A graph-spectral approach to shape-from-shading

In this paper, we explore how graph-spectral methods can be used to develop a new shape-from-shading algorithm. We characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction. Modeling the blocks of the weight matrix as distinct surface patches, we use a graph seriation method to find a surface integration path that maximizes the sum of curvature-dependent weights and that can be used for the purposes of height reconstruction. To smooth the reconstructed surface, we fit quadrics to the height data for each patch. The smoothed surface normal directions are updated ensuring compliance with Lambert's law. The processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained. We provide results on synthetic and real-world imagery

09111 Abstracts Collection -- Computational Geometry

From March 8 to March 13, 2009, the Dagstuhl Seminar 09111 ``Computational Geometry \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Towards a constrained Willmore conjecture

We give an overview of the constrained Willmore problem and address some conjectures arising from partial results and numerical experiments. Ramifications of these conjectures would lead to a deeper understanding of the Willmore functional over conformal immersions from compact surfaces.Comment: 17page

Geometric data understanding : deriving case specific features

There exists a tradition using precise geometric modeling, where uncertainties in data can be considered noise. Another tradition relies on statistical nature of vast quantity of data, where geometric regularity is intrinsic to data and statistical models usually grasp this level only indirectly. This work focuses on point cloud data of natural resources and the silhouette recognition from video input as two real world examples of problems having geometric content which is intangible at the raw data presentation. This content could be discovered and modeled to some degree by such machine learning (ML) approaches like deep learning, but either a direct coverage of geometry in samples or addition of special geometry invariant layer is necessary. Geometric content is central when there is a need for direct observations of spatial variables, or one needs to gain a mapping to a geometrically consistent data representation, where e.g. outliers or noise can be easily discerned. In this thesis we consider transformation of original input data to a geometric feature space in two example problems. The first example is curvature of surfaces, which has met renewed interest since the introduction of ubiquitous point cloud data and the maturation of the discrete differential geometry. Curvature spectra can characterize a spatial sample rather well, and provide useful features for ML purposes. The second example involves projective methods used to video stereo-signal analysis in swimming analytics. The aim is to find meaningful local geometric representations for feature generation, which also facilitate additional analysis based on geometric understanding of the model. The features are associated directly to some geometric quantity, and this makes it easier to express the geometric constraints in a natural way, as shown in the thesis. Also, the visualization and further feature generation is much easier. Third, the approach provides sound baseline methods to more traditional ML approaches, e.g. neural network methods. Fourth, most of the ML methods can utilize the geometric features presented in this work as additional features.Geometriassa käytetään perinteisesti tarkkoja malleja, jolloin datassa esiintyvät epätarkkuudet edustavat melua. Toisessa perinteessä nojataan suuren datamäärän tilastolliseen luonteeseen, jolloin geometrinen säännönmukaisuus on datan sisäsyntyinen ominaisuus, joka hahmotetaan tilastollisilla malleilla ainoastaan epäsuorasti. Tämä työ keskittyy kahteen esimerkkiin: luonnonvaroja kuvaaviin pistepilviin ja videohahmontunnistukseen. Nämä ovat todellisia ongelmia, joissa geometrinen sisältö on tavoittamattomissa raakadatan tasolla. Tämä sisältö voitaisiin jossain määrin löytää ja mallintaa koneoppimisen keinoin, esim. syväoppimisen avulla, mutta joko geometria pitää kattaa suoraan näytteistämällä tai tarvitaan neuronien lisäkerros geometrisia invariansseja varten. Geometrinen sisältö on keskeinen, kun tarvitaan suoraa avaruudellisten suureiden havainnointia, tai kun tarvitaan kuvaus geometrisesti yhtenäiseen dataesitykseen, jossa poikkeavat näytteet tai melu voidaan helposti erottaa. Tässä työssä tarkastellaan datan muuntamista geometriseen piirreavaruuteen kahden esimerkkiohjelman suhteen. Ensimmäinen esimerkki on pintakaarevuus, joka on uudelleen virinneen kiinnostuksen kohde kaikkialle saatavissa olevan datan ja diskreetin geometrian kypsymisen takia. Kaarevuusspektrit voivat luonnehtia avaruudellista kohdetta melko hyvin ja tarjota koneoppimisessa hyödyllisiä piirteitä. Toinen esimerkki koskee projektiivisia menetelmiä käytettäessä stereovideosignaalia uinnin analytiikkaan. Tavoite on löytää merkityksellisiä paikallisen geometrian esityksiä, jotka samalla mahdollistavat muun geometrian ymmärrykseen perustuvan analyysin. Piirteet liittyvät suoraan johonkin geometriseen suureeseen, ja tämä helpottaa luonnollisella tavalla geometristen rajoitteiden käsittelyä, kuten väitöstyössä osoitetaan. Myös visualisointi ja lisäpiirteiden luonti muuttuu helpommaksi. Kolmanneksi, lähestymistapa suo selkeän vertailumenetelmän perinteisemmille koneoppimisen lähestymistavoille, esim. hermoverkkomenetelmille. Neljänneksi, useimmat koneoppimismenetelmät voivat hyödyntää tässä työssä esitettyjä geometrisia piirteitä lisäämällä ne muiden piirteiden joukkoon

Methods for Real-time Visualization and Interaction with Landforms

This thesis presents methods to enrich data modeling and analysis in the geoscience domain with a particular focus on geomorphological applications. First, a short overview of the relevant characteristics of the used remote sensing data and basics of its processing and visualization are provided. Then, two new methods for the visualization of vector-based maps on digital elevation models (DEMs) are presented. The first method uses a texture-based approach that generates a texture from the input maps at runtime taking into account the current viewpoint. In contrast to that, the second method utilizes the stencil buffer to create a mask in image space that is then used to render the map on top of the DEM. A particular challenge in this context is posed by the view-dependent level-of-detail representation of the terrain geometry. After suitable visualization methods for vector-based maps have been investigated, two landform mapping tools for the interactive generation of such maps are presented. The user can carry out the mapping directly on the textured digital elevation model and thus benefit from the 3D visualization of the relief. Additionally, semi-automatic image segmentation techniques are applied in order to reduce the amount of user interaction required and thus make the mapping process more efficient and convenient. The challenge in the adaption of the methods lies in the transfer of the algorithms to the quadtree representation of the data and in the application of out-of-core and hierarchical methods to ensure interactive performance. Although high-resolution remote sensing data are often available today, their effective resolution at steep slopes is rather low due to the oblique acquisition angle. For this reason, remote sensing data are suitable to only a limited extent for visualization as well as landform mapping purposes. To provide an easy way to supply additional imagery, an algorithm for registering uncalibrated photos to a textured digital elevation model is presented. A particular challenge in registering the images is posed by large variations in the photos concerning resolution, lighting conditions, seasonal changes, etc. The registered photos can be used to increase the visual quality of the textured DEM, in particular at steep slopes. To this end, a method is presented that combines several georegistered photos to textures for the DEM. The difficulty in this compositing process is to create a consistent appearance and avoid visible seams between the photos. In addition to that, the photos also provide valuable means to improve landform mapping. To this end, an extension of the landform mapping methods is presented that allows the utilization of the registered photos during mapping. This way, a detailed and exact mapping becomes feasible even at steep slopes

Evaluation of the soil moisture prediction accuracy of a space radar using simulation techniques

Image simulation techniques were employed to generate synthetic aperture radar images of a 17.7 km x 19.3 km test site located east of Lawrence, Kansas. The simulations were performed for a space SAR at an orbital altitude of 600 km, with the following sensor parameters: frequency = 4.75 GHz, polarization = HH, and angle of incidence range = 7 deg to 22 deg from nadir. Three sets of images were produced corresponding to three different spatial resolutions; 20 m x 20 m with 12 looks, 100 m x 100 m with 23 looks, and 1 km x 1 km with 1000 looks. Each set consisted of images for four different soil moisture distributions across the test site. Results indicate that, for the agricultural portion of the test site, the soil moisture in about 90% of the pixels can be predicted with an accuracy of = + or - 20% of field capacity. Among the three spatial resolutions, the 1 km x 1 km resolution gave the best results for most cases, however, for very dry soil conditions, the 100 m x 100 m resolution was slightly superior