Orthonormal Bases in the Orbit of Square-Integrable Representations of Nilpotent Lie Groups

Let $G$ be a connected, simply connected nilpotent group and $\pi$ be a square-integrable irreducible unitary representation modulo its center $Z(G)$ on $L^2(\mathbf{R}^d)$. We prove that under reasonably weak conditions on $G$ and $\pi$ there exist a discrete subset $\Gamma$ of $G/Z(G)$ and some (relatively) compact set $F \subseteq \mathbf{R}^d$ such that $$\bigl \{ |F|^{-1/2} \hspace{2pt} \pi(\gamma) 1_F \mid \gamma \in \Gamma \bigr\}$$ forms an orthonormal basis of $L^2(\mathbf{R}^d)$. This construction generalizes the well-known example of Gabor orthonormal bases in time-frequency analysis. The main theorem covers graded Lie groups with one-dimensional center. In the presence of a rational structure, the set $\Gamma$ can be chosen to be a uniform subgroup of $G/Z$

Roof plane segmentation by combining multiple images and point clouds

A new method for roof plane detection using multiple aerial images and a point cloud is presented. It takes advantage of the fact that segmentation results for different views look different even if the same parameters are used for the original segmentation algorithm. The point cloud can be generated by image matching or by airborne laserscanning. Plane detection starts by a segmentation that is applied to each of the images. The point cloud is used to determine which image segments correspond to planes. The best plane according to a criterion is selected and matched with segments in the other images. Matching of segments requires a DSM generated from the point cloud, and it takes into account the occlusions in each image. This procedure is repeated until no more planes can be found. After that, planar segments are extracted based on region growing in the point cloud in areas of severe under-segmentation, and the multiple-image segmentation procedure is repeated. Finally, neighbouring regions found to be co-planar are merged. First results are presented for test site with up to nine-fold overlap. Our tests show that the method can deliver a good separation of roof planes under difficult circumstances, though the level of detail that can be achieved is limited by the resolution of the point cloud

Classification of settlement areas in remote sensing imagery using conditional random fields

Land cover classification plays a key role for various geo-based applications. Numerous approaches for the classification of settlements in remote sensing imagery have been developed. Most of them assume the features of neighbouring image sites to be conditionally independent. Using spatial context information may enhance classification accuracy, because dependencies of neighbouring areas are taken into account. Conditional Random Fields (CRF) have become popular in the field of pattern recognition for incorporating contextual information because of their ability to model dependencies not only between the class labels of neighbouring image sites, but also between the labels and the image features. In this work we investigate the potential of CRF for the classification of settlements in high resolution satellite imagery. To highlight the power of CRF, tests were carried out using only a minimum set of features and a simple model of context. Experiments were performed on an Ikonos scene of a rural area in Germany. In our experiments, completeness and correctness values of 90% and better could be achieved, the CRF approach was clearly outperforming a standard Maximum-Likelihood-classification based on the same set of features

Using building and bridge information for adapting roads to ALS data by means of network snakes

In the German Authoritative Topographic Cartographic Information System (ATKIS), the 2D positions and the heights of objects such as roads are stored separately in the digital landscape model (DLM) and digital terrain model (DTM), which is often acquired by airborne laser scanning (ALS). However, an increasing number of applications require a combined processing and visualization of these two data sets. Due to different kinds of acquisition, processing, and modelling discrepancies exist between the DTM and DLM and thus a simple integration may lead to semantically incorrect 3D objects. For example, roads may be situated on strongly tilted DTM parts and rivers sometimes flow uphill. In this paper we propose an algorithm for the adaptation of 2D road centrelines to ALS data by means of network snakes. Generally, the image energy for the snakes is defined based on ALS intensity and height information and derived products. Additionally, buildings and bridges as strong features in height data are exploited in order to support the road adaptation process. Extracted buildings as priors modified by a distance transform are used to create a force of repulsion for the road vectors integrated in the image energy. In contrast, bridges give strong evidence for the correct road position in the height data. Therefore, the image energy is adapted for the bridge points. For that purpose bridge detection in the DTM is performed starting from an approximate position using template matching. Examples are given which apply the concept of network-snakes with new image energy for the adaptation of road networks to ALS data taking advantage of the prior known topology

Deep Descriptor Learning with Auxiliary Classification Loss for Retrieving Images of Silk Fabrics in the Context of Preserving European Silk Heritage

With the growing number of digitally available collections consisting of images depicting relevant objects from the past in relation with descriptive annotations, the need for suitable information retrieval techniques is becoming increasingly important to support historians in their work. In this context, we address the problem of image retrieval for searching records in a database of silk fabrics. The descriptors, used as an index to the database, are learned by a convolutional neural network, exploiting the available annotations to automatically generate training data. Descriptor learning is combined with auxiliary classification loss with the aim of supporting the clustering in the descriptor space with respect to the properties of the depicted silk objects, such as the place or time of origin. We evaluate our approach on a dataset of fabric images in a kNN-classification, showing promising results with respect to the ability of the descriptors to represent semantic properties of silk fabrics; integrating the auxiliary loss improves the overall accuracy by 2.7% and the average F1 score by 5.6%. It can be observed that the largest improvements can be obtained for variables with imbalanced class distributions. An evaluation on the WikiArt dataset demonstrates the transferability of our approach to other digital collection

Automatic road network extraction in suburban areas from high resolution aerial images

In this paper a road network extraction algorithm for suburban areas is presented. The algorithm uses colour infrared (CIR) images and digital surface models (DSM). The CIR data allow a good separation between vegetation and roads. The image is first segmented in two steps: an initial segmentation using the normalized cuts algorithm and a subsequent grouping of the segments. Road parts are extracted from the segments and then first connected locally to form subgraphs, because roads are often not extracted as a whole due to disturbances in their appearance. Subgraphs can contain several branches, which are resolved by a subsequent optimisation. The optimisation uses criteria describing the relations between the road parts as well as context objects such as trees, vehicles and buildings. The resulting road strings, represented by their centre lines, are then connected to a road network by searching for junctions at the ends of the roads. Small isolated roads are eliminated because they are likely to be false extractions. Results are presented for three image subsets coming from two different data sets, and a quantitative analysis of the completeness and correctness is shown from nine image subsets from the two data sets. The results show that the approach is suitable for the extraction of roads in suburban areas from aerial images

The ins and outs of peroxisomes: Co-ordination of membrane transport and peroxisomal metabolism

AbstractPeroxisomes perform a range of metabolic functions which require the movement of substrates, co-substrates, cofactors and metabolites across the peroxisomal membrane. In this review, we discuss the evidence for and against specific transport systems involved in peroxisomal metabolism and how these operate to co-ordinate biochemical reactions within the peroxisome with those in other compartments of the cell