs of the test subject may be described using other statistical relationships, such as Bayesian networks, dependency networks, and so forth. The statistical relationship may be determined using sparse representation modeling or ridge regression modeling. The HRTF engine  104  may determine the HRTF magnitude by applying the statistical relationship representation directly to the HRTF tensor data in the training data  110  to obtain the HRTF magnitude. 
     At block  604 , the HRTF engine  104  may determine a corresponding HRTF scaling factor for the HRTF magnitude based on a statistical relationship representation. The scaling factor for the test subject is a value that is multiplied with an average ITD for the multiple human subjects to derive an individual ITD for the test subject. In various embodiments, the HRTF engine  104  may apply the statistical relationship representation directly to the ITD scaling factors data included in the training data  110  to estimate the ITD scaling factor value for the test subject. Subsequently, the HRTF engine  104  may convert the time delay as a phase response for an ear of the test subject. 
     At block  606 , the HRTF engine  104  may combine the HRTF magnitude and the corresponding HRTF phase scaling factor to generate a personalized HRTF for the test subject. 
     The use of the techniques described herein may enable the rapid derivation of personalized HRTFs for a human subject based on the anthropometric feature parameters of the human subject. Accordingly, this means that the HRTFs for the human subject may be obtained without the use of specialized acoustic measuring equipment in an anechoic environment. The relative ease at which the personalized HRTFs are obtained for human subjects may lead to the widespread use of personalized HRTFs to develop personalized 3-dimensional audio experiences. 
     CONCLUSION 
     In closing, although the various embodiments have 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 representations is not necessarily limited to the specific features or acts described. Rather, the specific features and acts are disclosed as exemplary forms of implementing the claimed subject matter.