Normal

Abstract: In computer vision, the goal of which is to identify objects and their positions by examining images, one of the key steps is computing the surface normal of the visible surface at each point (“pixel”) in the image. Many sources of information are studied, such as outlines ofsuifaces, intensity gradients, object motion, and color. This article presents a method for analyzing a standard color image to determine the amount of interface (“specular”) and body (“diffuse”) reflection at each pixel. The interface reflection represents the highlights from the original image, and the body reflection represents the original image with highlights removed. Such intrinsic images are of interest because the geometric properties of each type of reflection are simpler than the geometric properties of intensity in a black-and-white image. The method is based upon a physical model of reflection which states that two distinct types of reflection–interface and body reflection–occur, and that each type can be decomposed into a relative spectral distribution and a geometric scale factor. This model is far more general than typical models used in computer vision and computer graphics, and includes most such models as special cases. In addition, the model does not assume a point light source or uniform illumination distribution over the scene. The properties of tristimulus integration are used to derive a new model of pixel-value color distribution, and this model is exploited in an algorithm to derive the desired quantities. Suggestions are provided for extending the model to deal with diffuse illumination and for analyzing the two components of reflection.

Abstract: Surveying techniques such as terrestrial laser scanner have recently been used to measure surface changes via 3D point cloud (PC) comparison. Two types of approaches have been pursued: 3D tracking of homologous parts of the surface to compute a displacement field, and distance calculation between two point clouds when homologous parts cannot be defined. This study deals with the second approach, typical of natural surfaces altered by erosion, sedimentation or vegetation between surveys. Current comparison methods are based on a closest point distance or require at least one of the PC to be meshed with severe limitations when surfaces present roughness elements at all scales. To solve these issues, we introduce a new algorithm performing a direct comparison of point clouds in 3D. The method has two steps: (1) surface normal estimation and orientation in 3D at a scale consistent with the local surface roughness; (2) measurement of the mean surface change along the normal direction with explicit calculation of a local confidence interval. Comparison with existing methods demonstrates the higher accuracy of our approach, as well as an easier workflow due to the absence of surface meshing or Digital Elevation Model (DEM) generation. Application of the method in a rapidly eroding, meandering bedrock river (Rangitikei River canyon) illustrates its ability to handle 3D differences in complex situations (flat and vertical surfaces on the same scene), to reduce uncertainty related to point cloud roughness by local averaging and to generate 3D maps of uncertainty levels. We also demonstrate that for high precision survey scanners, the total error budget on change detection is dominated by the point clouds registration error and the surface roughness. Combined with mm-range local georeferencing of the point clouds, levels of detection down to 6 mm (defined at 95% confidence) can be routinely attained in situ over ranges of 50 m. We provide evidence for the self-affine behaviour of different surfaces. We show how this impacts the calculation of normal vectors and demonstrate the scaling behaviour of the level of change detection. The algorithm has been implemented in a freely available open source software package. It operates in complex 3D cases and can also be used as a simpler and more robust alternative to DEM differencing for the 2D cases.

Abstract: A statistical model for the reflection of scalar plane waves from a rough surface leads to a plane wave in the direction of specular reflection and to a contribution with a finite angular spread about that direction, depending on the tangential correlation of the surface asperities. Based upon on this result, a new semiclassical model, which satisfies the requirement of flux conservation, is proposed for the boundary condition for the distribution function of the size effect in the electrical conductivity. In the absence of correlation, the resultant expression replaces the constant specularity parameter p of Fuchs by the function exp[−(4π(h/λ) cosθ0)2] with θ0 the angle of the electron wave vector with the surface normal. Correlation produces an additional forward component within the diffuse contribution. Numerical results of the size effect for zero correlation are compared to the Fuchs model as well as a more recent model, and show a different thickness dependence for thin samples. The effect of correlation is to add to the conductivity, as a result of the diffuse contribution whose velocity has a finite expectation value in the direction of the current.

Abstract: In this paper, we propose Geometric Neural Network (GeoNet) to jointly predict depth and surface normal maps from a single image. Building on top of two-stream CNNs, our GeoNet incorporates geometric relation between depth and surface normal via the new depth-to-normal and normal-to-depth networks. Depth-to-normal network exploits the least square solution of surface normal from depth and improves its quality with a residual module. Normal-to-depth network, contrarily, refines the depth map based on the constraints from the surface normal through a kernel regression module, which has no parameter to learn. These two networks enforce the underlying model to efficiently predict depth and surface normal for high consistency and corresponding accuracy. Our experiments on NYU v2 dataset verify that our GeoNet is able to predict geometrically consistent depth and normal maps. It achieves top performance on surface normal estimation and is on par with state-of-the-art depth estimation methods.