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

A locally adaptive kernel regression method for facies delineation

Facies delineation is defined as the separation of geological units with distinct intrinsic characteristics (grain size, hydraulic conductivity, mineralogical composition). A major challenge in this area stems from the fact that only a few scattered pieces of hydrogeological information are available to delineate geological facies. Several methods to delineate facies are available in the literature, ranging from those based only on existing hard data, to those including secondary data or external knowledge about sedimentological patterns. This paper describes a methodology to use kernel regression methods as an effective tool for facies delineation. The method uses both the spatial and the actual sampled values to produce, for each individual hard data point, a locally adaptive steering kernel function, self-adjusting the principal directions of the local anisotropic kernels to the direction of highest local spatial correlation. The method is shown to outperform the nearest neighbor classification method in a number of synthetic aquifers whenever the available number of hard data is small and randomly distributed in space. In the case of exhaustive sampling, the steering kernel regression method converges to the true solution. Simulations ran in a suite of synthetic examples are used to explore the selection of kernel parameters in typical field settings. It is shown that, in practice, a rule of thumb can be used to obtain suboptimal results. The performance of the method is demonstrated to significantly improve when external information regarding facies proportions is incorporated. Remarkably, the method allows for a reasonable reconstruction of the facies connectivity patterns, shown in terms of breakthrough curves performance

Optimal spectral reconstructions from deterministic and stochastic sampling geometries using compressive sensing and spectral statistical models

This dissertation focuses on the development of high-quality image reconstruction methods from a limited number of Fourier samples using optimized, stochastic and deterministic sampling geometries. Two methodologies are developed: an optimal image reconstruction framework based on Compressive Sensing (CS) techniques and a new, Spectral Statistical approach based on the use of isotropic models over a dyadic partitioning of the spectrum. The proposed methods are demonstrated in applications in reconstructing fMRI and remote sensing imagery. Typically, a reduction in MRI image acquisition time is achieved by sampling K-space at a rate below the Nyquist rate. Various methods using correlation between samples, sample averaging, and more recently, Compressive Sensing, are employed to mitigate the aliasing effects of under-sampled Fourier data. The proposed solution utilizes an additional layer of optimization to enhance the performance of a previously published CS reconstruction algorithm. Specifically, the new framework provides reconstructions of a desired image quality by jointly optimizing for the optimal K-space sampling geometry and CS model parameters. The effectiveness of each geometry is evaluated based on the required number of FFT samples that are available for image reconstructions of sufficient quality. A central result of this approach is that the fastest geometry, the spiral low-pass geometry has also provided the best (optimized) CS reconstructions. This geometry provided significantly better reconstructions than the stochastic sampling geometries recommended in the literature. An optimization framework for selecting appropriate CS model reconstruction parameters is also provided. Here, the term appropriate CS parameters\u27 is meant to infer that the estimated parameter ranges can provide some guarantee for a minimum level of image reconstruction performance. Utilizing the simplex search algorithm, the optimal TV-norm and Wavelet transform penalties are calculated for the CS reconstruction objective function. Collecting the functional evaluation values of the simplex search over a large data set allows for a range of objective function weighting parameters to be defined for the sampling geometries that were found to be effective. The results indicate that the CS parameter optimization framework is significant in that it can provide for large improvements over the standard use of non-optimized approaches. The dissertation also develops the use of a new Spectral Statistical approach for spectral reconstruction of remote sensing imagery. The motivation for pursuing this research includes potential applications that include, but are not limited to, the development of better image compression schemas based on a limited number of spectral coefficients. In addition, other applications include the use of spectral interpolation methods for remote sensing systems that directly sample the Fourier domain optically or electromagnetically, which may suffer from missing or degraded samples beyond and/or within the focal plane. For these applications, a new spectral statistical methodology is proposed that reconstructs spectral data from uniformly spaced samples over a dyadic partition of the spectrum. Unlike the CS approach that solves for the 2D FFT coefficients directly, the statistical approach uses separate models for the magnitude and phase, allowing for separate control of the reconstruction quality of each one. A scalable solution that partitions the spectral domain into blocks of varying size allows for the determination of the appropriate covariance models of the magnitude and phase spectra bounded by the blocks. The individual spectral models are then applied to solving for the optimal linear estimate, which is referred to in literature as Kriging. The use of spectral data transformations are also presented as a means for producing data that is better suited for statistical modeling and variogram estimation. A logarithmic transformation is applied to the magnitude spectra, as it has been shown to impart intrinsic stationarity over localized, bounded regions of the spectra. Phase spectra resulting from the 2D FFT can be best described as being uniformly distributed over the interval of -pi to pi. In this original state, the spectral samples fail to produce appropriate spectral statistical models that exhibit inter-sample covariance. For phase spectra modeling, an unwrapping step is required to ensure that individual blocks can be effectively modeled using appropriate variogram models. The transformed magnitude and unwrapped phase spectra result in unique statistical models that are optimal over individual frequency blocks, which produce accurate spectral reconstructions that account for localized variability in the spectral domain. The Kriging spectral estimates are shown to produce higher quality magnitude and phase spectra reconstructions than the cubic spline, nearest neighbor, and bilinear interpolators that are widely used. Even when model assumptions, such as isotropy, violate the spectral data being modeled, excellent reconstructions are still obtained. Finally, both of the spectral estimation methods developed in this dissertation are compared against one another, revealing how each one of the methods developed here is appropriate for different classes of images. For satellite images that contain a large amount of detail, the new spectral statistical approach, reconstructing the spectrum much faster, from a fraction of the original high frequency content, provided significantly better reconstructions than the best reconstructions from the optimized CS geometries. This result is supported not only by comparing image quality metrics, but also by visual assessment.\u2

Review of the mathematical foundations of data fusion techniques in surface metrology

The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed

Ricerche di Geomatica 2011

Questo volume raccoglie gli articoli che hanno partecipato al Premio AUTeC 2011. Il premio è stato istituito nel 2005. Viene conferito ogni anno ad una tesi di Dottorato giudicata particolarmente significativa sui temi di pertinenza del SSD ICAR/06 (Topografia e Cartografia) nei diversi Dottorati attivi in Italia

A novel iterative approach for mapping local singularities from geochemical data

International audienceThere are many phenomena in nature, such as earthquakes, landslides, floods, and large-scale mineralization that are characterized by singular functions exhibiting scale invariant properties. A local singularity analysis based on multifractal modeling was developed for detection of local anomalies for mineral exploration. An iterative approach is proposed in the current paper for improvement of parameter estimations involved in the local singularity analysis. The advantage of this new approach is demonstrated with de Wijs's zinc data from a sphalerite-quartz vein near Pulacayo in Bolivia. The semivariogram method was used to illustrate the differences between the raw data and the estimated data by the new algorithm. It has been shown that the outcome of the local singularity analysis consists of two components: singularity component characterized by local singularity index and the non-singular component by prefractal parameter