We introduce a method for accurate three dimensional head pose estimation using a commodity depth camera. We perform pose estimation by registering a morphable face model to the measured depth data, using a combination of particle swarm optimization (PSO) and the iterative closest point (ICP) algorithm, which minimizes a cost function that includes a 3D registration and a 2D overlap term. The pose is estimated on the fly without requiring an explicit initialization or training phase. Our method handles large pose angles and partial occlusions by dynamically adapting to the reliable visible parts of the face. It is robust and generalizes to different depth sensors without modification. On the Biwi Kinect dataset, we achieve best-in-class performance, with average angular errors of 2.1, 2.1 and 2.4 degrees for yaw, pitch, and roll, respectively, and an average translational error of 5.9 mm, while running at 6 fps on a graphics processing unit.

We demonstrate that layered spatial light modulators (SLMs), subject to fixed lateral displacements and refreshed at staggered intervals, can synthesize images with greater spatiotemporal resolution than that afforded by any single SLM used in their construction. Dubbed cascaded displays , such architectures enable superresolution flat panel displays (e.g., using thin stacks of liquid crystal displays (LCDs)) and digital projectors (e.g., relaying the image of one SLM onto another). We introduce a comprehensive optimization framework, leveraging non-negative matrix and tensor factorization, that decomposes target images and videos into multi-layered, time-multiplexed attenuation patterns---offering a flexible trade-off between apparent image brightness, spatial resolution, and refresh rate. Through this analysis, we develop a real-time dual-layer factorization method that quadruples spatial resolution and doubles refresh rate. Compared to prior superresolution displays, cascaded displays place fewer restrictions on the hardware, offering thin designs without moving parts or the necessity of temporal multiplexing. Furthermore, cascaded displays are the first use of multi-layer displays to increase apparent temporal resolution. We validate these concepts using two custom-built prototypes: a dual-layer LCD and a dual-modulation liquid crystal on silicon (LCoS) projector, with the former emphasizing head-mounted display (HMD) applications.

We present a theory that addresses the problem of determining shape from the (small or differential) motion of an object with unknown isotropic reflectance, under arbitrary unknown distant illumination, for both orthographic and perpsective projection. Our theory imposes fundamental limits on the hardness of surface reconstruction, independent of the method involved. Under orthographic projection, we prove that three differential motions suffice to yield an invariant that relates shape to image derivatives, regardless of BRDF and illumination. Under perspective projection, we show that four differential motions suffice to yield depth and a linear constraint on the surface gradient, with unknown BRDF and lighting. Further, we delineate the topological classes up to which reconstruction may be achieved using the invariants. Finally, we derive a general stratification that relates hardness of shape recovery to scene complexity. Qualitatively, our invariants are homogeneous partial differential equations for simple lighting and inhomogeneous for complex illumination. Quantitatively, our framework shows that the minimal number of motions required to resolve shape is greater for more complex scenes. Prior works that assume brightness constancy, Lambertian BRDF or a known directional light source follow as special cases of our stratification. We illustrate with synthetic and real data how potential reconstruction methods may exploit our framework.

We study the problem of adaptive compressive sensing (CS) of a time-varying signal with slowly changing sparsity and rapidly varying support. We are specifically interested in visual surveillance applications such as background subtraction and tracking. Classical CS theory assumes prior knowledge of signal sparsity in order to determine the number of sensor measurements needed to ensure adequate signal reconstruction. However, when dealing with time-varying signals such as video, prior information regarding the exact sparsity may be difficult to obtain. Assuming a sensor that is able to take an adaptive number of compressive measurements, we present an algorithm based on cross validation that quantitatively evaluates the current measurement rate and adjusts it as needed.

We describe an imaging architecture for compressive video sensing termed programmable pixel compressive camera (P2C2). P2C2 allows us to capture fast phenomena at frame rates higher than the camera sensor. In P2C2, each pixel has an independent shutter that is modulated at a rate higher than the camera frame-rate. The observed intensity at a pixel is an integration of the incoming light modulated by its specific shutter. We propose a reconstruction algorithm that uses the data from P2C2 along with additional priors about videos to perform temporal super-resolution. We model the spatial redundancy of videos using sparse representations and the temporal redundancy using brightness constancy constraints inferred via optical flow. We show that by modeling such spatio-temporal redundancies in a video volume, one can faithfully recover the underlying high-speed video frames from the observed low speed coded video. The imaging architecture and the reconstruction algorithm allows us to achieve temporal super-resolution without loss in spatial resolution. We implement a prototype of P2C2 using an LCOS modulator and recover several videos at 200 fps using a 25 fps camera.

We show that, via temporal modulation, one can observe and capture a high-speed periodic video well beyond the abilities of a low-frame-rate camera. By strobing the exposure with unique sequences within the integration time of each frame, we take coded projections of dynamic events. From a sequence of such frames, we reconstruct a high-speed video of the high-frequency periodic process. Strobing is used in entertainment, medical imaging, and industrial inspection to generate lower beat frequencies. But this is limited to scenes with a detectable single dominant frequency and requires high-intensity lighting. In this paper, we address the problem of sub-Nyquist sampling of periodic signals and show designs to capture and reconstruct such signals. The key result is that for such signals, the Nyquist rate constraint can be imposed on the strobe rate rather than the sensor rate. The technique is based on intentional aliasing of the frequency components of the periodic signal while the reconstruction algorithm exploits recent advances in sparse representations and compressive sensing. We exploit the sparsity of periodic signals in the Fourier domain to develop reconstruction algorithms that are inspired by compressive sensing.

The ability of Compressive Sensing (CS) to recover sparse signals from limited measurements has been recently exploited in computational imaging to acquire high-speed periodic and near-periodic videos using only a low-speed camera with coded exposure and intensive off-line processing. Each low-speed frame integrates a coded sequence of high-speed frames during its exposure time. The high-speed video can be reconstructed from the low-speed coded frames using a sparse recovery algorithm. This paper presents a new streaming CS algorithm specifically tailored to this application. Our streaming approach allows causal on-line acquisition and reconstruction of the video, with a small, controllable, and guaranteed buffer delay and low computational cost. The algorithm adapts to changes in the signal structure and, thus, outperforms the off-line algorithm in realistic signals.

Surface reconstruction from gradient fields is an important final step in several applications involving gradient manipulations and estimation. Typically, the resulting gradient field is non-integrable due to linear/non-linear gradient manipulations, or due to presence of noise/outliers in gradient estimation. In this paper, we analyze integrability as error correction, inspired from recent work in compressed sensing, particulary ℓ0- ℓ1equivalence. We propose to obtain the surface by finding the gradient field which best fits the corrupted gradient field in ℓ1sense. We present an exhaustive analysis of the properties of ℓ1solution for gradient field integration using linear algebra and graph analogy. We consider three cases: (a) noise, but no outliers (b) no-noise but outliers and (c) presence of both noise and outliers in the given gradient field. We show that ℓ1solution performs as well as least squares in the absence of outliers. While previous ℓ0- ℓ1equivalence work has focused on the number of errors (outliers), we show that the location of errors is equally important for gradient field integration. We characterize the ℓ1solution both in terms of location and number of outliers, and outline scenarios where ℓ1solution is equivalent to ℓ0solution. We also show that when ℓ1solution is not able to remove outliers, the property of local error confinement holds: i.e., the errors do not propagate to the entire surface as in least squares. We compare with previous techniques and show that ℓ1solution performs well across all scenarios without the need for any tunable parameter adjustments.

Compressed sensing (CS) suggests that a signal, sparse in some basis, can be recovered from a small number of random projections. In this paper, we apply the CS theory on sparse background-subtracted silhouettes and show the usefulness of such an approach in various multi-view estimation problems. The sparsity of the silhouette images corresponds to sparsity of object parameters (location, volume etc.) in the scene. We use random projections (compressed measurements) of the silhouette images for directly recovering object parameters in the scene coordinates. To keep the computational requirements of this recovery procedure reasonable, we tessellate the scene into a bunch of non-overlapping lines and perform estimation on each of these lines. Our method is scalable in the number of cameras and utilizes very few measurements for transmission among cameras. We illustrate the usefulness of our approach for multi-view tracking and 3-D voxel reconstruction problems.