Properties of Gauss digitized sets and digital surface integration

International audienceThis paper presents new topological and geometrical properties of Gauss digitizations of Euclidean shapes, most of them holding in arbitrary dimension $d$. We focus on $r$-regular shapes sampled by Gauss digitization at gridstep $h$. The digitized boundary is shown to be close to the Euclidean boundary in the Hausdorff sense, the minimum distance $\frac{\sqrt{d}}{2}h$ being achieved by the projection map $\xi$ induced by the Euclidean distance. Although it is known that Gauss digitized boundaries may not be manifold when $d \ge 3$, we show that non-manifoldness may only occur in places where the normal vector is almost aligned with some digitization axis, and the limit angle decreases with $h$. We then have a closer look at the projection of the digitized boundary onto the continuous boundary by $\xi$. We show that the size of its non-injective part tends to zero with $h$. This leads us to study the classical digital surface integration scheme, which allocates a measure to each surface element that is proportional to the cosine of the angle between an estimated normal vector and the trivial surface element normal vector. We show that digital integration is convergent whenever the normal estimator is multigrid convergent, and we explicit the convergence speed. Since convergent estimators are now available in the litterature, digital integration provides a convergent measure for digitized objects

Scale-space Feature Extraction on Digital Surfaces

International audienceA classical problem in many computer graphics applications consists in extracting significant zones or points on an object surface,like loci of tangent discontinuity (edges), maxima or minima of curvatures, inflection points, etc. These places have specific localgeometrical properties and often called generically features. An important problem is related to the scale, or range of scales,for which a feature is relevant. We propose a new robust method to detect features on digital data (surface of objects in Z^3 ),which exploits asymptotic properties of recent digital curvature estimators. In [1, 2], authors have proposed curvature estimators(mean, principal and Gaussian) on 2D and 3D digitized shapes and have demonstrated their multigrid convergence (for C^3 -smoothsurfaces). Since such approaches integrate local information within a ball around points of interest, the radius is a crucial parameter.In this article, we consider the radius as a scale-space parameter. By analyzing the behavior of such curvature estimators as the ballradius tends to zero, we propose a tool to efficiently characterize and extract several relevant features (edges, smooth and flat parts)on digital surfaces

Detail Enhancing Denoising of Digitized 3D Models from a Mobile Scanning System

The acquisition process of digitizing a large-scale environment produces an enormous amount of raw geometry data. This data is corrupted by system noise, which leads to 3D surfaces that are not smooth and details that are distorted. Any scanning system has noise associate with the scanning hardware, both digital quantization errors and measurement inaccuracies, but a mobile scanning system has additional system noise introduced by the pose estimation of the hardware during data acquisition. The combined system noise generates data that is not handled well by existing noise reduction and smoothing techniques. This research is focused on enhancing the 3D models acquired by mobile scanning systems used to digitize large-scale environments. These digitization systems combine a variety of sensors – including laser range scanners, video cameras, and pose estimation hardware – on a mobile platform for the quick acquisition of 3D models of real world environments. The data acquired by such systems are extremely noisy, often with significant details being on the same order of magnitude as the system noise. By utilizing a unique 3D signal analysis tool, a denoising algorithm was developed that identifies regions of detail and enhances their geometry, while removing the effects of noise on the overall model. The developed algorithm can be useful for a variety of digitized 3D models, not just those involving mobile scanning systems. The challenges faced in this study were the automatic processing needs of the enhancement algorithm, and the need to fill a hole in the area of 3D model analysis in order to reduce the effect of system noise on the 3D models. In this context, our main contributions are the automation and integration of a data enhancement method not well known to the computer vision community, and the development of a novel 3D signal decomposition and analysis tool. The new technologies featured in this document are intuitive extensions of existing methods to new dimensionality and applications. The totality of the research has been applied towards detail enhancing denoising of scanned data from a mobile range scanning system, and results from both synthetic and real models are presented

An active contour for range image segmentation

In this paper a new classification of range image segmentation method is proposed according to the criterion of homogeneity which obeys the segmentation, then, a deformable model-type active contour 201C;Snake201D; is applied to segment range images

지상레이저스캐너와 인공신경망을 이용한 암반 노출면의 절리 거칠기 지수 측정

학위논문(석사) -- 서울대학교대학원 : 공과대학 에너지시스템공학부, 2023. 2. 전석원.Joint Roughness Coefficient (JRC) is a parameter representing degree of roughness of rock discontinuities in Barton-Bandis joint model. It can be measured by visual comparison between roughness profiles acquired from target discontinuities and the reference profiles. Although performing this method is much convenient than lab or field tests on joint specimens, it can be time-consuming and unsafe. In this thesis, a method to estimate JRC using Terrestrial Laser Scanner (TLS) is suggested for quick and safe assessment of JRC. After obtaining 3D point cloud of rock exposure in distance, JRC of discontinuities on it is estimated. According to several previous works, measuring small-scale roughness using TLS scan data is challenging due to noise existent in it. The strategy used in this thesis is to employ an ANN for 3D point clouds. The ANN can receive point clouds of discontinuities as input and output their JRC. By training the ANN with a number of point clouds containing TLS noise, it was expected that the ANN can learn how to estimate their JRC regardless of the existence of noise. Since it is not attainable to make a real dataset, point clouds of synthetic rough surfaces are generated using a fractal based algorithm instead of real TLS scan data. Each surface is labeled with its JRC, and TLS noise is artificially applied on it to imitate actual TLS scan data. After being trained with the synthetic training dataset, the ANN is tested on joint surfaces on actual TLS scan data. It is shown that the trained ANN can estimate JRC of the joint surfaces regardless of noise level of TLS scan data while an existing method does not work well on data with larger noise level. In addition, methods to deal with scale effect of JRC are also introduced.절리 거칠기 지수(Joint Roughness Coefficient; JRC)는 Barton-Bandis 절리 모델에서 암반 불연속면의 거칠기 정도를 나타내는 인자이다. 이는 원하는 불연속면으로부터 취득한 거칠기 프로파일을 기준 프로파일과 시각적으로 비교함으로써 측정할 수 있다. 이 방법은 절리 시료를 취득하여 실험실 또는 현장 시험을 실시하는 것보다는 훨씬 편리하지만 경우에 따라 실시하는 데 오랜 시간이 필요하거나 위험할 수 있다. 본 논문에서는 이러한 문제를 해결하기 위하여 지상레이저스캐너 (Terrestrial Laser Scanner; TLS)를 이용하여 빠르고 안전하게 절리 거칠기 지수를 산정하는 방법을 제시하고자 한다. 지상레이저스캐너를 이용하여 암반 노출면의 삼차원 점군을 원거리에서 취득하고 점군 내 불연속면들의 절리 거칠기 지수를 추정할 것이다. 몇몇의 기존 연구들에 따르면 지상레이저스캐너를 이용하여 작은 규모의 거칠기를 산정하는 것은 데이터에 존재하는 노이즈 때문에 매우 어렵다고 한다. 본 논문에서는 이를 해결하기 위한 전략으로 3차원 점군을 위한 인공신경망을 사용하고자 하였다. 사용된 인공신경망은 불연속면의 점군을 입력받아 그것의 절리 거칠기 지수를 예측할 수 있다. 해당 인공신경망을 노이즈를 포함하는 다량의 점군 데이터셋으로 학습시킴으로써 인공신경망이 노이즈의 존재와 상관없이 점군의 절리 거칠기 지수를 산정하는 방법을 학습하도록 하였다. 지상레이저스캐너를 이용하여 실제 데이터셋을 구축하는 것이 불가능했기 때문에 실제 암반 스캔 자료 대신 프랙탈 이론을 기반으로 한 알고리즘을 사용하여 가상의 거친 표면 점군 데이터셋을 생성하였다. 각 표면을 해당 표면의 절리 거칠기 지수로 라벨링한 후, 실제 스캔 자료를 모사하기 위하여 표면들에 지상레이저스캐너의 노이즈를 인공적으로 입혀주었다. 인공신경망은 가상 학습 데이터셋으로 학습된 후 실제 암반 스캔 자료에 대하여 검증되었다. 그 결과 학습된 인공신경망은 스캔 데이터 내에 존재하는 노이즈의 수준과 상관 없이 절리 표면의 절리 거칠기 지수를 산정할 수 있었다. 반면에 기존에 존재하던 방법으로 같은 데이터에 대하여 절리 거칠기 지수 산정을 시도하였을 때에는 노이즈가 클 경우 예측이 크게 잘못됨을 확인하였다. 추가적으로, 절리 거칠기 지수가 가지는 크기 효과에 대응하는 방법들 또한 제시되었다.Chapter 1. Introduction 1 1.1. Motivation 1 1.2. Agendas and overview 3 Chapter 2. Measuring JRC of 3D point clouds 5 2.1. Joint roughness coefficient 5 2.2. JRC calculation using digitized data of surface geometry 10 2.3. Issues relevant to JRC 15 2.4. Synthetic surface generation 20 2.5. Calculating JRC of the generated surfaces 23 Chapter 3. TLS precision 25 3.1. Basics of TLS 25 3.2. Factors disturbing TLS precision 30 3.3. Measuring roughness of joint using TLS 31 3.4. Range and angular noise 33 3.5. Mixed-pixel effect 36 3.6. Synthetic noise application 42 3.7. Training data generation 49 Chapter 4. ANN estimating JRC of TLS data 52 4.1. PointNet 52 4.2. Test data acquisition 54 4.3. Training procedure 61 4.4. Test results and comparative analysis 62 4.5. How to deal with scale effect 66 Chapter 5. Conclusion 68 References 71 Appendix A. Figures of test data 78 Appendix B. Large scale roughness profiles 83 Abstract in Korean 86석

Continuous Modeling of 3D Building Rooftops From Airborne LIDAR and Imagery

In recent years, a number of mega-cities have provided 3D photorealistic virtual models to support the decisions making process for maintaining the cities' infrastructure and environment more effectively. 3D virtual city models are static snap-shots of the environment and represent the status quo at the time of their data acquisition. However, cities are dynamic system that continuously change over time. Accordingly, their virtual representation need to be regularly updated in a timely manner to allow for accurate analysis and simulated results that decisions are based upon. The concept of "continuous city modeling" is to progressively reconstruct city models by accommodating their changes recognized in spatio-temporal domain, while preserving unchanged structures. However, developing a universal intelligent machine enabling continuous modeling still remains a challenging task. Therefore, this thesis proposes a novel research framework for continuously reconstructing 3D building rooftops using multi-sensor data. For achieving this goal, we first proposes a 3D building rooftop modeling method using airborne LiDAR data. The main focus is on the implementation of an implicit regularization method which impose a data-driven building regularity to noisy boundaries of roof planes for reconstructing 3D building rooftop models. The implicit regularization process is implemented in the framework of Minimum Description Length (MDL) combined with Hypothesize and Test (HAT). Secondly, we propose a context-based geometric hashing method to align newly acquired image data with existing building models. The novelty is the use of context features to achieve robust and accurate matching results. Thirdly, the existing building models are refined by newly proposed sequential fusion method. The main advantage of the proposed method is its ability to progressively refine modeling errors frequently observed in LiDAR-driven building models. The refinement process is conducted in the framework of MDL combined with HAT. Markov Chain Monte Carlo (MDMC) coupled with Simulated Annealing (SA) is employed to perform a global optimization. The results demonstrates that the proposed continuous rooftop modeling methods show a promising aspects to support various critical decisions by not only reconstructing 3D rooftop models accurately, but also by updating the models using multi-sensor data