Keywords

1 Introduction

Context. The real time RGB-D stream output of modern commodity consumer depth cameras can feed a growing set of end applications, from human computer interaction and augmented reality to industrial design. Although such devices are constantly improving, the limited quality of their stream still restraints their impact spectrum. This mostly originates in the low resolution of the frames and the inherent noise, incompleteness and temporal inconsistency stemming from single view capture. With Proxy Clouds, we aim at improving real time RGB-D streams by analyzing them. A sparse set of detected 3D planes are parameterized to record statistics extracted from the stream and form a structure that we call proxy. This superstructure substitutes the RGB-D data and approximates the geometry of the scene. Using these time-evolving statistics, our plane-based framework improves the RGB-D stream on the fly by reinforcing features, removing noise and outliers or filling missing parts, under the memory-limited and real time embedded constraints of mobile capture in indoor environments (Fig. 1). We design such a lightweight planar superstructure to be stable through time and space, which gives priors to apply several signal-inspired processing primitives to the RGB-D frames. They include filtering to remove noise and temporal flickering, hole filling or resampling (Sect. 4). This allows structuring the data and simplifying or lightening subsequent operations, e.g. tracking and mapping, measurements, data transmission, rendering or physical simulations. While our primary goal is the enhancement of the RGB-D data stream, our framework can additionally be applied to compression and scene reconstruction (Sect. 6), as the generated structure is a representation of the observed scene.

Fig. 1.
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Proxy clouds overview. From a stream of RGB-D frames (left), proxies are built on-the-fly and updated over time (bottom) and used to apply different real-time processing primitives to the incoming RGB-D frames (top). The system outputs an enhanced data stream and a planar model of the observed scene (right). The “build & update” procedure is detailed in Fig. 4.

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Fig. 2.
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Proxy clouds workflow. From a stream of 2.5D RGB-D frames, proxies are built on-the-fly and updated through time (Sect. 3). They are used as priors to process incoming frames through filtering, resampling or hole filling which allows better tracking, mapping, automated navigation or measurement. A selection of proxies based on the current RGB-D frame can be used for lightened transmission of the data. Proxies can be used as priors for triangulation and fast depth data meshing, with application to rendering or simulation. Eventually, the consolidation of the depth stream within the proxies leads to a reconstruction of planar areas in the observed scene. Processing modules are described in Sect. 4 and the consolidation of data is presented in Sect.  6.

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Overview. In practice, our system takes a raw RGB-D stream as input to build and update a set of planar proxies on-the-fly. It outputs an enhanced stream together with a model of planar areas in the observed scene (see Fig. 2). On the contrary to previous approaches, which mostly rely on a full volumetric reconstruction to consolidate data, our approach is light weight, with a moderate memory footprint and a transparent interfacing to any higher-level RGB-D pipeline. To summarize, our contributions are:

  • a stable and lightweight multiplanar superstructure for RGB-D data,

  • construction and updating methods which are spatially and temporally consistent,

  • a collection of RGB-D enhancement methods based on our structure which run on-the-fly.

2 Previous Work

Camera Motion Estimation. Endres et al. [1] describe an egomotion estimation method that uses point features detected in the color component of the RGB-D frame. After detecting and matching SIFT, SURF or ORB features in subsequent color images, their 3D position in both frames is computed using the depth component. Using these matching 3D points, a robust RANSAC-based [2] estimation of the motion matrix allows discarding false positive matches. Sets of three matching points are randomly picked and the matrix transforming a set in the first frame into the second set is computed using a Least-Squares method [3]. Inliers of the transformation are estimated using their 3D position and orientation and the one giving the most inliers is kept. It is important to note that any existing method or device that localizes an RGB-D camera in its environment can be used instead. Some of them are presented in Sect. 2.

Plane Detection in RGB-D Stream. Methods that build high level models of captured 3D data are mostly based on RANSAC [2], the Hough transform [4] or Region Growing algorithms. In our embedded, real time, memory-limited context, we take inspiration from the RANSAC-based method of Schnabel et al. [5] for its time and memory efficiency, by repeating plane detection through time to acquire a consistent model and cope with the stochastic nature of RANSAC.

Their Efficient RANSAC implementation gives stochastic improvements to the critical steps of the algorithm in terms of complexity. For a regular RANSAC-based plane detection, minimal sets of three points would be randomly picked a fixed and large number of times. Then, the shape parameters are estimated from this minimal set and inliers of the estimated plane are computed. The shape with the highest score is kept, its inliers are removed from the point cloud and the algorithm is ran again on the remaining data. Schnabel et al. replace the fixed number of loops with a stochastic condition, based on the number of detected shapes and number of randomly picked minimal sets, to stop looking for planes in the dataset. Also, instead of searching the full point cloud for inliers of a given shape, they estimate this count in a random subset of the dataset and extrapolate it to the full point cloud. Other modifications allow improving the quality of detected shapes with a localized sampling and specific post-processing.

Again, our framework is not attached to a particular plane detection method, and other algorithms such as point clustering [6] or agglomerative hierarchical clustering [7], could be used. For a complete overview of plane detection methods in captured 3D data, we refer the reader to our survey [8].

Depth Processing. Depth maps can be denoised using spatial filters [9] e.g., Gaussian, median, bilateral [10,11,12], adaptive or anisotropic [13, 14] filters, often refined through time, with the resulting enhanced stream potentially used for a full 3D reconstruction [15]. Other methods include non-local means [16], bilateral filters with time [12], Kalman filters [17], over-segmentation [18] and region-growing [19]. Wu et al. [20] present a shape-from-shading method using the color component to improve the geometry, which allows adding details to the low quality input depth. They show applications of their method to improve volumetric reconstruction on multiple small scale and close range scenes. Depth maps can be upsampled using cross bilateral filters such as joint bilateral upsampling [21] or weighted mode filtering [22]. Such methods are particularly useful to recover sharp depth regions boundaries and enforce depth-based segmentation.

Hole Filling. Depth sensing range limits and high noise levels often create holes in RGB-D data. Given the material of observed objects and the type of technology used, e.g. time of flight, light coding or stereo vision, some surfaces are harder to detect. The orientation of the surface with regards to the sensor and the perturbations due to light sources can also lower the quality of certain areas. In order to fill these holes in the depth component, one can use the same spatial filters as those used for denoising [16], or morphological filters [13, 14].

Inpainting methods [23], over-segmentation [24] or multiscale [25] processing are also used to fill holes for e.g., depth image-based rendering (DIBR) under close viewing conditions.

Plane-Based Depth Processing. A set of 3D planes offers a faithful yet lightweight approximation for many indoor environments. Surprisingly, only a few methods have used planar proxies as priors to process 2.5D data, with in particular Schnabel et al. [26] who detect limits of planes to fill in holes in static 3D point clouds. Fast Sampling Plane Filtering [27] detects and merges planar patches in static indoor scenes. The detected planes allow filtering the planar surfaces of the input point cloud, however the primitives seem quite sensitive to the depth sensor noise and lack spatial consistency.

Dense SLAM. Online dense Simultaneous Localization And Mapping (SLAM) methods accumulate points within a map of the environment, while continuously localizing the sensor in this map. Recent dense SLAM systems include RGB-D SLAM [1], RTAB-Map [28], KDP SLAM [29] or ORB-SLAM2 [30]. Point-based fusion [31] is also used to accumulate points without the need of a full volumetric representation. Several methods have been developed to include planar primitives in the SLAM system, either to smooth and improve the reconstruction [32, 33] or improve the localization of the sensor [34,35,36]. Finally, a recent offline method [37] makes use of planes to estimate the geometry of a room in order to remove furnitures and model the lighting of the environment. This allows the user to re-light and re-furnish the room as desired.

Volumetric Depth Fusion. Online scene reconstruction methods using volumetric fusion were pioneered by KinectFusion [15], then made more efficient with VoxelHashing [38], and more accurate with BundleFusion [39]. However, the need for a voxel grid representing the space leads to high requirements of memory. Recent algorithms make use of planes to smooth and complete the data within the volume, such as methods by Zhang et al. [40] or Dzitsiuk et al. [41]. Offline improvement methods have been developed based on the volumetric representation of the scene, such as 3DLite [42] that builds a planar model of the observed scene and optimizes it to achieve a high quality texturing of the surfaces.

3 Proxy Clouds

Model. Basically, Proxy Clouds model RGB-D data which is often seen and consistent through frames and space, hence revealing the dominant structural elements in the scene. To do so, they take the form of a multiplanar superstructure, where each proxy is equipped with a local frame, bounds and, within the bounds, a regular 2D grid of rich statistics, mapped on the plane and gathered from the RGB-D data.

Each cell of the grid includes an occupancy probability as well as a statistical model of the depth values. We choose to represent this local distribution using smoothed local histograms [43] made of Gaussian kernels. The contribution of an inlier p of distance d(p) to the proxy is given in Eq. 1.

$$\begin{aligned} \begin{aligned} h_p(s) = \frac{1}{\sigma \sqrt{2\pi }} e^{\frac{(s - d(p))^2}{2\sigma ^2}} ~~~~ h'_p(s) = - \frac{s - d(p)}{\sigma ^2} h_p(s) \end{aligned} \end{aligned}$$
(1)

This compressed model stores the repartition of plane inliers distances to the proxy and makes possible estimating the diversity of the values within each cell by counting the number of modes in the distribution. If it has a single mode, then all values are similar and the surface of the proxy within the cell is most likely flat. If the distribution has two or more modes, then the values belong to different groups and the cell likely overlaps a salient area of the surface.

Fig. 3.
figure 3

Planar proxy model. Built upon a plane in 3D space, our proxy model is made of a local frame, bounds and a grid of cells which contain statistics. These statistics are the occupancy probability as well as a collection of mean \(\mu \) and variance \(\sigma \) values for depth, representing a smoothed local histogram and gathered from the RGB-D data. Activated cells are the ones containing inliers from many frames.

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Cells have a fixed size of 5 cm \(\times \) 5 cm, which corresponds to about four times the area of a depth pixel at a typical distance of 8 metersFootnote 1. Hence, this size ensures a minimum sampling of proxy cells by depth points even at far capture distances.

Cells are activated when their visitation percentage over the recent frames (the last 100 frames in our experiments) is greater than a threshold (25% in practice). Once activated, a cell stays so until the end of the processing. We consider a cell as visited as soon as it admits at least one inlier data point i.e., a data point located within a threshold distance to the cell under a projection in the direction from the sensor origin to the point. This activation threshold allows modeling the actual geometry of the observed scene, while discarding outliers observations due to the low quality of the sensor. Figure 3 gives visual insight of a planar proxy.

Building Proxies. We build planar proxies on-the-fly and update them through time using solely incoming raw RGB-D frames from the live stream. More precisely, for each new RGB-D image \(X_t = \{I_t, D_t\}\) (color and depth), we run the procedure described in Algorithm 1 and Fig. 4.

Fig. 4.
figure 4

Building proxies. This procedure is ran for each new RGB-D image \(X_t\) at frame t, made of a color image \(I_t\) and a depth map \(D_t\). \(D_t^f\): low-pass filtered version of \(D_t\); \(M_t\): camera motion matrix; \(N_t\): normal vectors associated with \(D_t\); \(P_{t-1}\): proxies detected at frame \(t-1\); \(P_t^c\): candidate proxies; \(P_t\): proxies at frame t; \(D_t^f \scriptstyle |in\): low-pass filtered depth points without inliers from \(P_t\);

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figure a
Fig. 5.
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Proxy building procedure. The input RGB-D frame is converted into a raw point cloud on which a low-pass filter is applied, followed by normal estimation (top). RANSAC-based plane detection [5] is applied and used as a basis for the construction or the update of our proxies, following the structure shown in Fig. 3 (bottom right). Accumulated proxy cells (bottom) are visualized with colors weighted by their occupancy probabilities: darker cells have a low probability and represent low confidence areas, whereas brighter cells represent areas with high confidence. Proxies are then used to generate enhanced RGB-D frames. The whole process runs on-the-fly.

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The initial depth filtering (step 1) is based on a bilateral convolution [10] of the depth map using a Gaussian kernel associated with a range check to discard points further than a depth threshold from the current point, which could create artificial depth values if taken into account. In our experiments, we choose to set this threshold to 20 cm, which allows filtering together parts of the same object, while ignoring the influence of unrelated objects. Due to the embedded processing constraint, we estimate the normal field (step 2) through the simple computation of the depth gradient at each pixel, using the sensor topology as domain. The estimation of the camera motion from the previous frame (step 3) is inspired from the method introduced by Endres et al. [1], using point features from \(I_t\). As previously stated, any egomotion estimation algorithm can be used at this step, as all we need is the values of the six degrees of freedom modeling the camera motion. Examples of such algorithms are given in Sect. 2. In order to keep or discard previously detected proxies (step 4.2), we define a voting scheme where samples of \(X_t\) which are inliers of a given previous proxy cast their vote to this proxy and are marked. Then, the per-proxy vote count indicates whether the proxy is preserved or discarded (step 4.3). Preserved proxies are updated with \(X_t\), hence see their parameters refined and occupancy statistics updated with new inliers. Discarded proxies are placed in probation state for near-future recheck with new incoming frames, and purged if discarded for too long. However, in order to avoid losing information on non-observed parts of the scene, we do not purge proxies that have been seen long enough, which stay in probation instead. When new proxies have been detected (step 5.1), similar ones are merged together in order to avoid modeling different parts of planar surfaces with multiple proxy instances (step 5.2). The proxy is then generated (step 5.3) with a bounding rectangle and a local frame computed to be aligned with the scene orientation (more details in the supplemental material). Using the global scene axes to compute the local frame leads to a fixed resolution and spatial consistency for the grid of all proxies and allows efficient recovery and fusion (step 5.2). Finally, occupancy statistics are initialized using \(X_t\) (step 5.4). In order to take into account the point of view when modeling the scene, inlier depth points are projected upon the detected shape following the direction between the camera and the point. The coordinates of the corresponding cell of the proxy grid are then recovered to update its statistics. As a last step, proxies are transformed from local depth frame into global 3D space in order to be tracked in the next frames (step 5.5).

Figure 5 shows the different steps of the construction of the proxy cloud on one specific example.

4 RGB-D Stream Processing

Our Proxy Cloud allows online recovery of the underlying structure of piecewise planar scenes (e.g., indoor) and is used as a prior to run on-the-fly processing on the incoming RGB-D frames. The different processing modules applied to the frames are presented below.

Filtering. While projecting the sensor’s data points onto their associated proxy would allow removing the acquisition noise and quantization errors due to the sensor, this would lead to the flattening of all plane inliers. In order to minimize the loss of details on the planar surfaces while keeping a lightweight data structure, we instead use the planar proxies as a simple collaborative filter model. To that end, we designed a custom filter to leverage the smoothed local histograms stored in each cell of the proxies. As explained in Sect. 3, the number of detected modes allows distinguishing flat areas of the proxy surface from salient ones. For flat cells whose distribution has a single mode, we project the depth points on the plane along the direction between the camera and the point. We offset the points of the average distance to the plane only if it is above the noise threshold at the corresponding distance to the camera (see details on the noise threshold in the supplemental material). This allows smoothing surface areas that are exactly on the plane while keeping flat areas offset from the plane as they are in the scene. For flat cells whose distribution has two or more modes, we do not perform any projection in order to keep the saliency of the surface.

Equation 2 details the smoothed local histograms-based filtering of inlier \(\mathbf p \) to \(\mathbf p _f\), belonging to cell c with \(m_c\) modes and an average distance to the proxy of \(d_c\), and a noise threshold of \(\alpha \). The proxy is based on a plane of normal \(\mathbf N \) and distance to origin l.

(2)

The proxy can also be used as a high level range space for cross bilateral filtering [21], where inliers of different proxies will not be processed together.

Based on time-evolving data points, the proxies consolidate the stable geometry of the scene by accumulating observations in multiple frames. Averaging those observations over time removes temporal flickering, after a few frames only.

Hole Filling. Missing data in depth is often due to specular and transparent surfaces such as glass or screens. With our Proxy Cloud, observed data is reinforced over multiple frames from the support of stable proxies, augmenting the current frame with missing samples from previous ones. In practice, the depth data that is often seen in incoming frames creates activated cells with sufficient occupancy probability to survive within the model even when samples for these cells are missing.

This hole filling, stemming naturally from the proxy structure, is completed by two additional steps. First, the extent of the proxies is extrapolated to the intersection of adjacent proxies - this is particularly useful to complete unseen areas under furniture for example. Second, we perform a morphological closing [44] on the grid of cells, with a square structural element having a fixed side of seven cells. This corresponds to closing holes of maximum 35 cm by 35 cm, which allows filling missing data due to small specular surfaces, e.g. computer screens or glass-door cabinets, while keeping larger openings such as windows or doors.

Resampling. RGB-D streams can be super-sampled on the fly, by enriching their low definition geometric component using the higher resolution color component structured in the proxies to guide the process. This results in high definition RGB-D data with controllable point density on the surface of the shapes.

Lossy Compression. Compression of the input data is achieved by using directly the proxy cloud as a compressed, lightweight geometric substitute to the huge amount of depth data carried in the stream, avoiding storing uncertain and highly noisy depth regions, while still being able to upsample back to high resolution depth using a bilateral upsampling. In particular, this is convenient to broadcast captures of indoor scenes where planar regions are frequent.

5 Experiments

Proxy Clouds are implemented through hardware and software components. The hardware setup is made of a computer with Intel Core i7 at 3.5 GHz and 10 GB memory. No GPU is used. The software setup has a client-server architecture, where the server runs in a single thread within an embedded environment with low computational power and limited memory to trigger the sensor and process the data. The client’s graphical user interface allows controlling the processing parameters and getting a real time feedback of the stream. A limited range of intuitive parameters allow the user to control the trade-off between quality of the output and performance of the processing.

We run all of our experiments on the 3DLite [42] datasetFootnote 2, containing 10 scenes acquired with a Structure sensorFootnote 3 under the form of RGB-D image sequences. This choice was motivated by the availability of ground truth poses along with the visual data, as well as result meshes and performance metrics provided from processing with both BundleFusion [39] and 3DLite [42], with which we compare our method in Sect. 6.

Geometric statistics on the generated proxies are available as supplemental material for all processed scenes (Table 1). We also provide in Fig. 1 of the supplemental material, a plot of the increment of the average depth over time, to show the fast convergence of the proxy statistics after about 30 accumulated samples. The accuracy of the proxy representation can be quantitatively assessed through the PSNR values in Table 1.

Performance. The current time required to build and update planar proxies using our (single-threaded) implementation is around 130 ms for an input depth image of 320\(\,\times \,\)240 pixels. A detailed graph presenting the time needed for all steps is available as supplemental material (Fig. 2).

Live RGB-D Stream Processing. Figure 6 shows examples of data improvement using the processing modules of our framework. Experiments show that the Proxy Cloud is particularly efficient to remove noise over walls and floors while keeping salient parts, and helps reducing holes due to unseen areas, specular areas, such as lights or glass, and low confidence areas, such as distant points. Resampling the point cloud allows recovering structure if the sensor did not give enough data samples, e.g. on lateral planar surfaces. More examples of RGB-D stream improvement on other scenes are available as supplemental material.

Fig. 6.
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Data improvement. Raw RGB-D and Proxy Clouds-improved data showing results of real time filtering, hole filling and resampling. The texture applied to the completed data is extracted from the raw color frame, which does not make sense for all parts of unseen geometry, as we can see on the hole filling and resampling examples. (Color figure online)

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Compression. Substituting the Proxy Cloud to the RGB-D stream provides a simple yet effective lossy compression scheme for transmission, with the practical side effect of removing many outliers. Our efficient data structure leads to good compression ratios while keeping high Peak Signal-to-Noise Ratio (PSNR) and being fast for compression and decompression (see Table 1 for evaluation metrics of the compression using proxies). The proxies are stored as simple grids of statistics with a local frame and bounding rectangle. As such, the compressed structure itself, i.e. the proxies, can benefit from image-based compression schemes such as JPEG [45] for offline export and storage, for which we report compression ratios and PSNR values in Table 1. In addition to the bandwidth saving, the compressed Proxy Cloud representation enables smooth super-sampling of the geometric data, where the output point cloud density over proxy surfaces can be increased as desired. The planar parameterization of each proxy offers a suitable domain for point upsampling operators, while a similar approach performed directly on the RGB-D stream is blind to the scene structure.

Table 1. Compression metrics for all processed scenes. Compression ratios are based on the raw size of a 320\(\,\times \,\)240 depth map and the size of the proxies without the outliers. The JPEG export ratio is between the sizes of the raw and exported proxy clouds. The export and load procedure for all proxies takes an average of about 40 ms. The Peak Signal-to-Noise Ratio (PSNR) is computed using the average Root Mean Square Error (RMSE) between raw depth points and proxy-filtered ones. The time values correspond to the compression and decompression. The former is the building of proxies averaged over all frames, while the latter is the generation of a depth map by applying visibility tests to the proxies. We compare our compression performance to a state-of-the-art method based on H.264 [46] with a quality profile of 50. The corresponding compression and decompression times are given for the whole frame set.
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6 RGB-D Stream Consolidation

While being lightweight and fast to compute, the Proxy Cloud represents a superstructure modeling the dominant planar elements of an indoor scene. In addition to being used to filter the input point cloud and generate an enhanced RGB-D stream as output, proxies themselves are a way to consolidate the input RGB-D frames. Hence, meshing the proxy cells leads to a lightened organized structure and aggregating all proxies in the global space allows reconstructing a higher quality surface model of the observed scene, generated on-the-fly. In this section, we compare the performance and quality of scene reconstruction using Proxy Clouds to state-of-the-art methods BundleFusion [39] and 3DLite [42].

Qualitative Results. Figure 7 presents the reconstructed planar models based on the corresponding Proxy Cloud. More reconstructed scenes are available as supplemental material. As we can see, most large planar surfaces such as walls and floors are modeled with a single proxy instance.

Fig. 7.
figure 7

Scene reconstruction. Examples of reconstructed scenes of the 3DLite [42] dataset using Proxy Clouds. The meshes are made of quads when four activated cells are adjacent, and triangles otherwise.

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Quantitative Results. Tables 2 and 3 present performance and quality metrics for the 10 scenes of the dataset. The reconstruction using proxies can be quantitatively assessed and compared to 3DLite through the values of RMSE with BundleFusion. These metrics show that the lightweight and simple structure of the Proxy Cloud leads to better performance both in timing and memory consumption, while keeping a quality comparable to that of state-of-the art methods.

With its low runtime and memory needs, Proxy Clouds offer a lighter alternative to most recent reconstruction methods characterized by volumetric or deep learning approaches, which have high requirements in computation costs and memory consumption. The generic format and implementation of the proxies avoid the need for tedious platform-specific tuning and make them well suited for embedded operation and modern mobile applications. In addition to the fact that our proxies are built and updated on the fly, the processing runs in a single thread and requires far less memory than modern embedded devices offer.

Table 2. Quantitative comparison of scene reconstruction processing. The metrics are compared between BundleFusion (BF), 3DLite (3DL) and our Proxy Clouds (PC). The processing time to process one frame is averaged over all frames in the scene. The memory consumption is the maximum used memory during processing.
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Table 3. Quantitative comparison of scene reconstruction data. We compare our Proxy Clouds (PC) to BundleFusion (BF) and 3DLite (3DL). The model size for BF and 3DL includes texture information, while the PC model only contains geometry. The Root Mean Square Error (RMSE) is computed using the Metro tool [47] between the BundleFusion mesh, taken as reference, and the 3DLite and Proxy Clouds meshes.
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7 Conclusion and Future Work

We introduced Proxy Clouds, a unified plane-based framework for real-time processing of RGB-D streams. It takes the form of stable proxies modeling the dominant geometric scene structure through a set of rich statistics. Our method provides a compact, lightweight and consistent spatio-temporal support for the processing primitives designed to enhance data or lighten subsequent operations. It runs at interactive rates on mobile platforms and allows fast enhancement and transmission of the captured data. Our structure can be meshed and used as a model of the observed scene, generated on-the-fly. Its implementation makes possible real-time feedback and its control relies on a limited range of parameters. Compared to BundleFusion and 3DLite, Proxy Clouds provide a good balance between processing time, memory consumption and approximation quality.

In the future, we plan to develop a parallel implementation using multi-core CPU and mobile GPUs to achieve a higher processing rate on embedded platforms. To that end, the primitives we use in our algorithm are naturally parallel scalable. While our current proxy model stores statistics on a uniform (yet sparse) grid, it could be improved using a sparse adaptive structure [48]. We also plan to extend the geometry of proxies to other simple shapes, such as boxes, spheres and cylinders, while still maintaining a unified representation for all of them, interfacing them seamlessly to the processing primitives. Last, we plan to use our stable proxies to estimate the position and orientation of the camera and track it within the scene, in a similar spirit to Raposo et al. [49].