Global, and Local Optimization Beamforming for Acoustic Broadband Sources

This paper presents an extension to global optimization beamforming for acoustic broadband sources. Given, that properties such as the source location, spatial shape, multipole rotation, or flow properties can be parameterized over the frequency, a CSM-fitting can be performed for all frequencies at the same time. A numerical analysis shows that the non-linear error function for the standard global optimization problem is similar to a Point Spread Function and contains local minima, but can be improved with the proposed broadband optimization. Not only increases the broadband optimization process the ratio of equations to unknown variables, but it also smooths out the cost function. It also simplifies the process of identifying sources and reconstructing their spectra from the results. The paper shows that the method is superior on synthetic monopoles compared to standard global optimization and CLEAN-SC. For real-world data the results of broadband global optimization, standard global optimization, and CLEAN-SC are similar. However, the proposed method does not require the identification and integration of Regions Of Interest. It is shown, that by using reasonable initial values the global optimization problem reduces to a local optimization problem with similar results. Further, it is shown that the proposed method is able to identify multipoles with different pole amplitudes and unknown pole rotations.Comment: Submitted to Journal of Sound and Vibratio

Gauss-Newton Deformable Part Models for face alignment in-the-wild

Arguably, Deformable Part Models (DPMs) are one of the most prominent approaches for face alignment with impressive results being recently reported for both controlled lab and unconstrained settings. Fitting in most DPM methods is typically formulated as a two-step process during which discriminatively trained part templates are first correlated with the image to yield a filter response for each landmark and then shape optimization is performed over these filter responses. This process, although computationally efficient, is based on fixed part templates which are assumed to be independent, and has been shown to result in imperfect filter responses and detection ambiguities. To address this limitation, in this paper, we propose to jointly optimize a part-based, trained in-the-wild, flexible appearance model along with a global shape model which results in a joint translational motion model for the model parts via Gauss-Newton (GN) optimization. We show how significant computational reductions can be achieved by building a full model during training but then efficiently optimizing the proposed cost function on a sparse grid using weighted least-squares during fitting. We coin the proposed formulation Gauss-Newton Deformable Part Model (GN-DPM). Finally, we compare its performance against the state-of-the-art and show that the proposed GN-DPM outperforms it, in some cases, by a large margin. Code for our method is available from http://ibug.doc.ic.ac.uk/resources

Outlier Detection for Shape Model Fitting

Medical image analysis applications often benefit from having a statistical shape model in the background. Statistical shape models are generative models which can generate shapes from the same family and assign a likelihood to the generated shape. In an Analysis-by-synthesis approach to medical image analysis, the target shape to be segmented, registered or completed must first be reconstructed by the statistical shape model. Shape models accomplish this by either acting as regression models, used to obtain the reconstruction, or as regularizers, used to limit the space of possible reconstructions. However, the accuracy of these models is not guaranteed for targets that lie out of the modeled distribution of the statistical shape model. Targets with pathologies are an example of out-of-distribution data. The target shape to be reconstructed has deformations caused by pathologies that do not exist on the healthy data used to build the model. Added and missing regions may lead to false correspondences, which act as outliers and influence the reconstruction result. Robust fitting is necessary to decrease the influence of outliers on the fitting solution, but often comes at the cost of decreased accuracy in the inlier region. Robust techniques often presuppose knowledge of outlier characteristics to build a robust cost function or knowledge of the correct regressed function to filter the outliers. This thesis proposes strategies to obtain the outliers and reconstruction simultaneously without previous knowledge about either. The assumptions are that a statistical shape model that represents the healthy variations of the target organ is available, and that some landmarks on the model reference that annotate locations with correspondence to the target exist. The first strategy uses an EM-like algorithm to obtain the sampling posterior. This is a global reconstruction approach that requires classical noise assumptions on the outlier distribution. The second strategy uses Bayesian optimization to infer the closed-form predictive posterior distribution and estimate a label map of the outliers. The underlying regression model is a Gaussian Process Morphable Model (GPMM). To make the reconstruction obtained through Bayesian optimization robust, a novel acquisition function is proposed. The acquisition function uses the posterior and predictive posterior distributions to avoid choosing outliers as next query points. The algorithms give as outputs a label map and a a posterior distribution that can be used to choose the most likely reconstruction. To obtain the label map, the first strategy uses Bayesian classification to separate inliers and outliers, while the second strategy annotates all query points as inliers and unused model vertices as outliers. The proposed solutions are compared to the literature, evaluated through their sensitivity and breakdown points, and tested on publicly available datasets and in-house clinical examples. The thesis contributes to shape model fitting to pathological targets by showing that: - performing accurate inlier reconstruction and outlier detection is possible without case-specific manual thresholds or input label maps, through the use of outlier detection. - outlier detection makes the algorithms agnostic to pathology type i.e. the algorithms are suitable for both sparse and grouped outliers which appear as holes and bumps, the severity of which influences the results. - using the GPMM-based sequential Bayesian optimization approach, the closed-form predictive posterior distribution can be obtained despite the presence of outliers, because the Gaussian noise assumption is valid for the query points. - using sequential Bayesian optimization instead of traditional optimization for shape model fitting brings forth several advantages that had not been previously explored. Fitting can be driven by different reconstruction goals such as speed, location-dependent accuracy, or robustness. - defining pathologies as outliers opens the door for general pathology segmentation solutions for medical data. Segmentation algorithms do not need to be dependent on imaging modality, target pathology type, or training datasets for pathology labeling. The thesis highlights the importance of outlier-based definitions of pathologies in medical data that are independent of pathology type and imaging modality. Developing such standards would not only simplify the comparison of different pathology segmentation algorithms on unlabeled datsets, but also push forward standard algorithms that are able to deal with general pathologies instead of data-driven definitions of pathologies. This comes with theoretical as well as clinical advantages. Practical applications are shown on shape reconstruction and labeling tasks. Publicly-available challenge datasets are used, one for cranium implant reconstruction, one for kidney tumor detection, and one for liver shape reconstruction. Further clinical applications are shown on in-house examples of a femur and mandible with artifacts and missing parts. The results focus on shape modeling but can be extended in future work to include intensity information and inner volume pathologies

5-axis double-flank CNC machining of spiral bevel gears via custom-shaped milling tools -- Part I: modeling and simulation

A new category of 5-axis flank computer numerically controlled (CNC) machining, called \emph{double-flank}, is presented. Instead of using a predefined set of milling tools, we use the shape of the milling tool as a free parameter in our optimization-based approach and, for a given input free-form (NURBS) surface, compute a custom-shaped tool that admits highly-accurate machining. Aimed at curved narrow regions where the tool may have double tangential contact with the reference surface, like spiral bevel gears, the initial trajectory of the milling tool is estimated by fitting a ruled surface to the self-bisector of the reference surface. The shape of the tool and its motion then both undergo global optimization that seeks high approximation quality between the input free-form surface and its envelope approximation, fairness of the motion and the tool, and prevents overcutting. That is, our double-flank machining is meant for the semi-finishing stage and therefore the envelope of the motion is, by construction, penetration-free with the references surface. Our algorithm is validated by a commercial path-finding software and the prototype of the tool for a specific gear model is 3D printed.RYC-2017-22649 BERC 2014-201

Multilinear Wavelets: A Statistical Shape Space for Human Faces

We present a statistical model for $3$D human faces in varying expression, which decomposes the surface of the face using a wavelet transform, and learns many localized, decorrelated multilinear models on the resulting coefficients. Using this model we are able to reconstruct faces from noisy and occluded $3$D face scans, and facial motion sequences. Accurate reconstruction of face shape is important for applications such as tele-presence and gaming. The localized and multi-scale nature of our model allows for recovery of fine-scale detail while retaining robustness to severe noise and occlusion, and is computationally efficient and scalable. We validate these properties experimentally on challenging data in the form of static scans and motion sequences. We show that in comparison to a global multilinear model, our model better preserves fine detail and is computationally faster, while in comparison to a localized PCA model, our model better handles variation in expression, is faster, and allows us to fix identity parameters for a given subject.Comment: 10 pages, 7 figures; accepted to ECCV 201

Interactive Brain Tumor Segmentation with Inclusion Constraints

This thesis proposes an improved interactive brain tumor segmentation method based on graph cuts, which is an efficient global optimization framework for image segmentation, and star shape, which is a general segmentation shape prior with minimal user assistance. Our improvements lie in volume ballooning, compactness measure and inclusion constraints. Volume ballooning is incorporated to help to balloon segmentation for situations where the foreground and background have similar appearance models and changing relative weight between appearance model and smoothness term cannot help to achieve an accurate segmentation. We search different ballooning parameters for different slices since an appropriate ballooning force may vary between slices. As the evaluation for goodness of segmentation in parameter searching, two new compactness measures are introduced, ellipse fitting and convexity deviation. Ellipse fitting is a measure of compactness based on the deviation from an ellipse of best fit, which prefers segmentation with an ellipse shape. And convexity deviation is a more strict measure for preferring convex segmentation. It uses the number of convexity violation pixels as the measure for compactness. Inclusion constraints is added between slices to avoid side slice segmentation larger than the middle slice problem. The inclusion constraints consist of mask inclusion, which is implemented by an unary term in graph cuts, and pairwise inclusion, which is implemented by a pairwise term. Margin is allowed in inclusion so that the inclusion region is enlarged. With all these improvements, the final result is promising. The best performance for our dataset is 88% compared to the previous system that achieved 87%