Surface Patches for 3D Curve Network Based on Its Design Intent

학위논문 (석사)-- 서울대학교 대학원 : 기계항공공학부, 2014. 2. 이건우.최근 스케치 기반 인터페이스를 이용한 자연스러운 기하모델링 방법들이 제시됨에 따라, 스케치를 통해 얻어진 3차원 곡선 네트워크로부터 모델을 생성하는 방법에 대한 다양한 연구가 진행되어왔다. 하지만 3차원 곡선들로부터 곡면 패치를 생성하는 것은 기하학적 정보의 부재로 인해 최적의 해가 존재하기 보다는 다양한 방법으로 해석할 수 있는 모호한 문제이다. 이 논문에서는 3차원 곡선 네트워크로부터 곡면 패치를 생성하는 알고리듬을 제안하며, 문제의 모호성을 해결하기 위해 스케치 특성에 따른 기하 구속조건을 추가적으로 부가한다. 각각의 기하 구속조건들은 곡면의 법선 벡터에 관하여 수식화되며, 최적 해를 찾는 방법으로 디자인 의도를 고려한 곡면의 법선 벡터를 추정한다. 이렇게 추정된 법선 벡터를 이용하여 곡선 네트워크가 이루는 곡면 모델을 생성하게 된다. 제안한 알고리듬은 다양한 곡선 네트워크에 대한 모델 생성을 통해 검증하였으며, 디자인 의도를 충분히 반영하기 위해 곡선에 기하 구속조건을 정의하여 새로운 기하정보를 추정했다는 점에서 기존의 논문들에 비해 시각적으로 합리적인 결과를 얻었다. 이 연구의 3차원 곡선의 기하정보를 추정하는 기술은 스케치를 기반으로 하는 모델링 방식에서 새로운 정보를 추출하기 위한 방법으로 사용될 수 있다. 더 나아가, 곡선 네트워크의 각각의 곡면에서 구한 곡선의 법선 벡터들은 인접 곡면의 법선 벡터 정보와 더해져 사용자 의도에 더욱 가까운 곡면 모델을 얻을 수 있을 것이다. 또한 곡선 네트워크 생성기술과의 결합은 3차원 모델링의 새로운 프레임워크를 제시할 수 있을 것으로 기대된다.초록 목차 그림 목차 표 목차 제 1 장 서론 1 1.1 곡선 네트워크 2 1.2 3차원 곡면 모델 생성 3 1.3 디자인 의도를 고려한 모델 생성 4 제 2 장 관련 연구 6 2.1 스케치 기반 모델링 인터페이스 6 2.2 곡선 네트워크로부터 곡면 패치/모델 생성 8 제 3 장 전체 과정 개괄 12 3.1 곡면 법선 벡터의 추정 12 3.2 곡면 모델 생성 13 제 4 장 기하정보 추정 15 4.1 기하정보 추정을 위한 기준 17 4.1.1 스케치의 연속성 17 4.1.2 곡선의 접선 벡터 조건 17 4.1.3 닫힌곡선 스케치 18 4.1.4 곡면 굽힘 최소화 18 4.2 법선 벡터 추정 20 4.2.1 회전 최소화 프레임 21 4.2.2 회전 최소화 프레임의 경계조건 23 4.2.3 곡면 굽힘 에너지 최소화 24 제 5 장 곡면 모델 생성 27 5.1 초기 메시 생성 27 5.2 메시 Refine 28 5.3 추정 법선 벡터 적용 31 제 6 장 결과 36 제 7 장 결론 42 참고문헌 43 Abstract 49Maste

On the use of the Rotation Minimizing Frame for Variational Systems with Euclidean Symmetry

We study variational systems for space curves, for which the Lagrangian or action principle has a Euclidean symmetry, using the Rotation Minimizing frame, also known as the Normal, Parallel or Bishop frame (see [1], [36]). Such systems have previously been studied using the Frenet–Serret frame. However, the Rotation Minimizing frame has many advantages, and can be used to study a wider class of examples. We achieve our results by extending the powerful symbolic invariant cal- culus for Lie group based moving frames, to the Rotation Minimizing frame case. To date, the invariant calculus has been developed for frames defined by algebraic equations. By contrast, the Rotation Minimizing frame is defined by a differential equation. In this paper, we derive the recurrence formulae for the symbolic invariant differentiation of the symbolic invariants. We then derive the syzygy operator needed to obtain Noether’s conservation laws as well as the Euler–Lagrange equations directly in terms of the invariants, for variational problems with a Euclidean symmetry. We show how to use the six Noether laws to ease the integration problem for the minimizing curve, once the Euler–Lagrange equations have been solved for the generating differential invariants. Our applications include variational problems used in the study of strands of pro- teins, nucleid acids and polymers

Characterizing envelopes of moving rotational cones and applications in CNC machining

Motivated by applications in CNC machining, we provide a characterization of surfaces which are enveloped by a one-parametric family of congruent rotational cones. As limit cases, we also address ruled surfaces and their offsets. The characterizations are higher order nonlinear PDEs generalizing the ones by Gauss and Monge for developable surfaces and ruled surfaces, respectively. The derivation includes results on local approximations of a surface by cones of revolution, which are expressed by contact order in the space of planes. To this purpose, the isotropic model of Laguerre geometry is used as there rotational cones correspond to curves (isotropic circles) and higher order contact is computed with respect to the image of the input surface in the isotropic model. Therefore, one studies curve-surface contact that is conceptually simpler than the surface-surface case. We show that, in a generic case, there exist at most six positions of a fixed rotational cone that have third order contact with the input surface. These results are themselves of interest in geometric computing, for example in cutter selection and positioning for flank CNC machining.RYC-2017-2264

Development of an Atlas-Based Segmentation of Cranial Nerves Using Shape-Aware Discrete Deformable Models for Neurosurgical Planning and Simulation

Twelve pairs of cranial nerves arise from the brain or brainstem and control our sensory functions such as vision, hearing, smell and taste as well as several motor functions to the head and neck including facial expressions and eye movement. Often, these cranial nerves are difficult to detect in MRI data, and thus represent problems in neurosurgery planning and simulation, due to their thin anatomical structure, in the face of low imaging resolution as well as image artifacts. As a result, they may be at risk in neurosurgical procedures around the skull base, which might have dire consequences such as the loss of eyesight or hearing and facial paralysis. Consequently, it is of great importance to clearly delineate cranial nerves in medical images for avoidance in the planning of neurosurgical procedures and for targeting in the treatment of cranial nerve disorders. In this research, we propose to develop a digital atlas methodology that will be used to segment the cranial nerves from patient image data. The atlas will be created from high-resolution MRI data based on a discrete deformable contour model called 1-Simplex mesh. Each of the cranial nerves will be modeled using its centerline and radius information where the centerline is estimated in a semi-automatic approach by finding a shortest path between two user-defined end points. The cranial nerve atlas is then made more robust by integrating a Statistical Shape Model so that the atlas can identify and segment nerves from images characterized by artifacts or low resolution. To the best of our knowledge, no such digital atlas methodology exists for segmenting nerves cranial nerves from MRI data. Therefore, our proposed system has important benefits to the neurosurgical community

Mixed Structural Models for 3D Audio in Virtual Environments

In the world of ICT, strategies for innovation and development are increasingly focusing on applications that require spatial representation and real-time interaction with and within 3D media environments. One of the major challenges that such applications have to address is user-centricity, reflecting e.g. on developing complexity-hiding services so that people can personalize their own delivery of services. In these terms, multimodal interfaces represent a key factor for enabling an inclusive use of the new technology by everyone. In order to achieve this, multimodal realistic models that describe our environment are needed, and in particular models that accurately describe the acoustics of the environment and communication through the auditory modality. Examples of currently active research directions and application areas include 3DTV and future internet, 3D visual-sound scene coding, transmission and reconstruction and teleconferencing systems, to name but a few. The concurrent presence of multimodal senses and activities make multimodal virtual environments potentially flexible and adaptive, allowing users to switch between modalities as needed during the continuously changing conditions of use situation. Augmentation through additional modalities and sensory substitution techniques are compelling ingredients for presenting information non-visually, when the visual bandwidth is overloaded, when data are visually occluded, or when the visual channel is not available to the user (e.g., for visually impaired people). Multimodal systems for the representation of spatial information will largely benefit from the implementation of audio engines that have extensive knowledge of spatial hearing and virtual acoustics. Models for spatial audio can provide accurate dynamic information about the relation between the sound source and the surrounding environment, including the listener and his/her body which acts as an additional filter. Indeed, this information cannot be substituted by any other modality (i.e., visual or tactile). Nevertheless, today's spatial representation of audio within sonification tends to be simplistic and with poor interaction capabilities, being multimedia systems currently focused on graphics processing mostly, and integrated with simple stereo or multi-channel surround-sound. On a much different level lie binaural rendering approaches based on headphone reproduction, taking into account that possible disadvantages (e.g. invasiveness, non-flat frequency responses) are counterbalanced by a number of desirable features. Indeed, these systems might control and/or eliminate reverberation and other acoustic effects of the real listening space, reduce background noise, and provide adaptable and portable audio displays, which are all relevant aspects especially in enhanced contexts. Most of the binaural sound rendering techniques currently exploited in research rely on the use of Head-Related Transfer Functions (HRTFs), i.e. peculiar filters that capture the acoustic effects of the human head and ears. HRTFs allow loyal simulation of the audio signal that arrives at the entrance of the ear canal as a function of the sound source's spatial position. HRTF filters are usually presented under the form of acoustic signals acquired on dummy heads built according to mean anthropometric measurements. Nevertheless, anthropometric features of the human body have a key role in HRTF shaping: several studies have attested how listening to non-individual binaural sounds results in evident localization errors. On the other hand, individual HRTF measurements on a significant number of subjects result both time- and resource-expensive. Several techniques for synthetic HRTF design have been proposed during the last two decades and the most promising one relies on structural HRTF models. In this revolutionary approach, the most important effects involved in spatial sound perception (acoustic delays and shadowing due to head diffraction, reflections on pinna contours and shoulders, resonances inside the ear cavities) are isolated and modeled separately with a corresponding filtering element. HRTF selection and modeling procedures can be determined by physical interpretation: parameters of each rendering blocks or selection criteria can be estimated from real and simulated data and related to anthropometric geometries. Effective personal auditory displays represent an innovative breakthrough for a plethora of applications and structural approach can also allow for effective scalability depending on the available computational resources or bandwidth. Scenes with multiple highly realistic audiovisual objects are easily managed exploiting parallelism of increasingly ubiquitous GPUs (Graphics Processing Units). Building individual headphone equalization with perceptually robust inverse filtering techniques represents a fundamental step towards the creation of personal virtual auditory displays (VADs). To this regard, several examples might benefit from these considerations: multi-channel downmix over headphones, personal cinema, spatial audio rendering in mobile devices, computer-game engines and individual binaural audio standards for movie and music production. This thesis presents a family of approaches that overcome the current limitations of headphone-based 3D audio systems, aiming at building personal auditory displays through structural binaural audio models for an immersive sound reproduction. The resulting models allow for an interesting form of content adaptation and personalization, since they include parameters related to the user's anthropometry in addition to those related to the sound sources and the environment. The covered research directions converge to a novel framework for synthetic HRTF design and customization that combines the structural modeling paradigm with other HRTF selection techniques (inspired by non-individualized HRTF selection procedures) and represents the main novel contribution of this thesis: the Mixed Structural Modeling (MSM) approach considers the global HRTF as a combination of structural components, which can be chosen to be either synthetic or recorded components. In both cases, customization is based on individual anthropometric data, which are used to either fit the model parameters or to select a measured/simulated component within a set of available responses. The definition and experimental validation of the MSM approach addresses several pivotal issues towards the acquisition and delivery of binaural sound scenes and designing guidelines for personalized 3D audio virtual environments holding the potential of novel forms of customized communication and interaction with sound and music content. The thesis also presents a multimodal interactive system which is used to conduct subjective test on multi-sensory integration in virtual environments. Four experimental scenarios are proposed in order to test the capabilities of auditory feedback jointly to tactile or visual modalities. 3D audio feedback related to user’s movements during simple target following tasks is tested as an applicative example of audio-visual rehabilitation system. Perception of direction of footstep sounds interactively generated during walking and provided through headphones highlights how spatial information can clarify the semantic congruence between movement and multimodal feedback. A real time, physically informed audio-tactile interactive system encodes spatial information in the context of virtual map presentation with particular attention to orientation and mobility (O&M) learning processes addressed to visually impaired people. Finally, an experiment analyzes the haptic estimation of size of a virtual 3D object (a stair-step) whereas the exploration is accompanied by a real-time generated auditory feedback whose parameters vary as a function of the height of the interaction point. The collected data from these experiments suggest that well-designed multimodal feedback, exploiting 3D audio models, can definitely be used to improve performance in virtual reality and learning processes in orientation and complex motor tasks, thanks to the high level of attention, engagement, and presence provided to the user. The research framework, based on the MSM approach, serves as an important evaluation tool with the aim of progressively determining the relevant spatial attributes of sound for each application domain. In this perspective, such studies represent a novelty in the current literature on virtual and augmented reality, especially concerning the use of sonification techniques in several aspects of spatial cognition and internal multisensory representation of the body. This thesis is organized as follows. An overview of spatial hearing and binaural technology through headphones is given in Chapter 1. Chapter 2 is devoted to the Mixed Structural Modeling formalism and philosophy. In Chapter 3, topics in structural modeling for each body component are studied, previous research and two new models, i.e. near-field distance dependency and external-ear spectral cue, are presented. Chapter 4 deals with a complete case study of the mixed structural modeling approach and provides insights about the main innovative aspects of such modus operandi. Chapter 5 gives an overview of number of a number of proposed tools for the analysis and synthesis of HRTFs. System architectural guidelines and constraints are discussed in terms of real-time issues, mobility requirements and customized audio delivery. In Chapter 6, two case studies investigate the behavioral importance of spatial attribute of sound and how continuous interaction with virtual environments can benefit from using spatial audio algorithms. Chapter 7 describes a set of experiments aimed at assessing the contribution of binaural audio through headphones in learning processes of spatial cognitive maps and exploration of virtual objects. Finally, conclusions are drawn and new research horizons for further work are exposed in Chapter 8

Information Extraction and Modeling from Remote Sensing Images: Application to the Enhancement of Digital Elevation Models

To deal with high complexity data such as remote sensing images presenting metric resolution over large areas, an innovative, fast and robust image processing system is presented. The modeling of increasing level of information is used to extract, represent and link image features to semantic content. The potential of the proposed techniques is demonstrated with an application to enhance and regularize digital elevation models based on information collected from RS images

Inferring Room Geometries

Determining the geometry of an acoustic enclosure using microphone arrays has become an active area of research. Knowledge gained about the acoustic environment, such as the location of reflectors, can be advantageous for applications such as sound source localization, dereverberation and adaptive echo cancellation by assisting in tracking environment changes and helping the initialization of such algorithms. A methodology to blindly infer the geometry of an acoustic enclosure by estimating the location of reflective surfaces based on acoustic measurements using an arbitrary array geometry is developed and analyzed. The starting point of this work considers a geometric constraint, valid both in two and three-dimensions, that converts time-of-arrival and time-difference-pf-arrival information into elliptical constraints about the location of reflectors. Multiple constraints are combined to yield the line or plane parameters of the reflectors by minimizing a specific cost function in the least-squares sense. An iterative constrained least-squares estimator, along with a closed-form estimator, that performs optimally in a noise-free scenario, solve the associated common tangent estimation problem that arises from the geometric constraint. Additionally, a Hough transform based data fusion and estimation technique, that considers acquisitions from multiple source positions, refines the reflector localization even in adverse conditions. An extension to the geometric inference framework, that includes the estimation of the actual speed of sound to improve the accuracy under temperature variations, is presented that also reduces the required prior information needed such that only relative microphone positions in the array are required for the localization of acoustic reflectors. Simulated and real-world experiments demonstrate the feasibility of the proposed method.Open Acces