arXiv subjects

Peter Wonka

Publications and source records attributed to Peter Wonka.

174 records · Page 10Linked to original sources

arXiv2018

Fast Convolutional Sparse Coding in the Dual Domain

Convolutional sparse coding (CSC) is an important building block of many computer vision applications ranging from image and video compression to deep learning. We present two contributions to the state of the art in CSC. First, we significantly speed up the computation by proposing a new optimization framework that tackles the problem in the dual domain. Second, we extend the original formulation to higher dimensions in order to process a wider range of inputs, such as RGB images and videos. Our results show up to 20 times speedup compared to current state-of-the-art CSC solvers.

cs.CV↗

arXiv2018

Supervised Convolutional Sparse Coding

Convolutional Sparse Coding (CSC) is a well-established image representation model especially suited for image restoration tasks. In this work, we extend the applicability of this model by proposing a supervised approach to convolutional sparse coding, which aims at learning discriminative dictionaries instead of purely reconstructive ones. We incorporate a supervised regularization term into the traditional unsupervised CSC objective to encourage the final dictionary elements to be discriminative. Experimental results show that using supervised convolutional learning results in two key advantages. First, we learn more semantically relevant filters in the dictionary and second, we achieve improved image reconstruction on unseen data.

cs.CV↗

arXiv2016

TRex: A Tomography Reconstruction Proximal Framework for Robust Sparse View X-Ray Applications

We present TRex, a flexible and robust Tomographic Reconstruction framework using proximal algorithms. We provide an overview and perform an experimental comparison between the famous iterative reconstruction methods in terms of reconstruction quality in sparse view situations. We then derive the proximal operators for the four best methods. We show the flexibility of our framework by deriving solvers for two noise models: Gaussian and Poisson; and by plugging in three powerful regularizers. We compare our framework to state of the art methods, and show superior quality on both synthetic and real datasets.

math.OC↗

arXiv2016

Curve Networks for Surface Reconstruction

Man-made objects usually exhibit descriptive curved features (i.e., curve networks). The curve network of an object conveys its high-level geometric and topological structure. We present a framework for extracting feature curve networks from unstructured point cloud data. Our framework first generates a set of initial curved segments fitting highly curved regions. We then optimize these curved segments to respect both data fitting and structural regularities. Finally, the optimized curved segments are extended and connected into curve networks using a clustering method. To facilitate effectiveness in case of severe missing data and to resolve ambiguities, we develop a user interface for completing the curve networks. Experiments on various imperfect point cloud data validate the effectiveness of our curve network extraction framework. We demonstrate the usefulness of the extracted curve networks for surface reconstruction from incomplete point clouds.

cs.GR↗

arXiv2015

Computational Network Design from Functional Specifications

Connectivity and layout of underlying networks largely determine the behavior of many environments. For example, transportation networks determine the flow of traffic in cities, or maps determine the difficulty and flow in games. Designing such networks from scratch is challenging as even local network changes can have large global effects. We investigate how to computationally create networks starting from {\em only} high-level functional specifications. Such specifications can be in the form of network density, travel time versus network length, traffic type, destination locations, etc. We propose an integer programming-based approach that guarantees that the resultant networks are valid by fulfilling all specified hard constraints, and score favorably in terms of the objective function. We evaluate our algorithm in three different design settings (i.e., street layout, floorplanning, and game level design) and demonstrate, for the first time, that diverse networks can emerge purely from high-level functional specifications.

cs.CG↗

arXiv2015

RAID: A Relation-Augmented Image Descriptor

As humans, we regularly interpret images based on the relations between image regions. For example, a person riding object X, or a plank bridging two objects. Current methods provide limited support to search for images based on such relations. We present RAID, a relation-augmented image descriptor that supports queries based on inter-region relations. The key idea of our descriptor is to capture the spatial distribution of simple point-to-region relationships to describe more complex relationships between two image regions. We evaluate the proposed descriptor by querying into a large subset of the Microsoft COCO database and successfully extract nontrivial images demonstrating complex inter-region relations, which are easily missed or erroneously classified by existing methods.

cs.GR↗

arXiv2014

Lasso Screening Rules via Dual Polytope Projection

Lasso is a widely used regression technique to find sparse representations. When the dimension of the feature space and the number of samples are extremely large, solving the Lasso problem remains challenging. To improve the efficiency of solving large-scale Lasso problems, El Ghaoui and his colleagues have proposed the SAFE rules which are able to quickly identify the inactive predictors, i.e., predictors that have $0$ components in the solution vector. Then, the inactive predictors or features can be removed from the optimization problem to reduce its scale. By transforming the standard Lasso to its dual form, it can be shown that the inactive predictors include the set of inactive constraints on the optimal dual solution. In this paper, we propose an efficient and effective screening rule via Dual Polytope Projections (DPP), which is mainly based on the uniqueness and nonexpansiveness of the optimal dual solution due to the fact that the feasible set in the dual space is a convex and closed polytope. Moreover, we show that our screening rule can be extended to identify inactive groups in group Lasso. To the best of our knowledge, there is currently no "exact" screening rule for group Lasso. We have evaluated our screening rule using synthetic and real data sets. Results show that our rule is more effective in identifying inactive predictors than existing state-of-the-art screening rules for Lasso.

cs.LG↗

arXiv2014

Inverse Procedural Modeling of Facade Layouts

In this paper, we address the following research problem: How can we generate a meaningful split grammar that explains a given facade layout? To evaluate if a grammar is meaningful, we propose a cost function based on the description length and minimize this cost using an approximate dynamic programming framework. Our evaluation indicates that our framework extracts meaningful split grammars that are competitive with those of expert users, while some users and all competing automatic solutions are less successful.

cs.GR↗

arXiv2013

Fused Multiple Graphical Lasso

In this paper, we consider the problem of estimating multiple graphical models simultaneously using the fused lasso penalty, which encourages adjacent graphs to share similar structures. A motivating example is the analysis of brain networks of Alzheimer's disease using neuroimaging data. Specifically, we may wish to estimate a brain network for the normal controls (NC), a brain network for the patients with mild cognitive impairment (MCI), and a brain network for Alzheimer's patients (AD). We expect the two brain networks for NC and MCI to share common structures but not to be identical to each other; similarly for the two brain networks for MCI and AD. The proposed formulation can be solved using a second-order method. Our key technical contribution is to establish the necessary and sufficient condition for the graphs to be decomposable. Based on this key property, a simple screening rule is presented, which decomposes the large graphs into small subgraphs and allows an efficient estimation of multiple independent (small) subgraphs, dramatically reducing the computational cost. We perform experiments on both synthetic and real data; our results demonstrate the effectiveness and efficiency of the proposed approach.

cs.LG↗

arXiv2013

Scaling SVM and Least Absolute Deviations via Exact Data Reduction

The support vector machine (SVM) is a widely used method for classification. Although many efforts have been devoted to develop efficient solvers, it remains challenging to apply SVM to large-scale problems. A nice property of SVM is that the non-support vectors have no effect on the resulting classifier. Motivated by this observation, we present fast and efficient screening rules to discard non-support vectors by analyzing the dual problem of SVM via variational inequalities (DVI). As a result, the number of data instances to be entered into the optimization can be substantially reduced. Some appealing features of our screening method are: (1) DVI is safe in the sense that the vectors discarded by DVI are guaranteed to be non-support vectors; (2) the data set needs to be scanned only once to run the screening, whose computational cost is negligible compared to that of solving the SVM problem; (3) DVI is independent of the solvers and can be integrated with any existing efficient solvers. We also show that the DVI technique can be extended to detect non-support vectors in the least absolute deviations regression (LAD). To the best of our knowledge, there are currently no screening methods for LAD. We have evaluated DVI on both synthetic and real data sets. Experiments indicate that DVI significantly outperforms the existing state-of-the-art screening rules for SVM, and is very effective in discarding non-support vectors for LAD. The speedup gained by DVI rules can be up to two orders of magnitude.

cs.LG↗

arXiv2013

Gap Processing for Adaptive Maximal Poisson-Disk Sampling

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or have their radius changed. We build on the concepts of the regular triangulation and the power diagram. Third, we will show how our analysis can make a contribution to the state-of-the-art in surface remeshing.

cs.GR↗

arXiv2013

A Safe Screening Rule for Sparse Logistic Regression

The l1-regularized logistic regression (or sparse logistic regression) is a widely used method for simultaneous classification and feature selection. Although many recent efforts have been devoted to its efficient implementation, its application to high dimensional data still poses significant challenges. In this paper, we present a fast and effective sparse logistic regression screening rule (Slores) to identify the 0 components in the solution vector, which may lead to a substantial reduction in the number of features to be entered to the optimization. An appealing feature of Slores is that the data set needs to be scanned only once to run the screening and its computational cost is negligible compared to that of solving the sparse logistic regression problem. Moreover, Slores is independent of solvers for sparse logistic regression, thus Slores can be integrated with any existing solver to improve the efficiency. We have evaluated Slores using high-dimensional data sets from different applications. Extensive experimental results demonstrate that Slores outperforms the existing state-of-the-art screening rules and the efficiency of solving sparse logistic regression is improved by one magnitude in general.

cs.LG↗