Patent Publication Number: US-10311378-B2

Title: Depth from time-of-flight using machine learning

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of and claims priority to U.S. application Ser. No. 15/068,632, entitled “DEPTH FROM TIME-OF-FLIGHT USING MACHINE LEARNING,” filed Mar. 13, 2016, which is incorporated herein in its entirety. 
    
    
     BACKGROUND 
     Time-of-flight (TOF) cameras are increasingly used in a variety of applications, for example, human computer interaction, automotive applications, measurement applications and machine vision. A TOF camera can be used to compute depth maps which contain information relating to the depth of an object in a scene from the camera. The depth refers to the projection of distance on an imaginary line that extends from the camera, where the distance is the absolute radial distance. A light source at the TOF camera illuminates the scene and the light is reflected by objects in the scene. The camera receives the reflected light that, dependent on the distance of an object to the camera, experiences a delay. Given the fact that the speed of light is known, a depth map is computable. 
     However, the time of flight measurement is subject to a number of errors and uncertainties which lead to errors in the computed depth maps. For example, the reflected light often undergoes multiple reflections from different surfaces within the scene which cause significant errors in the calculated depth. 
     The embodiments described below are not limited to implementations which solve any or all of the disadvantages of known TOF cameras or TOF data processing systems. 
     SUMMARY 
     The following presents a simplified summary of the disclosure in order to provide a basic understanding to the reader. 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. Its sole purpose is to present a selection of concepts disclosed herein in a simplified form as a prelude to the more detailed description that is presented later. 
     A depth detection apparatus is described which has a memory storing raw time-of-flight sensor data received from a time-of-flight sensor. The depth detection apparatus also has a trained machine learning component having been trained using training data pairs. A training data pair comprises at least one simulated raw time-of-flight sensor data value and a corresponding simulated ground truth depth value. The trained machine learning component is configured to compute in a single stage, for an item of the stored raw time-of-flight sensor data, a depth value of a surface depicted by the item, by pushing the item through the trained machine learning component. 
     Many of the attendant features will be more readily appreciated as the same becomes better understood by reference to the following detailed description considered in connection with the accompanying drawings. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       The present description will be better understood from the following detailed description read in light of the accompanying drawings, wherein: 
         FIG. 1  is a schematic diagram of a trained machine learning component deployed with a time-of-flight camera; 
         FIG. 2  is a schematic diagram of a time-of-flight camera; 
         FIG. 3  is a flow diagram of a method of using a trained machine learning component such as that of  FIG. 1 ; 
         FIG. 4  is a graph of empirical results of depth values computed using the arrangement of  FIG. 1  and various other arrangements; 
         FIG. 5  is a schematic diagram of components used to create a trained machine learning component, such as that of  FIG. 1 ; 
         FIG. 6  is a schematic diagram of components used to generate training data pairs such as the training data pairs of  FIG. 5 ; 
         FIG. 7  is a graph of data output by a time-of-flight simulator such as that of  FIG. 6 ; 
         FIG. 8  is a flow diagram of a method of training a random decision forest using training data pairs such as those of  FIG. 6 ; 
         FIG. 9  is a schematic diagram of a plurality of random decision trees; 
         FIG. 10  is a flow diagram of a method of using a trained random decision forest at test time, such as the trained machine learning component of  FIG. 1 ; 
         FIG. 11  is a flow diagram of a method of training a convolutional neural network using training data pairs such as those of  FIG. 6 ; 
         FIG. 12  is a flow diagram of using a trained convolutional neural network; 
         FIG. 13  illustrates an exemplary computing-based device in which embodiments of a trained machine learning component for use with a time-of-flight camera are implemented. 
     
    
    
     Like reference numerals are used to designate like parts in the accompanying drawings. 
     DETAILED DESCRIPTION 
     The detailed description provided below in connection with the appended drawings is intended as a description of the present examples and is not intended to represent the only forms in which the present example are constructed or utilized. The description sets forth the functions of the example and the sequence of operations for constructing and operating the example. However, the same or equivalent functions and sequences may be accomplished by different examples. 
     Time-of-flight cameras output raw sensor data which is then processed to derive depth values. The act of processing the raw sensor data to compute the depth values is time consuming and complex. In addition, the depth values which are computed suffer from inaccuracy due to multi-path interference and noise in the raw sensor data. However, time-of-flight cameras are increasingly used for real time applications and/or where highly accurate depth values are needed. For example, hand tracking, body tracking, 3D scene reconstruction and others. 
     By using a trained machine learning system as described herein, it is possible to directly derive highly accurate depth values from raw time-of-flight sensor data in real time. This is achieved in a single stage, without the need to compute depth values using conventional, non-machine learning methods. The trained machine learning system takes raw time-of-flight sensor data as input and computes depth values as output, where the depth values already take into account multi-path interference and optionally also take into account sensor noise. This improves the speed with which the depth values are computed, since there is a single stage. For example, there is no need to compute the depth values and then subsequently process the depth values to correct for multi-path interference and/or sensor noise. The result gives a better computing device which is able to control a downstream system using accurate depth values obtained from one or more time-of-flight sensors. Usability from the point of view of the end user is improved since the accurate depth values give a better correspondence with reality such as for hand tracking, body tracking, augmented reality and others. 
     The machine learning system has been trained using pairs of simulated raw time-of-flight sensor data frames and corresponding depth maps. The simulated raw time-of-flight sensor data frames are calculated using a modified computer graphics renderer as described in more detail below. The simulated raw time-of-flight sensor data frames are simulated assuming that multi-path interference occurs. Therefore it is possible to learn a mapping from simulated raw time-of-flight sensor data direct to depth values which are already corrected for multi-path interference. There is no need to apply a subsequent stage to correct the depth values for multi-path interference. As a result processing is significantly simplified and speeded up. Because the processing is simpler than two stage processes, the processing is implementable at a dedicated chip, field programmable gate array (FPGA) or similar. This is particularly useful where the processing is to be carried out at a time-of-flight camera itself, or on a resource constrained device such as a wearable or mobile computing device which has an integral time-of-flight camera. 
     The machine learning component described herein is found to give highly accurate depth values, especially for situations where depth values are difficult to compute accurately using existing approaches. For example, at corners of rooms, where the floor meets the wall, where the wall meets the ceiling, in the case of highly reflective surfaces such as shiny floors, and others. Accuracy improvements are believed to be due, at least in part, to the fact that the machine learning component has been trained with the particular type of training data. 
       FIG. 1  is a schematic diagram of a depth detection apparatus  100  comprising a memory  122  and a trained machine learning component  124 . A time-of-flight camera  104 , which is a phase modulation time-of-flight depth camera or a gated time-of-flight depth camera (or another future type of TOF camera), captures a stream of raw sensor data  108  depicting a scene  102 . One or more objects in the scene  102  and/or the time-of-flight camera itself are moving in some examples. For example, in the scenario of  FIG. 1  the scene comprises a child doing a cartwheel so that there are several moving objects in the scene (the child&#39;s limbs). The time-of-flight camera is wall-mounted in the room or in some examples is body worn or head-mounted or mounted on a robot or vehicle. 
     The stream of raw sensor data  108  comprises a plurality of frames of raw sensor data which have been captured by the time-of-flight camera. For example, for some types of time-of-flight camera a frame of raw sensor data comprises, for each pixel of the camera sensor, complex numbers which are amplitude and phase measurements of reflected light. For example, for another type of time-of-flight camera, a frame of raw sensor data comprises, for each pixel of the camera sensor, a plurality of intensity values of reflected light sensed at the pixel, for different exposure periods. 
     The time-of-flight camera uses one or more measurement patterns  106  also referred to as exposure profiles. A measurement pattern is a set of values of configurable parameters of the time-of-flight camera, to be used when a frame of raw sensor data is captured by the camera. Where different measurement patterns  106  are available, the time-of-flight camera is able to capture different frames using different measurement patterns. 
     The stream of raw sensor data  108  is input to a depth detection apparatus  100  comprising a memory  122  and a trained machine learning component  124 . The trained machine learning component  124  computes depth maps, or depth values of individual pixels, in a single stage process which takes into account multi-path interference and/or sensor noise so that an accurate depth map stream  110  is output. A depth map comprises a plurality of depth values, each depth value being for an individual pixel of the time of flight image sensor. In some examples, depth values of individual pixels are output. In some examples the trained machine learning component  100  also outputs uncertainty data associated with the depth values. The stream  110  of depth values and optional uncertainty data is input to a downstream system  112  such as a scene reconstruction engine  114 , a gesture detection system  116 , an augmented reality system  118 , a touch-less user interface  120  or others. 
     The depth detection apparatus  100  operates in real-time in some examples. In some cases the depth detection apparatus  100  is integral with the time-of-flight camera  104 . In some cases the depth detection apparatus  100  is in a computing device such as a smart phone, tablet computer, head worn augmented reality computing device, or other computing device which has a time-of-flight camera. The memory  122  holds raw time-of-flight sensor data from the stream  108  and makes this available to the trained machine learning component  124  for processing. The trained machine learning component  124  has been trained using pairs of simulated raw time-of-flight sensor data frames and corresponding depth maps. The simulated raw time-of-flight sensor data frames are simulated assuming that multi-path interference occurs. In some examples the trained machine learning component  124  has been trained using pairs of raw time-of-flight sensor data values associated with individual sensor pixels and corresponding depth values. 
     In some examples, the trained machine learning component  124  comprises a trained regressor such as a random decision forest, directed acyclic graph, support vector machine, neural network, or other trained regressor. The trained regressor is a pixel independent trained regressor in some examples, in that it is trained using pairs comprising individual pixels and associated individual depth values, and where dependencies between the pairs are not taken into account. In other examples, the trained regressor does take dependencies between individual pixels into account. An example, of a trained regressor which does take dependencies between individual pixels into account is a convolutional neural network. An example in which the trained regressor is a pixel independent regressor is a random decision forest which is given below with reference to  FIGS. 8 to 10 . An example in which the trained regressor is a convolutional neural network taking into account dependencies between pixels is given with respect to  FIGS. 11 to 12  below. 
       FIG. 2  is a schematic diagram of a time-of-flight depth camera  200  which is a phase modulation time-of-flight depth camera or a gated time of flight depth camera or any other future type of time-of-flight depth camera. The time-of-flight camera  200  comprises a source of transmitted light  202 . In an example the source of transmitted light is an incoherent light source. In another example the source of transmitted light is a coherent light source. An example of an appropriate light source is a near infra-red laser or light emitting diode (LED) however another appropriate light source may be used. In the case of a phase modulated time of flight camera the transmitted light is modulated at a modulation frequency. In an example the modulation frequency may be a radio frequency (RF) frequency in the range kHz-GHz (kilo hertz to giga hertz), for example the modulation frequency may be in the MHz (mega hertz) range. In the case of a gated time-of-flight camera the transmitted light is pulsed where the pulses may be of picosecond to nanosecond duration. 
     A time-of-flight depth camera comprises an image sensor  204  that receives light reflected from objects within the scene. The image sensor  204  comprises a charge-coupled device (CCD) sensor, a complementary metal-oxide-semiconductor (CMOS) sensor, for example a Photonic Mixer Device (PMD) sensor or other appropriate sensor which is arranged to detect light reflected from objects, people and surfaces within the camera range. In the case of a gated time-of-flight camera the image sensor  204  has a resolution compatible with the duration of the pulses emitted by the light source. 
     The camera comprises an optical system  206  that is arranged to gather and focus reflected light from the environment on to the image sensor  204 . In an example the optical system comprises an optical band pass filter, which allows only light of the same wavelength as the light source to be received by the sensor. The use of an optical band pass filter helps to suppress background light. The camera comprises driver electronics  208  which control both the light source and an image sensor, for example, to enable highly accurate phase difference measurements to be made or to enable a train of light pulses to be emitted and for the image sensor to be “shuttered” on and off. An image sensor may be shuttered on and off electronically rather than with physical shutters. 
     In one example the camera comprises a processor  208  and a memory  210  which stores raw time-of-flight data, depth maps and other data. A trained machine learning component  214  is available at the camera  212  in some examples and in other examples this trained machine learning component is at another computing device which receives and processes the raw sensor data from the camera. Where the trained machine learning component  214  is at the camera  212  it comprises software stored at memory  210  and executed at processor  208  in some cases. In some examples the trained machine learning component  214  is an FPGA or a dedicated chip. For example, the functionality of the trained machine learning component  214  is implemented, in whole or in part, by one or more hardware logic components. For example, and without limitation, illustrative types of hardware logic components that can be used include Field-programmable Gate Arrays (FPGAs), Application-specific Integrated Circuits (ASICs), Application-specific Standard Products (ASSPs), System-on-a-chip systems (SOCs), Complex Programmable Logic Devices (CPLDs), Graphics Processing Units (GPUs). 
     The trained machine learning component  214  is arranged to execute the methods described herein with respect to  FIGS. 3, 10, 12  in order to compute depth in real time, using a single stage, from a stream of raw time-of-flight data in a manner which allows for multi-path interference. This is achieved without the need to compute corrections to the depth values and apply those subsequent to the depth values having been computed. 
       FIG. 3  is a flow diagram of a method at the depth detection apparatus  100 . Raw sensor data is received from the time-of-flight camera  104  and stored at memory  122 . A check  302  is made as to whether the process is to compute neighborhoods or not. The decision is made according to user input, or settings configured by an operator during manufacturing. In some examples, the depth detection apparatus automatically decides whether neighborhoods are to be computed according to the nature of the captured sensor data or other sensor data, such as sensors which detect motion of the time-of-flight camera. 
     In the case that neighborhoods are not computed the depth detection apparatus inputs  306  the raw sensor data  300  to the trained machine learning component. The input process comprises inputting raw sensor data associated with individual pixels and/or whole frames of raw sensor data. As a result, the depth detection apparatus receives  308 , from the trained machine learning component depth value(s) and optionally also uncertainty data. The depth detection apparatus outputs the depth values in real time  310  together with the uncertainty data in some cases. By real time, it is meant that the rate of the received raw sensor data  300  is at least matched by the output rate of the output depth values at operation  310 . The process of  FIG. 3  repeats as more raw sensor data is received  300 . 
     In the case that neighborhoods are computed the depth detection apparatus aggregates  304  raw sensor data values of pixels in a neighborhood of the pixel under current consideration. The neighborhood is either a spatial neighborhood or a temporal neighborhood or a combination of a spatial and temporal neighborhood. 
     The aggregated raw sensor data values are input to the trained machine learning component at operation  306 . In this case the trained machine learning component has been trained using training data which has been aggregated in the same manner. In the case that temporal neighborhoods are used, the training data allows for motion between the camera and the scene. For example, as a result of objects in the scene moving and/or as a result of the camera moving. This is achieved by using a model of motion between the camera and the scene. 
     The machine learning system outputs depth values associated with the neighborhoods at operation  308  and the process proceeds with operation  310  and returns to operation  300  as described above. 
     The table below has empirical data demonstrating how the depth detection apparatus  100  of  FIG. 1  has improved accuracy as compared with an alternative method using a probabilistic generative model of time-of-flight on which inference is possible. To obtain the data for the table below and the graph of  FIG. 4 , the alternative method used the same conditions, such as number of exposures per frame, as the present method. The results for the alternative method are in the column labeled “generative” in the table below. A probabilistic generative model of time-of-flight is a description, expressed using likelihoods, of how raw time-of-flight data is generated by a time-of-flight camera under specified imaging conditions comprising reflectivity of a surface generating reflected light received at the camera (also referred to as albedo), illumination of the surface, and depth of the surface from the camera. Inference is possible on the probabilistic generative model so that given known imaging conditions it is possible to infer corresponding raw sensor data and vice versa. The probabilistic generative model takes into account a single path for reflected light for each pixel. In the alternative approach raw time-of-flight sensor data is used to compute depth values from the probabilistic generative model, or from an approximation of the probabilistic generative model. 
     It can be seen from the table below that the present approach has a slightly lower median error but that the biggest improvement is with respect to the largest errors. There is a 44% reduction in the number of depth value errors where the depth error is more than 5 centimeters. 
     
       
         
           
               
               
               
             
               
                   
               
               
                   
                 Generative approach 
                 Approach of FIG. 1 
               
               
                   
               
             
            
               
                 Median error in 
                 17 
                 16 
               
               
                 millimeters 
                   
                   
               
               
                 90% quantile error in 
                 96 
                 63 
               
               
                 millimeters 
                   
                   
               
               
                 % reduction of errors 
                 baseline 
                 44 
               
               
                 above 50 millimeters 
               
               
                   
               
            
           
         
       
     
       FIG. 4  is a cumulative distribution plot of the empirical data of the above table and additional empirical data. The graph of  FIG. 4  plots the probability of the depth error being less than a threshold, against the size of the threshold in millimeters. Line  400  indicates the data for the approach using a generative model described above and lines  402 ,  404 ,  406  indicate data for the present approach using either four exposures per frame (line  402 ), six exposures per frame (line  406 ) or eight exposures per frame (line  404 ) of the time-of-flight camera. It is seen that the generative approach gives the worst performance. 
       FIG. 5  is a schematic diagram of how to create a trained machine learning component such as component  124  of  FIG. 1 . Millions of training data pairs (or more) are stored at a database  500  or other store. In some examples, a training data pair comprises a simulated raw time-of-flight sensor data frame and a corresponding ground truth depth map. In some examples a training data pair comprises a plurality of raw sensor data values associated with a pixel of the sensor, and a ground truth depth value associated with the pixel. In some examples a training data pair comprises a plurality of aggregated raw sensor data values, aggregated over a spatial or temporal neighborhood around a pixel of the sensor, and a ground truth depth value associated with the pixel. The raw sensor data values are obtained from a time-of-flight simulator which simulates multi-path interference as part of the simulation. The time-of-flight simulator comprises a renderer  606  and a viewpoint selector  604  and an example is described in more detail with reference to  FIG. 6 . The time-of-flight simulator is relatively complex and it is not possible to carry out inference on the time-of-flight simulator as it is for the generative model of time-of-flight mentioned above. 
     A trainer  504  accesses the training data pairs  500  and uses them to train and produce a trained machine learning component  506  such as a random decision forest, a convolutional neural network, a support vector machine or other trained regressor. The resulting trained machine learning component  506  may then be used as described above with respect to  FIGS. 1 and 3 . The type of training data used to train the machine learning component corresponds with the type of data input to the machine learning component at test time. Test time is the time in which the machine learning component is operational to compute depth values from previously unseen raw sensor data. By using a wide variety of training data examples performance of the trained machine learning system is improved both in terms of accuracy and in terms of ability to generalize to examples which are different from the training examples. However, it is difficult to obtain appropriate training data. Ways in which good variety of training data are obtained are now described with reference to  FIG. 6 . 
       FIG. 6  is a schematic diagram of a time-of-flight simulator  602  and other components used to create training data pairs  626  such as the training data pairs described above with reference to  FIG. 5 . 
     The time-of-flight simulator  602  comprises a renderer  606  such as a computer graphics renderer which uses ray-tracing to render an image from a model of a 3D object or environment. The renderer  606  is a physically-accurate renderer which produces realistic rendered images by using physical modeling of light scattering, light transport simulation, and integration of paths of light at every pixel. The renderer  606  records, for each pixel, an intensity weight and a path length (the length of the path of simulated light from the simulated emitter of the TOF camera to the simulated surface(s) in the world and back to the simulated TOF sensor) for each of a plurality N of light path samples. The number of light path samples is the same for each pixel and is fixed in advance in some cases, such as a few thousand light path samples. In other examples, the number of light path samples is selected adaptively during simulation, for example, so that more complex areas in the scene are allocated more simulated light paths compared to simpler areas. More complex areas are identified in various ways such as according to the presence of corners, the presence of edges, the degree of surface reflectivity, or other factors. This gives per-pixel weighted point masses  608 . An example of a per-pixel weighted point mass is given in  FIG. 7  for a pixel depicting a surface in a corner of a room. The pixel in the example of  FIG. 7  receives light from multiple paths due to multi-path interference and so there are multiple peaks  700 ,  702  of the normalized light density. The first peak of the per-pixel weighted point mass gives an estimate of the ground truth depth which is input to the training data pair  624  in some examples. 
     As mentioned above the renderer  606  uses ray-tracing to render an image from a model of a 3D object or environment. It is time consuming and expensive to generate suitable models of 3D objects or environments. For example, where the time-of-flight camera is to be used in doors, the models are of typical indoor environments such as living rooms, offices, kitchens and other indoor environments. However, it is difficult to obtain a good range and variety of models of such 3D environments. In order to address this, the present technology uses a plurality of parametric 3D environment models  610 . A parametric 3D environment model  610  is a computer manipulable description of a 3D environment expressed using one or more parameters. An instance generator  612  accesses a parametric 3D environment model from a store of parametric 3D environment models  610  and creates a plurality of instances. An instance is a 3D environment model created from a parametric 3D environment model by selecting values of the parameters of the parametric 3D environment model. The instances are created by selecting values of the parameters at random and/or within a specified range of possible values of the parameters according to knowledge of feasible parameter value ranges. A non-exhaustive list of examples of parameters of a parametric 3D environment model is: geometry of individual objects in the 3D model, presence or absence of individual objects (including light sources), object location, object orientation, surface materials and textures, amount of ambient illumination. Using parametric models in this way enables a huge number of variations of 3D environment model to be generated in a fast, efficient manner. For example, in the case of a parametric 3D model of a living room, values of parameters can be adjusted to vary surface reflectivity of the flooring material, ceiling, walls, furniture, and also to vary geometry and/or position of objects in the room such as furniture, light fittings, windows other objects. As a result of the wide range and large number of 3D environment model instances the time-of-flight simulator  602  is able to render good variety of simulated raw time-of-flight data which incorporates multi-path interference. This gives improved quality training data pairs  626  and as a consequence, the trained machine learning component gives better quality depth values and uncertainty information. As a result there is a depth detection apparatus giving highly accurate depth values enabling better control by downstream computing systems. 
     The renderer  606  renders an image from a model of a 3D object or environment given a camera viewpoint. A camera viewpoint is a 3D position and orientation within a bounding box of the 3D environment model instance. The renderer  606  uses details of optical properties  600  of the time-of-flight camera such as the field of view of the camera, the focal length, and the spatial light emission intensity profile. The time-of-flight simulator has a viewpoint selector  604  which selects a large number of possible viewpoints of the camera within the instance of the 3D environment model. For example, the viewpoint selector  604  selects the viewpoints at random by choosing random 3D positions and orientations within a bounding box of the 3D environment model. The viewpoint selector  604  is arranged to reject viewpoints which are within a threshold distance of objects in the 3D environment model. For example, to reject viewpoints which face a wall of the 3D environment with only 20 centimeters between the camera viewpoint and the wall. For a given 3D environment model instance, the renderer computes simulated raw time-of-flight data for each of a plurality of viewpoints selected by the viewpoint selector  604 . For example, thousands of different viewpoints. As a result the training data pairs  624  exhibit good variety and the resulting trained machine learning component  124  is able to generalize well to unseen 3D environments with unseen camera viewpoints. 
     As mentioned above, the time-of-flight simulator  602  outputs per-pixel weighted point masses  608 . These do not take into account exposure profiles a time-of-flight camera has. This means that the time-of-flight simulator can be used for any type of time-of-flight camera. The per-pixel weighted point masses  608  are input to an exposure profile combiner  616  which incorporates information about a specified exposure profile of a time-of-flight camera into the raw time-of-flight data being simulated. The exposure profile is specified, by an operator during manufacturing, by selecting the exposure profile from a library of exposure profile details, or using user input. For example, the exposure profile is described using vector constant A and vector-valued function C. A vector-valued function is a function which takes a scalar argument and returns a vector. In an example, the exposure profile combiner  616  combines the per-pixel weighted point masses (values of weight w and path length t) with the vector constants A and the vector-valued function C using the following equation: 
               μ   →     =       τ   ⁢     A   →       +       ∑     i   =   1     N     ⁢           ⁢         ω   i       d   ⁡     (     t   i     )         ⁢       C   →     ⁡     (     t   i     )                   
Where N is the number of light path samples fixed at a value such as a few thousand samples and where the symbol z denotes the ambient light intensity used by the time-of-flight simulator. The values of the vector constant A and the values of the elements returned by the vector-valued function C in some examples are between zero and 2 12 .
 
     The above equation is expressed in words as a mean response vector {right arrow over (μ)} of simulated raw time-of-flight sensor intensity values (such as four intensity values one for each of four exposures) simulated as being observed at the same pixel of the sensor, is equal to the ambient light intensity τ times a vector constant {right arrow over (A)} which represents part of the exposure pattern of the time of flight camera, plus the sum over the number of light path samples N, of a vector-valued function {right arrow over (C)} evaluated at t i , which represents another part of the exposure pattern of the time-of-flight camera times the weight ω i  which is the point mass weight from the time-of-flight simulator output for the light path sample i, and taking into account a distance decay function d(t i ) where intensity falls away with distance from the camera of the surface which reflects the light. 
     In some examples, sensor noise is simulated. That is, the output of the exposure profile combiner is processed by a noise addition component  620  which adds noise to the simulated raw time-of-flight data. However it is not essential to use the noise addition component  620 . 
     The output of the noise addition component  620  is simulated raw intensity values  622  associated with a pixel, and which incorporate multi-path interference and sensor noise. This data is formed into a training data pair  624  by accessing the corresponding ground truth depth value (which is the true depth of the surface depicted by the pixel). The corresponding ground truth depth value is known either by computing it from the 3D environment instance  614  or by taking the first peak of the per-pixel weighted point mass. Given a 3D environment model instance the depth detection apparatus computes ground truth depth values  318  for a given camera viewpoint. 
     The process described above for computing a training data pair is repeated to obtain millions of training data pairs  626  which are stored. In some cases a training data pair comprises a frame of simulated raw time-of-flight sensor data and a corresponding ground truth depth map. This is achieved by repeating the process for individual pixels of the sensor to form a frame. 
     In some examples, the machine learning system comprises a random decision forest. A random decision forest comprises one or more decision trees each having a root node, a plurality of split nodes and a plurality of leaf nodes. Raw TOF sensor data is pushed through trees of a random decision forest from the root to a leaf node in a process whereby a decision is made at each split node. The decision is made according to values of parameters at the split nodes, where the values of the parameters have been learnt during training. At a split node the raw TOF sensor data proceeds to the next level of the tree down a branch chosen according to the results of the decision. 
     During training, parameter values (which specify decision criteria to be used at the split nodes) are learnt for use at the split nodes and data (Raw TOF sensor data with ground truth depth values) is accumulated at the leaf nodes. The training data accumulated at a leaf node during training is stored as a histogram, or in an aggregated manner, such as using a mean, median or mode or by fitting a probability distribution to the histogram and storing statistics describing the probability distribution. 
     At test time previously unseen raw TOF sensor data is input to the system to have one or more depth values predicted. This is described with reference to  FIG. 10 . 
     Referring to  FIG. 8 , to train the decision trees, the training set described above is first received  800 . The number of decision trees to be used in a random decision forest is selected  802 . A random decision forest is a collection of deterministic decision trees. Decision trees can be used in classification or regression algorithms, but can suffer from over-fitting, i.e. poor generalization. However, an ensemble of many randomly trained decision trees (a random forest) yields improved generalization. During the training process, the number of trees is fixed. 
     An example random decision forest is shown illustrated in  FIG. 9 . The illustrative decision forest of  FIG. 9  comprises three decision trees: a first tree  900 ; a second tree  902 ; and a third tree  904 . Each decision tree comprises a root node (e.g. root node  906  of the first decision tree  900 ), a plurality of internal nodes, called split nodes (e.g. split node  908  of the first decision tree  900 ), and a plurality of leaf nodes (e.g. leaf node  910  of the first decision tree  900 ). 
     A decision tree from the decision forest is selected  804  (e.g. the first decision tree  800 ) and the root node  806  is selected  806 . A random set of test parameter values are then generated  810  for use by a binary test performed at the root node. The parameters are thresholds or other parameters of a binary test. In the case that neighborhoods of pixels are used then the binary test optionally comprises pairwise tests comparing pairs of pixels. In the pixel-independent case pairwise tests are not essential. 
     Then, every combination of test parameter value is applied  812  to each raw TOF training data item which has reached the current node. For each combination, criteria (also referred to as objectives) are calculated  814 . In an example, the calculated criteria comprise the information gain (also known as the relative entropy). The combination of parameters that optimize the criteria (such as maximizing the information gain is selected  814  and stored at the current node for future use. As an alternative to information gain, other criteria can be used, such as the residual variance criterion or others. 
     It is then determined  816  whether the value for the calculated criteria is less than (or greater than) a threshold. If the value for the calculated criteria is less than the threshold, then this indicates that further expansion of the tree does not provide significant benefit. This gives rise to asymmetrical trees which naturally stop growing when no further nodes are beneficial. In such cases, the current node is set  818  as a leaf node. Similarly, the current depth of the tree is determined (i.e. how many levels of nodes are between the root node and the current node). If this is greater than a predefined maximum value, then the current node is set  818  as a leaf node. Each leaf node has labeled raw TOF data which accumulate at that leaf node during the training process as described below. 
     It is also possible to use another stopping criterion in combination with those already mentioned. For example, to assess the number of raw TOF data items that reach the node. If there are too few examples (compared with a threshold for example) then the process is arranged to stop to avoid overfitting. However, it is not essential to use this stopping criterion. 
     If the value for the calculated criteria is greater than or equal to the threshold, and the tree depth is less than the maximum value, then the current node is set  820  as a split node. As the current node is a split node, it has child nodes, and the process then moves to training these child nodes. Each child node is trained using a subset of the training time-of-flight data at the current node. The subset of training time-of-flight data sent to a child node is determined using the parameters that optimized the criteria. These parameters are used in the binary test, and the binary test performed  822  on all training time-of-flight data at the current node. The raw TOF data items that pass the binary test form a first subset sent to a first child node, and the raw TOF data items that fail the binary test form a second subset sent to a second child node. 
     For each of the child nodes, the process as outlined in blocks  810  to  822  of  FIG. 8  are recursively executed  824  for the subset of raw TOF data items directed to the respective child node. In other words, for each child node, new random test parameters are generated  810 , applied  812  to the respective subset of raw TOF data items, parameters optimizing the criteria selected  814 , and the type of node (split or leaf) determined  816 . If it is a leaf node, then the current branch of recursion ceases. If it is a split node, binary tests are performed  822  to determine further subsets of raw TOF data items and another branch of recursion starts. Therefore, this process recursively moves through the tree, training each node until leaf nodes are reached at each branch. As leaf nodes are reached, the process waits  826  until the nodes in all branches have been trained. Note that, in other examples, the same functionality can be attained using alternative techniques to recursion. 
     Once all the nodes in the tree have been trained to determine the parameters for the binary test optimizing the criteria at each split node, and leaf nodes have been selected to terminate each branch, then raw TOF data items with ground truth depth values are accumulated  828  at the leaf nodes of the tree. A representation of the accumulated depth values is stored  830  using various different methods. 
     Once the accumulated depth values have been stored it is determined  832  whether more trees are present in the decision forest. If so, then the next tree in the decision forest is selected, and the process repeats. If all the trees in the forest have been trained, and no others remain, then the training process is complete and the process terminates  834 . 
     Therefore, as a result of the training process, one or more decision trees are trained using synthetic raw TOF data. Each tree comprises a plurality of split nodes storing optimized test parameters, and leaf nodes storing associated ground truth depth values. Due to the random generation of parameters from a limited subset used at each node, the trees of the forest are distinct (i.e. different) from each other. 
     The training process is performed in advance of using the trained machine learning system to compute depth values of observed raw TOF data. The decision forest and the optimized test parameters is stored on a storage device for use in computing depth values at a later time. 
       FIG. 10  illustrates a flowchart of a process for predicting depth values from previously unseen raw TOF data using a decision forest that has been trained as described above. Firstly, an unseen raw TOF data item is received  1000 . A raw TOF data item is referred to as ‘unseen’ to distinguish it from a training TOF data item which has the depth value specified. 
     Optionally neighborhoods are computed  1002  from the unseen raw TOF data. The neighborhoods are spatial and/or temporal neighborhoods as described above. 
     A trained decision tree from the decision forest is selected  1004 . The selected raw TOF data item (whole frame, values for an individual pixel, values for a neighborhood) is pushed  1006  through the selected decision tree such that it is tested against the trained parameters values at a node, and then passed to the appropriate child in dependence on the outcome of the test, and the process repeated until the raw TOF data item reaches a leaf node. Once the raw TOF data item reaches a leaf node, the accumulated depth values associated with this leaf node are stored  1008  for this raw TOF data item. 
     If it is determined  1010  that there are more decision trees in the forest, then a new decision tree is selected  1004 , the raw TOF data item pushed  1006  through the tree and the accumulated depth values stored  1008 . This is repeated until it has been performed for all the decision trees in the forest. Note that the process for pushing a raw TOF data item through the plurality of trees in the decision forest can also be performed in parallel, instead of in sequence as shown in  FIG. 10 . 
     The data from the indexed leaf nodes is aggregated  1014  by averaging or in other ways. For example, where histograms of depth values are stored at the leaf nodes the histograms from the indexed leaf nodes are combined and used to identify one or more depth values associated with the raw TOF data item. The processes outputs  816  at least one depth value as a result, and is able to output a confidence weighting of the depth value. This helps any subsequent algorithm assess whether the proposal is good or not. More than one depth value may be output; for example, where there is uncertainty. 
     The random decision forest example described above is modified in some cases by implementing the random decision forest as a directed acyclic graph in order to reduce the number of nodes of the graph. This facilitates deployment of the machine learning component on resource constrained devices such as smart phones, tablet computers and wearable computing devices. 
       FIG. 11  is a flow diagram of a method of training a convolutional neural network. In this case a training data pair comprises a raw TOF frame and a corresponding depth map. Individual pixel locations of the TOF frame have one or more intensity values, for different exposures for example. The training data pair is accessed  1100  and input to the convolutional neural network  1102 . 
     A neural network is a plurality of weighted nodes which are interconnected by edges which may also be weighted. The neural network has input nodes, output nodes and internal nodes. In the present examples the output nodes are associated with depth values learnt during a training phase. 
     A convolutional neural network is a neural network where the nodes are arranged in multiple layers so that there are nodes in three dimensions, width, height and depth. Within each layer there are multiple receptive fields where a receptive field is a group of interconnected nodes which processes a portion of an input image (or TOF frame in the present examples). Within a layer the receptive fields are arranged so that their outputs partially overlap one another to give redundancy. A node of an internal layer is connected to neurons of one receptive field in the layer above. A convolutional neural network is typically a feed-forward neural network in which an input image (or TOF frame) is fed into input nodes, processed forwards through the network according to weights at the nodes, weighted connections between the nodes, and non-linear activation functions, and reaching a set of one or more output nodes. 
     During training the training data instance is fed forwards through the network, from the input nodes to the output nodes, with computations performed at the nodes which update  1104  the weights of the nodes and edges according to update rules. The update process is repeated for more training instances according to a check for convergence at check point  1106  of  FIG. 11 , such as to see if the amount of change from the most recent update was smaller than a threshold. When convergence is reached the training ends  1108 . 
     During test time, when the trained convolutional neural network is used to predict depth maps from raw time-of-flight data frames, the trained machine learning component  124  receives  1200  an unseen raw time-of-flight frame. It inputs  1202  the frame to the trained convolutional neural network. Values associated with individual pixel locations (or neighborhoods) of the frame are input to the plurality of input nodes and this triggers a feed forward process through the network. The values from the frame pass through a layer of the neural network and trigger input to subsequent layers via the overlapping receptive fields. Eventually output nodes are triggered and depth values associated with the triggered output nodes are retrieved from storage. The depth values are then stored as a depth map  1204  optionally with uncertainty data calculated from the neural network outputs. The depth map has smoothed depth values because the receptive fields of the convolutional neural network enable spatial relationships between the pixel locations to be taken into account. 
       FIG. 13  illustrates various components of an exemplary computing-based device  1300  which is implemented as any form of a computing and/or electronic device, and in which embodiments of a depth detection apparatus is implemented in cases where the depth detection apparatus is separate from the time-of-flight camera. A non-exhaustive list of examples of forms of the computing and/or electronic device is: augmented reality near eye computing system, augmented reality body worn computing system, augmented reality wearable computing device, smart phone, desk top computer, computer game console, touch-less user interface computing device, tablet computer, laptop computer. 
     Computing-based device  1300  comprises one or more processors  1302  which are microprocessors, controllers or any other suitable type of processors for processing computer executable instructions to control the operation of the device in order to compute depth values or depth maps from raw time-of-flight data. In some examples, the computing-based device computes a stream of depth maps from a stream of frames of raw time-of-flight data (received from time-of-flight camera  1326 ) in real time and in a manner which takes into account multipath interference. In some examples, for example where a system on a chip architecture is used, the processors  1302  include one or more fixed function blocks (also referred to as accelerators) which implement a part of the method of any of  FIG. 3, 5, 6, 8, 10, 11, 12  in hardware (rather than software or firmware). Platform software comprising an operating system  1304  or any other suitable platform software is provided at the computing-based device to enable application software  1006  to be executed on the device. A trained machine learning component  1308  is provided such as the trained machine learning component  124  of  FIG. 1 . 
     A data store  1310  at memory  1316  stores raw time-of-flight data, simulated raw time-of-flight data, parameter values, exposure profile data, 3D environment models and other data. 
     The computer executable instructions are provided using any computer-readable media that is accessible by computing based device  1300 . Computer-readable media includes, for example, computer storage media such as memory  1316  and communications media. Computer storage media, such as memory  1316 , 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 the like. Computer storage media includes, but is not limited to, random access memory (RAM), read only memory (ROM), erasable programmable read only memory (EPROM), electronic erasable programmable read only memory (EEPROM), flash memory or other memory technology, compact disc read only memory (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 is used to store information for access by a computing device. In contrast, communication media embody computer readable instructions, data structures, program modules, or the like in a modulated data signal, such as a carrier wave, or other transport mechanism. As defined herein, computer storage media does not include communication media. Therefore, a computer storage medium should not be interpreted to be a propagating signal per se. Although the computer storage media (memory  1316 ) is shown within the computing-based device  1300  it will be appreciated that the storage is, in some examples, distributed or located remotely and accessed via a network or other communication link (e.g. using communication interface  1318 ). 
     The computing-based device  1300  also comprises an input/output controller  1320  arranged to output display information to a display device  1324 , where used, which is separate from or integral to the computing-based device  1300 . The display information optionally graphically presents depth maps computed by the computing-based device. The input/output controller  1320  is also arranged to receive and process input from one or more devices, such as time-of-flight camera  1326 , a user input device  1322  (e.g. a stylus, mouse, keyboard, camera, microphone or other sensor). In some examples the user input device  1322  detects voice input, user gestures or other user actions and provides a natural user interface (NUI). This user input is used to specify 3D environment models, specify parameter values or for other purposes. In an embodiment the display device  1324  also acts as the user input device  1322  if it is a touch sensitive display device. The input/output controller  1320  outputs data to devices other than the display device in some examples, e.g. a locally connected printing device. 
     Any of the input/output controller  1320 , display device  1324  and the user input device  1322  comprise, in some examples, NUI technology which enables a user to interact with the computing-based device in a natural manner, free from artificial constraints imposed by input devices such as mice, keyboards, remote controls and the like. Examples of NUI technology that are provided in some examples include but are not limited to those relying on voice and/or speech recognition, touch and/or stylus recognition (touch sensitive displays), gesture recognition both on screen and adjacent to the screen, air gestures, head and eye tracking, voice and speech, vision, touch, gestures, and machine intelligence. Other examples of NUI technology that are used in some examples include intention and goal understanding systems, motion gesture detection systems using depth cameras (such as stereoscopic camera systems, infrared camera systems, red green blue (rgb) camera systems and combinations of these), motion gesture detection using accelerometers/gyroscopes, facial recognition, three dimensional (3D) displays, head, eye and gaze tracking, immersive augmented reality and virtual reality systems and technologies for sensing brain activity using electric field sensing electrodes (electro encephalogram (EEG) and related methods). 
     Alternatively or in addition to the other examples described herein, examples include any combination of the following: 
     A depth detection apparatus comprising: 
     a memory storing raw time-of-flight sensor data received from a time-of-flight sensor; and 
     a trained machine learning component having been trained using training data pairs, a training data pair comprising at least one simulated raw time-of-flight sensor data value and a corresponding simulated ground truth depth value; 
     the trained machine learning component configured to compute in a single stage, for an item of the stored raw time-of-flight sensor data, a depth value of a surface depicted by the item, by pushing the item through the trained machine learning component. 
     The apparatus mentioned above, the trained machine learning component having been trained using simulated raw time-of-flight sensor data values which incorporate simulated multi-path interference. 
     The apparatus mentioned above, the trained machine learning component having been trained using simulated raw time-of-flight sensor data values computed using a computer graphics renderer which simulates multi-path interference. 
     The apparatus mentioned above, the trained machine learning component having been trained using simulated raw time-of-flight sensor data values comprising, for an individual pixel, weighted intensity values at different depths potentially depicted by the pixel. 
     The apparatus mentioned above, the trained machine learning component having been trained using simulated raw time-of-flight sensor data values where information about an exposure profile of the time-of-flight sensor is combined with the simulated raw time-of-flight sensor data values. 
     The apparatus mentioned above, the trained machine learning component having been trained using simulated raw time-of-flight sensor data values where information about sensor noise of the time-of-flight sensor is combined with the simulated raw time-of-flight sensor data values. 
     The apparatus mentioned above, the trained machine learning component having been trained using simulated raw time-of-flight sensor data values computed using a computer graphics renderer from a plurality of instances of a parametric 3D environment model, where the instances of the parametric 3D environment model are computer generated automatically at random. 
     The apparatus mentioned above, where parameters of the parametric 3D environment model comprise one or more of: geometry of an object in the 3D environment model, position of an object in the 3D environment model, presence of an object in the 3D environment model, orientation of an object in the 3D environment model, surface materials and reflectivity, ambient illumination. 
     The apparatus mentioned above, wherein a training data pair comprises a frame of simulated raw time-of-flight sensor data values and a corresponding simulated ground truth depth map. 
     The apparatus mentioned above, the trained machine learning component having been trained using simulated raw time-of-flight sensor data values computed using a computer graphics renderer for a plurality of randomly selected viewpoints of the time-of-flight sensor, and where any of the viewpoints which are within a threshold distance of a surface in a 3D environment model used by the computer graphics renderer are omitted. 
     The apparatus mentioned above, the trained machine learning component having been trained using simulated raw time-of-flight sensor data values aggregated over a neighborhood of a pixel, where the neighborhood is a spatial neighborhood, or a temporal neighborhood, or a spatial and temporal neighborhood. 
     The apparatus mentioned above, where the trained machine learning component is a pixel independent regressor. 
     The apparatus mentioned above, where the trained machine learning component is regressor which takes into account relationships between pixels of the stored time-of-flight sensor data. 
     The apparatus mentioned above, where the trained machine learning component is a convolutional neural network and where each training data pair comprises a frame of simulated raw time-of-flight sensor data and a ground truth depth map. 
     The apparatus mentioned above, where the trained machine learning component is at least partially implemented using hardware logic selected from any one or more of: a field-programmable gate array, an application-specific integrated circuit, an application-specific standard product, a system-on-a-chip, a complex programmable logic device, a graphics processing unit. 
     A depth detection apparatus comprising: 
     a memory storing frames of raw time-of-flight sensor data received from a time-of-flight sensor; and 
     a trained machine learning component having been trained using training data pairs, a training data pair comprising a simulated raw time-of-flight sensor frame and a corresponding simulated ground truth depth map; 
     the trained machine learning component configured to compute in a single stage, for a frame of the stored raw time-of-flight sensor data, a depth map of surfaces depicted by the frame, by pushing the frame through the trained machine learning component. 
     The apparatus mentioned above, where the trained machine learning component is configured to operate in real time by computing the depth maps at a rate which is equivalent to or faster than a frame rate of the time-of-flight sensor. 
     The apparatus mentioned above, where the trained machine learning component comprises a convolutional neural network. 
     The apparatus mentioned above, where the trained machine learning component comprises a pixel independent regressor which is a regressor that does not take into account relationships between pixels of a time-of-flight sensor frame. 
     A computer-implemented method comprising: 
     storing, at a memory, raw time-of-flight sensor data received from a time-of-flight sensor; and 
     operating a trained machine learning component having been trained using training data pairs, a training data pair comprising at least one simulated raw time-of-flight sensor data value and a corresponding simulated ground truth depth value; 
     wherein operating the trained machine learning component comprises computing, in a single stage, for an item of the stored raw time-of-flight sensor data, a depth value of a surface depicted by the item, by pushing the item through the trained machine learning component. 
     An apparatus comprising: 
     means for storing raw time-of-flight sensor data received from a time-of-flight sensor; and 
     means for operating a trained machine learning component having been trained using training data pairs, a training data pair comprising at least one simulated raw time-of-flight sensor data value and a corresponding simulated ground truth depth value; wherein operating the trained machine learning component comprises computing, in a single stage, for an item of the stored raw time-of-flight sensor data, a depth value of a surface depicted by the item, by pushing the item through the trained machine learning component. 
     The examples illustrated and described herein as well as examples not specifically described herein but within the scope of aspects of the disclosure constitute exemplary means for storing raw time-of-flight sensor data, executing a trained machine learning system, computing depth values or computing depth maps. For example, the memory of  FIG. 2 or 13  constitutes exemplary means for storing raw time-of-flight sensor data. For example, the processor of  FIG. 2 or 13  constitutes exemplary means for operating a trained machine learning component. 
     The term ‘computer’ or ‘computing-based device’ is used herein to refer to any device with processing capability such that it executes instructions. Those skilled in the art will realize that such processing capabilities are incorporated into many different devices and therefore the terms ‘computer’ and ‘computing-based device’ each include personal computers (PCs), servers, mobile telephones (including smart phones), tablet computers, set-top boxes, media players, games consoles, personal digital assistants, wearable computers, and many other devices. 
     The methods described herein are performed, in some examples, by software in machine readable form on a tangible storage medium e.g. in the form of a computer program comprising computer program code means adapted to perform all the operations of one or more of the methods described herein when the program is run on a computer and where the computer program is embodied on a computer readable medium. Examples of tangible storage media include computer storage devices comprising computer-readable media such as disks, thumb drives, memory etc. and do not include propagated signals. The software is suitable for execution on a parallel processor or a serial processor such that the method operations are carried out in any suitable order, or simultaneously. 
     This acknowledges that software is a valuable, separately tradable commodity. It is intended to encompass software, which runs on or controls “dumb” or standard hardware, to carry out the desired functions. It is also intended to encompass software which “describes” or defines the configuration of hardware, such as HDL (hardware description language) software, as is used for designing silicon chips, or for configuring universal programmable chips, to carry out desired functions. 
     Those skilled in the art will realize that storage devices utilized to store program instructions are optionally distributed across a network. For example, a remote computer is able to store an example of the process described as software. A local or terminal computer is able to access the remote computer and download a part or all of the software to run the program. Alternatively, the local computer may download pieces of the software as needed, or execute some software instructions at the local terminal and some at the remote computer (or computer network). Those skilled in the art will also realize that by utilizing conventional techniques known to those skilled in the art that all, or a portion of the software instructions may be carried out by a dedicated circuit, such as a digital signal processor (DSP), programmable logic array, or the like. 
     Any range or device value given herein may be extended or altered without losing the effect sought, as will be apparent to the skilled person. 
     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. 
     It will be understood that the benefits and advantages described above relate to one embodiment or relate to several embodiments. The embodiments are not limited to those that solve any or all of the stated problems or those that have any or all of the stated benefits and advantages. It will further be understood that reference to ‘an’ item refers to one or more of those items. 
     The operations of the methods described herein are carried out in any suitable order, or simultaneously where appropriate. Additionally, individual blocks may be deleted from any of the methods without departing from the scope of the subject matter described herein. Aspects of any of the examples described above are combined with aspects of any of the other examples described to form further examples without losing the effect sought. 
     The term ‘comprising’ is used herein to mean including the method blocks or elements identified, but that such blocks or elements do not comprise an exclusive list and a method or apparatus may contain additional blocks or elements. 
     It will be understood that the above description is given by way of example only and that various modifications may be made by those skilled in the art. The above specification, examples and data provide a complete description of the structure and use of exemplary embodiments. Although various embodiments have been described above with a certain degree of particularity, or with reference to one or more individual embodiments, those skilled in the art could make numerous alterations to the disclosed embodiments without departing from the scope of this specification.