Helena Cristina da Gama Leitão

Measuring the Information Content of Fracture Lines

Reassembling unknown broken objects from a large collection of fragments is a common problem in archaeology and other fields. Computer tools have recently been developed, by the authors and by others, which try to help by identifying pairs of fragments with matching outline shapes. Those tools have been successfully tested on small collections of fragments; here we address the question of whether they can be expected to work also for practical instances of the problem (103 to 105 fragments). To that end, we describe here a method to measure the average amount of information contained in the shape of a fracture line of given length. This parameter tells us how many false matches we can expect to find for it among a given set of fragments. In particular, the numbers we obtained for ceramic fragments indicate that fragment outline comparison should give useful results even for large instances of the problem.

A robust multi-scale integration method to obtain the depth from gradient maps

Highlights? A critical survey and classification of gradient integration methods. ? A new multi-scale integrator to recover the depth map from a gradient map. ? Use of an input weight map to identify missing data. ? A weight-sensitive Poisson formulation of the integration problem. ? Empirical comparison with state-of-art methods. We describe a robust method for the recovery of the depth map (or height map) from a gradient map (or normal map) of a scene, such as would be obtained by photometric stereo or interferometry. Our method allows for uncertain or missing samples, which are often present in experimentally measured gradient maps, and also for sharp discontinuities in the scenes depth, e.g. along object silhouette edges. By using a multi-scale approach, our integration algorithm achieves linear time and memory costs. A key feature of our method is the allowance for a given weight map that flags unreliable or missing gradient samples. We also describe several integration methods from the literature that are commonly used for this task. Based on theoretical analysis and tests with various synthetic and measured gradient maps, we argue that our algorithm is as accurate as the best existing methods, handling incomplete data and discontinuities, and is more efficient in time and memory usage, especially for large gradient maps.

A Multiscale Method for the Reassembly of Fragmented Objects.

We describe here an efficient algorithm for re-assembling on e r more unknown objects that have been broken or torn into a large numbe r N of irregular fragments—a problem that often arises in achaeolog y, art restoration, forensics, and other disciplines. The algorithm comp ares the curvatureencoded fragment outlines, using a modified dynamic program ming sequencematching algorithm, at progressively increasing scales of resolution. The total cost gets reduced from (N2L2) (whereL is the mean number of samples per fragment) to about O(N2L); which, in principle, allows the method to be used for problems of practical size ( N = 103 to 105 fragments,L = 103 to 104 samples). The performance of the algorithm is illustrated w ith an artificial but realistic example.

Robust 3D face capture using example-based photometric stereo

We show that using example-based photometric stereo, it is possible to achieve realistic reconstructions of the human face. The method can handle non-Lambertian reflectance and attached shadows after a simple calibration step. We use spherical harmonics to model and de-noise the illumination functions from images of a reference object with known shape, and a fast grid technique to invert those functions and recover the surface normal for each point of the target object. The depth coordinate is obtained by weighted multi-scale integration of these normals, using an integration weight mask obtained automatically from the images themselves. We have applied these techniques to improve the PhotoFace system of Hansen et al. (2010).

Matching Photometric Observation Vectors with Shadows and Variable Albedo

We describe a procedure to solve the basic problem of variable lighting photometric stereo - namely, recovering the normal directions and intrinsic albedos at all visible points of an opaque object, by analyzing three or more photos of the same taken with different illuminations. We follow the gauge-based approach, where the lighting conditions and light scattering properties of the surface are given indirectly by photographing a gauge object with known shape and albedo, under the same lighting conditions. Unlike previous solutions, our method yields reliable results even when some of the images contain cast shadows, penumbras, highlights, or inter-object lighting, at a cost. The cost of inner loop grows quadratically, (rather than exponentially) with the number m of input images. Usable approximations can be obtained in m log m time.

Multi-Scale Depth from Slope with Weights

We describe a robust method to recover the depth coordinate from a normal or slope map of a scene, obtained e.g. through photometric stereo or interferometry. The key feature of our method is the fast solution of the Poisson-like integration equations by a multi-scale iterative technique. The method accepts a weight map that can be used to exclude regions where the slope information is missing or untrusted, and to allow the integration of height maps with linear discontinuities (such as along object silhouettes) which are not recorded in the slope maps. Except for pathological cases, the memory and time costs of our method are typically proportional to the number of pixels N. Tests show that our method is as accurate as the best weighted slope integrators, but substantially more efficient in time and space.

Multi-scale integration of slope data on an irregular mesh

We describe a fast and robust gradient integration method that computes scene depths (or heights) from surface gradient (or surface normal) data such as would be obtained by photometric stereo or interferometry. Our method allows for uncertain or missing samples, which are often present in experimentally measured gradient maps; for sharp discontinuities in the scenes depth, e.g. along object silhouette edges; and for irregularly spaced sampling points. To accommodate these features of the problem, we use an original and flexible representation of slope data, the weight-delta mesh. Like other state of the art solutions, our algorithm reduces the problem to a system of linear equations that is solved by Gauss-Seidel iteration with multi-scale acceleration. Its novel key step is a mesh decimation procedure that preserves the connectivity of the initial mesh. Tests with various synthetic and measured gradient data show that our algorithm is as accurate and efficient as the best available integrators for uniformly sampled data. Moreover our algorithm remains accurate and efficient even for large sets of weakly-connected instances of the problem, which cannot be efficiently handled by any existing algorithm.

A Bucket Grid Structure to Speed Up Table Lookup in Gauge-Based Photometric Stereo

In this paper, we show how to speed up the table lookup step in gauge-based multi-image photometric stereo. In that step, one must find a pixel of a gauge object, of known shape and color, whose appearance under m different illumination fields is similar to that of a given scene pixel. This search reduces to finding the closest match to a given m- vector in a table with a thousand or more m-vectors. Our speed-up method exploits the fact that the table is in fact a fairly flat two-dimensional manifold in m-dimensional space, so that the search can be efficiently solved with a two-dimensional bucket grid structure.

A novel approach to photometric motion

Abstract Photometric motion, as introduced by Pentland, employs both reflectance map and optical flow information for the estimation of shape from image sequences of dynamic scenes. It is thus a coupled geometric/photometric process, similarly as the disparity-based photometric stereo, which combines matching and image irradiance equations for surface reconstruction from photometric stereo input. Exploiting the parallel between those two processes, we have arrived at a novel formulation for the photometric-motion shape estimation problem, whose distinctive feature is that of being based on the irradiance change, due to the motion, at a given point in the image plane, and not, as in Pentlands proposal, at a fixed location on the moving surface. We are thus able to obtain an easily implementable procedure which yields good-quality shape estimates for rotating surfaces, and which can also be extended to single-input shape reconstruction.

A novel photometric motion approach

Photometric motion is a computer vision process for the estimation of shape from image sequences of dynamic scenes. It was introduced by Pentland, based on his observation that the photometric effects of motion: the intensity change of a moving point, could dominate the purely geometric ones, due to projective distortion. We present a novel formulation for the same shape estimation problem, whose distinctive feature is that of being based on the irradiance change, due to the motion, at a given point in the image plane, and not, as in the original proposal, at a fixed location on the moving surface. Thus we obtain an easily implementable procedure which yields good-quality estimates, and which can be extended to single-input shape reconstruction.