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**1 - 9**of**9**### PACV 2007, Rio de Janeiro: Brazil (2007)" Integration of a Normal Field without Boundary Condition

, 2008

"... We show how to use two existing methods of integration of a normal field in the absence of boundary condition, which makes them more realistic. Moreover, we show how perspective can be taken into account, in order to render the 3D-reconstruction more accurate. Finally, the joint use of both these me ..."

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We show how to use two existing methods of integration of a normal field in the absence of boundary condition, which makes them more realistic. Moreover, we show how perspective can be taken into account, in order to render the 3D-reconstruction more accurate. Finally, the joint use of both these methods of integration allows us to obtain very satisfactory results, from the point of view of CPU time as well as that of the accuracy of the reconstructions. As an application, we use this new combined method of integration of a normal field in the framework of photometric stereo, a technique which aims at computing a normal field to the surface of a scene from several images of this scene illuminated from various directions. The performances of the proposed method are illustrated on synthetic, as well as on real images. 1.

### Surface Shape and Reflectance Analysis Using Polarisation

"... When unpolarised light is reflected from a smooth dielectric surface, it becomes partially polarised. This is due to the orientation of dipoles induced in the reflecting medium and applies to both specular and diffuse reflection. This thesis aims to exploit the polarising properties of surface refle ..."

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When unpolarised light is reflected from a smooth dielectric surface, it becomes partially polarised. This is due to the orientation of dipoles induced in the reflecting medium and applies to both specular and diffuse reflection. This thesis aims to exploit the polarising properties of surface reflection for computer vision applications. Most importantly, the thesis proposes novel shape and reflectance function estimation techniques. The methods presented rely on polarisation data acquired using a standard digital camera and a linear polariser. Fresnel theory lies at the heart of the thesis and is used to process the polarisation data in order to estimate the surface normals of target objects. Chapter 2 surveys the related literature in the fields of polarisation vision, shape-fromshading, stereo techniques, and reflectance function analysis. Chapter 3 commences by presenting the underlying physics of polarisation by reflection, starting with the Fresnel equations. The outcome of this theory is a means to ambiguously estimate surface normals from polarisation data, given a rough estimate of the material refractive index. The first novel technique is then presented, which is a simple single-view approach to shape reconstruction. In this case, efficiency is given priority over accuracy. Chapter 3 ends

### Shape from Diffuse Polarisation

"... When unpolarised light is reflected from a smooth dielectric surface, it is spontaneously partially polarised. This process applies to both specular and diffuse reflection, although the effect is greatest for specular reflection. This paper is concerned with exploiting this phenomenon by processing ..."

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When unpolarised light is reflected from a smooth dielectric surface, it is spontaneously partially polarised. This process applies to both specular and diffuse reflection, although the effect is greatest for specular reflection. This paper is concerned with exploiting this phenomenon by processing images of smooth dielectric objects to recover surface normals and hence height. The paper presents the underlying physics of polarisation by reflection, starting with the Fresnel equations. It is explained how these equations can be used to obtain the shape of objects and some experimental results are presented to illustrate the usefulness of the theory. 1

### IEEE TRANSACTIONS ON IMAGE PROCESSING 1 Recovery of Surface Orientation from Diffuse

"... Abstract — When unpolarized light is reflected from a smooth dielectric surface, it becomes partially polarized. This is due to the orientation of dipoles induced in the reflecting medium and applies to both specular and diffuse reflection. This paper is concerned with exploiting polarization by sur ..."

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Abstract — When unpolarized light is reflected from a smooth dielectric surface, it becomes partially polarized. This is due to the orientation of dipoles induced in the reflecting medium and applies to both specular and diffuse reflection. This paper is concerned with exploiting polarization by surface reflection, using images of smooth dielectric objects, to recover surface normals and hence height. The paper presents the underlying physics of polarization by reflection, starting with the Fresnel equations. These equations are used to interpret images taken with a linear polarizer and digital camera, revealing the shape of the objects. Experimental results are presented that illustrate that the technique is accurate near object limbs, as the theory predicts, with less precise, but still useful, results elsewhere. A detailed analysis of the accuracy of the technique for a variety of materials is presented. A method for estimating refractive indices using a laser and linear polarizer is also given. Index Terms — Surface recovery, diffuse polarization, refractive index, sensitivity study

### Surface Acquisition From Single Gray-Scale Images

- IEEE International Conference on Image Processing
, 2003

"... In this paper we show how a system for performing automatic surface model acquisition from single object views can be designed. The surface acquisition process is a two step one. Firstly, the surface normals are computed using a shape-from-shading algorithm. Secondly, the field of surface normals is ..."

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In this paper we show how a system for performing automatic surface model acquisition from single object views can be designed. The surface acquisition process is a two step one. Firstly, the surface normals are computed using a shape-from-shading algorithm. Secondly, the field of surface normals is integrated into a 3D surface. For the surface integration step, we have performed experiments with two alternatives. The first of these is a geometric surface integration algorithm. The second alternative comprises a graph-spectral surface integration algorithm. We present results on images of classical statues and provide a preliminary quantitative study.

### unknown title

"... We show how to use two existing methods of integration of a normal field in the absence of boundary condition, which makes them more realistic. Moreover, we show how perspective can be taken into account, in order to render the 3D-reconstruction more accurate. Finally, the joint use of both these me ..."

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We show how to use two existing methods of integration of a normal field in the absence of boundary condition, which makes them more realistic. Moreover, we show how perspective can be taken into account, in order to render the 3D-reconstruction more accurate. Finally, the joint use of both these methods of integration allows us to obtain very satisfactory results, from the point of view of CPU time as well as that of the accuracy of the reconstructions. As an application, we use this new combined method of integration of a normal field in the framework of photometric stereo, a technique which aims at computing a normal field to the surface of a scene from several images of this scene illuminated from various directions. The performances of the proposed method are illustrated on synthetic, as well as on real images. 2. Relation between Normal and Gradient Due to lack of space, no state-of-the-art on the integration of a normal field is given here (see e.g. [8, 10, 7, 1]). Suppose that, in each point Q = (x, y) in the image of a surface S, we know the unit outgoing normal − → n (x, y) to S: n (x, y) = ⎣ nX(x, y) nY (x, y) nZ(x, y) ⎦. (1) The vectorial function − → n is called a “normal field”. The problem of integrating a normal field consists in searching for a shape S i.e., for three functions X, Y and Z (Z is called the “height”), such that the object point P conjugated with Q has X(x, y), Y (x, y) and Z(x, y) as coordinates. It can be solved only if the model of projection is known. 2.1. Orthographic Projection 1.

### Chapter 1 On Depth Recovery from Gradient Vector Fields

"... Depth recovery from gradient vector fields is required when reconstructing a surface (in three-dimensional space) from its gradients. Such a reconstruction task results, for example, for techniques in computer vision aiming at calculat-ing surface normals (such as shape from shading, photometric ste ..."

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Depth recovery from gradient vector fields is required when reconstructing a surface (in three-dimensional space) from its gradients. Such a reconstruction task results, for example, for techniques in computer vision aiming at calculat-ing surface normals (such as shape from shading, photometric stereo, shape from texture, shape from contours and so on). Surprisingly, discrete integration has not been studied very intensively so far. This chapter presents three classes of methods for solving problems of depth recovery from gradient vector fields: a two-scan method, a Fourier-transform based method, and a wavelet-transform based method. These methods extend previously known techniques, and related proofs are given in a short but concise form. The two-scan method consists of two different scans through a given gradient vector field. The final surface height values can be determined by averaging these two scans. Fourier-transform based methods are noniterative so that boundary conditions are not needed, and their robustness to noisy gradient estimates can be improved by choosing associated weighting parameters. The wavelet-transform