PDE Face: A Novel 3D Face Model

YesWe introduce a novel approach to face models, which exploits the use of Partial Differential Equations (PDE) to generate the 3D face. This addresses some common problems of existing face models. The PDE face benefits from seamless merging of surface patches by using only a relatively small number of parameters based on boundary curves. The PDE face also provides users with a great degree of freedom to individualise the 3D face by adjusting a set of facial boundary curves. Furthermore, we introduce a uv-mesh texture mapping method. By associating the texels of the texture map with the vertices of the uv mesh in the PDE face, the new texture mapping method eliminates the 3D-to-2D association routine in texture mapping. Any specific PDE face can be textured without the need for the facial expression in the texture map to match exactly that of the 3D face model

Mathematically gifted elementary students\u27 revisiting of Euler\u27s polyhedron theorem

This paper explores how the constructions of mathematically gifted fifth and sixth grade students using Euler’s polyhedron theorem compare to those of mathematicians as discussed by Lakatos (1976). Eleven mathematically gifted elementary school students were asked to justify the theorem, find counterexamples, and resolve conflicts between the theorem and counterexamples. The students provided two types of justification of the theorem. The solid figures suggested as counterexamples were categorized as 1) solids with curved surfaces, 2) solids made of multiple polyhedra sharing points, lines, or faces, 3) polyhedra with holes, and 4) polyhedra containing polyhedra. In addition to using the monster-barring method, the students suggested two new types of conjectures to resolve the conflicts between counterexamples and the theorem, the exception-baring method and the monster-adjustment method. The students’ constructions resembled those presented by mathematicians as discussed by Lakatos

System integration report

Several areas that arise from the system integration issue were examined. Intersystem analysis is discussed as it relates to software development, shared data bases and interfaces between TEMPUS and PLAID, shaded graphics rendering systems, object design (BUILD), the TEMPUS animation system, anthropometric lab integration, ongoing TEMPUS support and maintenance, and the impact of UNIX and local workstations on the OSDS environment

A Rule Based System for Assisting the Spatial Adjustment Process

This thesis describes a set of rules for control point matching between an original and an upgraded cadastre. The application of these rules results in the creation of shift vectors or links. The links can be supplied to any suitable spatial adjustment algorithm to adjust map layers captured from an old cadastre, for example, census blocks, to bring them into line with an upgraded cadastre. The solution requires no user supplied search-distance parameters

Freeform User Interfaces for Graphical Computing

報告番号: 甲15222 ; 学位授与年月日: 2000-03-29 ; 学位の種別: 課程博士 ; 学位の種類: 博士(工学) ; 学位記番号: 博工第4717号 ; 研究科・専攻: 工学系研究科情報工学専

A new method for simplification and compression of 3D meshes

We focus on the lossy compression of manifold triangle meshes. Our SwingWrapper approach partitions the surface of an original mesh M into simply-connected regions, called triangloids. We compute a new mesh M\u27. Each triangle of M\u27 is a close approximation of a pseudo-triangle of M. By construction, the connectivity of M\u27 is fairly regular and can be compressed to less than a bit per triangle using EdgeBreaker or one of the other recently developed schemes. The locations of the vertices of M\u27 are compactly encoded with our new prediction scheme, which uses a single correction parameter per vertex. For example, a variety of popular models retiled with our approach yield 10 times fewer triangles without exceeding an error of 1% of the radius of the bounding ball. Vertices of M\u27 are encoded with an average of 6 bits, which results in a total storage of 0.4 bits per triangle of the original mesh. The proposed solution may also be used to encode crude meshes for adaptive transmission and for controlling subdivision surfaces

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

3D Reconstruction of Building Rooftop and Power Line Models in Right-of-Ways Using Airborne LiDAR Data

The research objectives aimed to achieve thorough the thesis are to develop methods for reconstructing models of building and PL objects of interest in the power line (PL) corridor area from airborne LiDAR data. For this, it is mainly concerned with the model selection problem for which model is more optimal in representing the given data set. This means that the parametric relations and geometry of object shapes are unknowns and optimally determined by the verification of hypothetical models. Therefore, the proposed method achieves high adaptability to the complex geometric forms of building and PL objects. For the building modeling, the method of implicit geometric regularization is proposed to rectify noisy building outline vectors which are due to noisy data. A cost function for the regularization process is designed based on Minimum Description Length (MDL) theory, which favours smaller deviation between a model and observation as well as orthogonal and parallel properties between polylines. Next, a new approach, called Piecewise Model Growing (PMG), is proposed for 3D PL model reconstruction using a catenary curve model. It piece-wisely grows to capture all PL points of interest and thus produces a full PL 3D model. However, the proposed method is limited to the PL scene complexity, which causes PL modeling errors such as partial, under- and over-modeling errors. To correct the incompletion of PL models, the inner and across span analysis are carried out, which leads to replace erroneous PL segments by precise PL models. The inner span analysis is performed based on the MDL theory to correct under- and over-modeling errors. The across span analysis is subsequently carried out to correct partial-modeling errors by finding start and end positions of PLs which denotes Point Of Attachment (POA). As a result, this thesis addresses not only geometrically describing building and PL objects but also dealing with noisy data which causes the incompletion of models. In the practical aspects, the results of building and PL modeling should be essential to effectively analyze a PL scene and quickly alleviate the potentially hazardous scenarios jeopardizing the PL system

Analysis and Construction of Engaging Facial Forms and Expressions: Interdisciplinary Approaches from Art, Anatomy, Engineering, Cultural Studies, and Psychology

The topic of this dissertation is the anatomical, psychological, and cultural examination of a human face in order to effectively construct an anatomy-driven 3D virtual face customization and action model. In order to gain a broad perspective of all aspects of a face, theories and methodology from the fields of art, engineering, anatomy, psychology, and cultural studies have been analyzed and implemented. The computer generated facial customization and action model were designed based on the collected data. Using this customization system, culturally-specific attractive face in Korean popular culture, “kot-mi-nam (flower-like beautiful guy),” was modeled and analyzed as a case study. The “kot-mi-nam” phenomenon is overviewed in textual, visual, and contextual aspects, which reveals the gender- and sexuality-fluidity of its masculinity. The analysis and the actual development of the model organically co-construct each other requiring an interwoven process. Chapter 1 introduces anatomical studies of a human face, psychological theories of face recognition and an attractive face, and state-of-the-art face construction projects in the various fields. Chapter 2 and 3 present the Bezier curve-based 3D facial customization (BCFC) and Multi-layered Facial Action Model (MFAF) based on the analysis of human anatomy, to achieve a cost-effective yet realistic quality of facial animation without using 3D scanned data. In the experiments, results for the facial customization for gender, race, fat, and age showed that BCFC achieved enhanced performance of 25.20% compared to existing program Facegen , and 44.12% compared to Facial Studio. The experimental results also proved the realistic quality and effectiveness of MFAM compared with blend shape technique by enhancing 2.87% and 0.03% of facial area for happiness and anger expressions per second, respectively. In Chapter 4, according to the analysis based on BCFC, the 3D face of an average kot-mi-nam is close to gender neutral (male: 50.38%, female: 49.62%), and Caucasian (66.42-66.40%). Culturally-specific images can be misinterpreted in different cultures, due to their different languages, histories, and contexts. This research demonstrates that facial images can be affected by the cultural tastes of the makers and can also be interpreted differently by viewers in different cultures