Loïc Baboulaz

Sampling and Exact Reconstruction of Pulses with Variable Width

Recent sampling results enable the reconstruction of signals composed of streams of fixed-shaped pulses. These results have found applications in topics as varied as channel estimation, biomedical imaging and radio astronomy. However, in many real signals, the pulse shapes vary throughout the signal. In this paper, we show how to sample and perfectly reconstruct Lorentzian pulses with variable width. In the noiseless case, perfect recovery is guaranteed by a set of theorems. In addition, we verify that our algorithm is robust to model mismatch and noise. This allows us to apply the technique to two practical applications: electrocardiogram (ECG) compression and bidirectional reflectance distribution function (BRDF) sampling. ECG signals are one dimensional, but the BRDF is a higher dimensional signal, which is more naturally expressed in a spherical coordinate system; this motivated us to extend the theory to the 2D and spherical cases. Experiments on real data demonstrate the viability of the proposed model for ECG acquisition and compression, as well as the efficient representation and low-rate sampling of specular BRDFs.

Light field panorama by a plenoptic camera

Consumer-grade plenoptic camera Lytro draws a lot of interest from both academic and industrial world. However its low resolution in both spatial and angular domain prevents it from being used for fine and detailed light field acquisition. This paper proposes to use a plenoptic camera as an image scanner and perform light field stitching to increase the size of the acquired light field data. We consider a simplified plenoptic camera model comprising a pinhole camera moving behind a thin lens. Based on this model, we describe how to perform light field acquisition and stitching under two different scenarios: by camera translation or by camera translation and rotation. In both cases, we assume the camera motion to be known. In the case of camera translation, we show how the acquired light fields should be resampled to increase the spatial range and ultimately obtain a wider field of view. In the case of camera translation and rotation, the camera motion is calculated such that the light fields can be directly stitched and extended in the angular domain. Simulation results verify our approach and demonstrate the potential of the motion model for further light field applications such as registration and super-resolution.

Shapes From Pixels

Continuous-domain visual signals are usually captured as discrete (digital) images. This operation is not invertible in general, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image, unless it satisfies certain constraints (e.g., bandlimitedness). In this paper, we study the problem of recovering shape images with smooth boundaries from a set of samples. Thus, the reconstructed image is constrained to regenerate the same samples (consistency), as well as forming a shape (bilevel) image. We initially formulate the reconstruction technique by minimizing the shape perimeter over the set of consistent binary shapes. Next, we relax the non-convex shape constraint to transform the problem into minimizing the total variation over consistent non-negative-valued images. We also introduce a requirement (called reducibility) that guarantees equivalence between the two problems. We illustrate that the reducibility property effectively sets a requirement on the minimum sampling density. We also evaluate the performance of the relaxed alternative in various numerical experiments.

Handheld Reflectance Acquisition of Paintings

Relightable photographs are alternatives to traditional photographs as they provide a richer viewing experience. However, the complex acquisition systems of existing techniques have restricted its usage to specialized setups. We introduce an easy-to-use and affordable solution for using smartphones to acquire the reflectance of paintings and similar almost-planar objects like tablets, engravings and textile. Our goal is to enable interactive relighting of such artifacts by everyone. In our approach, we nonuniformly sample the reflectance functions by moving the LED light of a smartphone, and simultaneously, tracking the position of the smartphone by using its camera. We then propose a compressive-sensing-based approach for reconstructing the light transport matrix from the nonuniformly sampled data. As shown with experiments, we accurately reconstruct the light transport matrix that can then be used to create relightable photographs.

VITRAIL: Acquisition, Modeling, and Rendering of Stained Glass

Stained glass windows are designed to reveal their powerful artistry under diverse and time-varying lighting conditions; virtual relighting of stained glass, therefore, represents an exceptional tool for the appreciation of this age old art form. However, as opposed to most other artifacts, stained glass windows are extremely difficult if not impossible to analyze using controlled illumination because of their size and position. In this paper, we present novel methods built upon image based priors to perform virtual relighting of stained glass artwork by acquiring the actual light transport properties of a given artifact. In a preprocessing step, we build a material-dependent dictionary for light transport by studying the scattering properties of glass samples in a laboratory setup. We can now use the dictionary to recover a light transport matrix in two ways: under controlled illuminations the dictionary constitutes a sparsifying basis for a compressive sensing acquisition, while in the case of uncontrolled illuminations the dictionary is used to perform sparse regularization. The proposed basis preserves volume impurities and we show that the retrieved light transport matrix is heterogeneous, as in the case of real world objects. We present the rendering results of several stained glass artifacts, including the Rose Window of the Cathedral of Lausanne, digitized using the presented methods.

Light Transport Matrix recovery for nearly planar objects

The light transport matrix has become a powerful tool for scene relighting, owing to the versatility of its representational power of various light transport phenomenon. We argue that scenes with an almost planar surface geometry, even with significant amounts of surface roughness, have a banded structure in the light transport matrix. In this paper, we propose a method that exploits this structure of the light transport matrix and provide significant savings in terms of both acquisition time and computation time, while retaining a high accuracy. We validate the proposed algorithm, by recovering the light transport of real objects that exhibit multiple scattering and with rendered scenes exhibiting inter-reflections.