Higher order SVD analysis for dynamic texture synthesis.

Videos representing flames, water, smoke, etc., are often defined as dynamic textures: "textures" because they are characterized by the redundant repetition of a pattern and "dynamic" because this repetition is also in time and not only in space. Dynamic textures have been modeled as linear dynamic systems by unfolding the video frames into column vectors and describing their trajectory as time evolves. After the projection of the vectors onto a lower dimensional space by a singular value decomposition (SVD), the trajectory is modeled using system identification techniques. Synthesis is obtained by driving the system with random noise. In this paper, we show that the standard SVD can be replaced by a higher order SVD (HOSVD), originally known as Tucker decomposition. HOSVD decomposes the dynamic texture as a multidimensional signal (tensor) without unfolding the video frames on column vectors. This is a more natural and flexible decomposition, since it permits us to perform dimension reduction in the spatial, temporal, and chromatic domain, while standard SVD allows for temporal reduction only. We show that for a comparable synthesis quality, the HOSVD approach requires, on average, five times less parameters than the standard SVD approach. The analysis part is more expensive, but the synthesis has the same cost as existing algorithms. Our technique is, thus, well suited to dynamic texture synthesis on devices limited by memory and computational power, such as PDAs or mobile phones.

Dynamic measurement of room impulse responses using a moving microphone.

A technique for the recording of large sets of room impulse responses or head-related transfer functions is presented. The technique uses a microphone moving with constant speed. Given a setup (e.g., length of the room impulse response), a careful choice of the recording parameters (excitation signal, speed of movement) leads to the reconstruction of all impulse responses along the trajectory. In the case of a moving microphone along a circle, the maximal angular speed is given as a function of the length of the impulse response, its maximal temporal frequency, the speed of sound propagation, and the radius of the circle. As a result of the presented algorithm, head-related transfer functions sampled at 44.1 kHz can be measured at all angular positions along the horizontal plane in less than 1 s. The presented theory is compared with a real system implementation using a precision moving microphone holder. The practical setup is discussed together with its limitations.

Bits from photons: oversampled image acquisition using binary Poisson statistics.

We study a new image sensor that is reminiscent of a traditional photographic film. Each pixel in the sensor has a binary response, giving only a 1-bit quantized measurement of the local light intensity. To analyze its performance, we formulate the oversampled binary sensing scheme as a parameter estimation problem based on quantized Poisson statistics. We show that, with a single-photon quantization threshold and large oversampling factors, the Cramér-Rao lower bound (CRLB) of the estimation variance approaches that of an ideal unquantized sensor, i.e., as if there were no quantization in the sensor measurements. Furthermore, the CRLB is shown to be asymptotically achievable by the maximum-likelihood estimator (MLE). By showing that the log-likelihood function of our problem is concave, we guarantee the global optimality of iterative algorithms in finding the MLE. Numerical results on both synthetic data and images taken by a prototype sensor verify our theoretical analysis and demonstrate the effectiveness of our image reconstruction algorithm. They also suggest the potential application of the oversampled binary sensing scheme in high dynamic range photography.