The Ball to Ball Theorem

The ball to ball theorem is presented, which states that a map from the 4-ball to itself, restricting to a homeomorphism on the 3-sphere, whose inverse sets are null and have nowhere dense image, is approximable by homeomorphisms relative to the boundary. The approximating homeomorphisms are produced abstractly, as in the previous chapter, with no need to investigate the decomposition elements further. In the proof of the disc embedding theorem, a decomposition of the 4-ball will be constructed, called the gaps+ decomposition. The ball to ball theorem will be used to prove that this decomposition shrinks; this is called the β-shrink.

STATE OF THE ART IN DENSE IMAGE MATCHING COST COMPUTATION FOR HIGH-RESOLUTION SATELLITE STEREO

Large-scale Digital Surface Model (DSM) generated with high-resolution satellite images (HRSI) are comparable, cheaper, and more accessible when comparing to Light Detection and Ranging (LiDAR) data and aerial remotely sensed images. Several photogrammetric commercial/open-source software packages are being developed for satellite image-based 3D reconstruction, in which, most of them adopt a modified version of Semi-Global Matching (SGM) algorithm for dense image matching. With the continuous development of matching cost computation methods, the existing methods can be divided into classical (low-level) and learning-based algorithms (non-end-to-end learning and end-to-end learning methods). On Middlebury and KITTI datasets, learning-based algorithms has shown their superiority compared to SGM derived methods. In this context, we assume that matching cost is the key factor of DIM. This paper reviews and evaluates Census Transform, and MC-CNN on a WorldView-3 typical city scene satellite stereo images on the premise that the overall SGM framework remains unchanged, providing a preliminary comparison for academic and industrial. We first compute the cost valume of these two methods, obtains the final DSM after semi-global optimization, and compares their gemetric accuracy with the corresponding LiDAR derived ground truth. We presented our comparison and findings in the experimental section.

Building Change Detection of Airborne Laser Scanning and Dense Image Matching Point Clouds using Height and Class Information

Detecting changes is an important task to update databases and find irregularities in spatial data. Every couple of years, national mapping agencies (NMAs) acquire nation-wide point cloud data from Airborne Laser Scanning (ALS) as well as from Dense Image Matching (DIM) using aerial images. Besides deriving several other products such as Digital Elevation Models (DEMs) from them, those point clouds also offer the chance to detect changes between two points in time on a large scale. Buildings are an important object class in the context of change detection to update cadastre data. As detecting changes manually is very time consuming, the aim of this study is to provide reliable change detections for different building sizes in order to support NMAs in their task to update their databases. As datasets of different times may have varying point densities due to technological advancements or different sensors, we propose a raster-based approach, which is independent of the point density altogether. Within a raster cell, our approach considers the height distribution of all points for two points in time by exploiting the Jensen-Shannon distance to measure their similarity. Our proposed method outperforms simple threshold methods on detecting building changes with respect to the same or different point cloud types. In combination with our proposed class change detection approach, we achieve a change detection performance measured by the mean F1-Score of about 71% between two ALS and about 60% between ALS and DIM point clouds acquired at different times.

Concluding Remarks

After Hedda Gabler, Ibsen wrote four more plays: The Master Builder, Little Eyolf, John Gabriel Borkman, and When We Dead Awaken. With its darker tone and dense, image-laden prose, his late work has been described as melancholy. In each of these late plays, the topic of the past, of individual and collective history, features centrally. At least two of the late plays—three, if we include ...

Stereo Dense Image Matching by Adaptive Fusion of Multiple-Window Matching Results

Traditional stereo dense image matching (DIM) methods normally predefine a fixed window to compute matching cost, while their performances are limited by the matching window sizes. A large matching window usually achieves robust matching results in weak-textured regions, while it may cause over-smoothness problems in disparity jumps and fine structures. A small window can recover sharp boundaries and fine structures, while it contains high matching uncertainties in weak-textured regions. To address the issue above, we respectively compute matching results with different matching window sizes and then proposes an adaptive fusion method of these matching results so that a better matching result can be generated. The core algorithm designs a Convolutional Neural Network (CNN) to predict the probabilities of large and small windows for each pixel and then refines these probabilities by imposing a global energy function. A compromised solution of the global energy function is utilized by breaking the optimization into sub-optimizations of each pixel in one-dimensional (1D) paths. Finally, the matching results of large and small windows are fused by taking the refined probabilities as weights for more accurate matching. We test our method on aerial image datasets, satellite image datasets, and Middlebury benchmark with different matching cost metrics. Experiments show that our proposed adaptive fusion of multiple-window matching results method has a good transferability across different datasets and outperforms the small windows, the median windows, the large windows, and some state-of-the-art matching window selection methods.

INVESTIGATING STANDARDIZED 3D INPUT DATA FOR SOLAR PHOTOVOLTAIC POTENTIALS IN THE NETHERLANDS

This paper presents our contribution to the development of a standardized 3D input data model for solar photovoltaic potential estimation. Presently, different input data and processing steps influence the calculation for estimating the potential of solar energy in the Netherlands. The variety in characteristics of input data and issues with temporal accuracy extracted from the national registers and databases makes it challenging to obtain a consistent and reliable result. To address this issue, we created a point cloud dataset that integrated from LiDAR point cloud and dense image matching which is complete, recent and positionally accurate. Furthermore, we made a 3D building model from the integrated point cloud and identified the effect of finer resolution in the photovoltaic potential analysis.