A First Order Predicate Logic Formulation of the 3D Reconstruction Problem and its Solution Space

This paper defines the 3D reconstruction problem as the process of reconstructing a 3D scene from numerous 2D visual images of that scene. It is well known that this problem is ill-posed, and numerous constraints and assumptions are used in 3D reconstruction algorithms in order to reduce the solution space. Unfortunately, most constraints only work in a certain range of situations and often constraints are built into the most fundamental methods (e.g. Area Based Matching assumes that all the pixels in the window belong to the same object). This paper presents a novel formulation of the 3D reconstruction problem, using a voxel framework and first order logic equations, which does not contain any additional constraints or assumptions. Solving this formulation for a set of input images gives all the possible solutions for that set, rather than picking a solution that is deemed most likely. Using this formulation, this paper studies the problem of uniqueness in 3D reconstruction and how the solution space changes for different configurations of input images. It is found that it is not possible to guarantee a unique solution, no matter how many images are taken of the scene, their orientation or even how much color variation is in the scene itself. Results of using the formulation to reconstruct a few small voxel spaces are also presented. They show that the number of solutions is extremely large for even very small voxel spaces (5 x 5 voxel space gives 10 to 10(7) solutions). This shows the need for constraints to reduce the solution space to a reasonable size. Finally, it is noted that because of the discrete nature of the formulation, the solution space size can be easily calculated, making the formulation a useful tool to numerically evaluate the usefulness of any constraints that are added.

A combined spectrophotometric and morphometric study of the lunar mare dome fields near Cauchy, Arago, Hortensius, and Milichius

In this Study we examine the spectral and morphometric properties of the four important lunar mare dome fields near Cauchy, Arago, Hortensius. and Milichius. We utilize Clementine UV vis mulfispectral data to examine the soil composition of the mare domes while employing telescopic CCD imagery to compute digital elevation maps in order to determine their morphometric properties, especially flank slope, height, and edifice Volume. After reviewing previous attempts to determine topographic data for lunar domes, we propose an image-based 3D reconstruction approach which is based on a combination of photoclinometry and shape from shading. Accordingly, we devise a classification scheme for lunar Marc domes which is based on a principal component analysis of the determined spectral and morphometric features. For the effusive mare domes of the examined fields we establish four Classes, two of which are further divided into two subclasses, respectively, where each class represents distinct combinations of spectral and morphometric dome properties. As a general trend, shallow and steep domes formed out of low-TiO2 basalts are observed in the Hortensius and Milichius dome fields, while the domes near Cauchy and Arago that consist of high-TiO2 basalts are all very shallow. The intrusive domes of our data set cover a wide continuous range of spectral and morphometric quantities, generally characterized by larger diameters and shallower flank slopes than effusive domes. A comparison to effusive and intrusive mare domes in other lunar regions, highland domes, and lunar cones has shown that the examined four mare dome fields display Such a richness in spectral properties and 3D dome shape that the established representation remains valid in a more global context. Furthermore, we estimate the physical parameters of dome formation for the examined domes based on a rheologic model. Each class of effusive domes defined in terms of spectral and morphometric properties is characterized by its specific range of values for lava viscosity, effusion rate, and duration of the effusion process. For our data set we report lava viscosities between about 10(2) and 10(8) Pas, effusion rates between 25 and 600 m(3) s(-1), and durations of the effusion process between three weeks and 18 years. Lava viscosity decreases with increasing R-415/R-750 spectral ratio and thus TiO2 content; however, the correlation is not strong, implying an important influence of further parameters like effusion temperature on lava viscosity.

Rice morphogenesis and plant architecture: Measurement, specification and the reconstruction of structural development by 3D architectural modelling

Background and Aims The morphogenesis and architecture of a rice plant, Oryza sativa, are critical factors in the yield equation, but they are not well studied because of the lack of appropriate tools for 3D measurement. The architecture of rice plants is characterized by a large number of tillers and leaves. The aims of this study were to specify rice plant architecture and to find appropriate functions to represent the 3D growth across all growth stages. Methods A japonica type rice, 'Namaga', was grown in pots under outdoor conditions. A 3D digitizer was used to measure the rice plant structure at intervals from the young seedling stage to maturity. The L-system formalism was applied to create '3D virtual rice' plants, incorporating models of phenological development and leaf emergence period as a function of temperature and photoperiod, which were used to determine the timing of tiller emergence. Key Results The relationships between the nodal positions and leaf lengths, leaf angles and tiller angles were analysed and used to determine growth functions for the models. The '3D virtual rice' reproduces the structural development of isolated plants and provides a good estimation of the fillering process, and of the accumulation of leaves. Conclusions The results indicated that the '3D virtual rice' has a possibility to demonstrate the differences in the structure and development between cultivars and under different environmental conditions. Future work, necessary to reflect both cultivar and environmental effects on the model performance, and to link with physiological models, is proposed in the discussion.