Query: Colorization using optimization

Relevant passages:
Scale-Space and Edge Detection Using Anisotropic Diffusion <=SEP=> Abstracf-The scale-space technique introduced by Witkin involves generating coarser resolution images by convolving the original image with a Gaussian kernel. This approach has a major drawback: it is difficult to obtain accurately the locations of the “semantically meaningful” edges at coarse scales. In this paper we suggest a new definition of scale-space, and introduce a class of algorithms that realize it using a diffusion process. The diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing in preference to interregion smoothing. It is shown that the “no new maxima should be generated at coarse scales” property of conventional scale space is preserved. As the region boundaries in our approach remain sharp, we obtain a high quality edge detector which successfully exploits global information. Experimental results are shown on a number of images. The algorithm involves elementary, local operations replicated over the image making parallel hardware implementations feasible.

Segmentation using Eigenvectors: A Unifying View <=SEP=> Automatic grouping and segmentation of images remains a challenging problem in computer vision. Recently, a number of authors have demonstrated good performance on this task using methods that are based on eigenvectors of the a nity matrix. These approaches are extremely attractive in that they are based on simple eigendecomposition algorithms whose stability is well understood. Nevertheless, the use of eigendecompositions in the context of segmentation is far from well understood. In this paper we give a unied treatment of these algorithms, and show the close connections between them while highlighting their distinguishing features. We then prove results on eigenvectors of block matrices that allow us to analyze the performance of these algorithms in simple grouping settings. Finally, we use our analysis to motivate a variation on the existing methods that combines aspects from di erent eigenvector segmentation algorithms. We illustrate our analysis with results on real and synthetic images. Human perceiving a scene can often easily segment it into coherent segments or groups. There has been a tremendous amount of e ort devoted to achieving the same level of performance in computer vision. In many cases, this is done by associating with each pixel a feature vector (e.g. color, motion, texture, position) and using a clustering or grouping algorithm on these feature vectors. Perhaps the cleanest approach to segmenting points in feature space is based on mixture models in which one assumes the data were generated by multiple processes and estimates the parameters of the processes and the number of components in the mixture. The assignment of points to clusters can then be easily performed by calculating the posterior probability of a point belonging to a cluster. Despite the elegance of this approach, the estimation process leads to a notoriously di cult optimization. The frequently used EM algorithm [3] often converges to a local maximum that depends on the initial conditions.

An Iterative Image Registration Technique with an Application to Stereo Vision <=SEP=> Image registration finds a variety of applications in computer vision. Unfortunately, traditional image registration techniques tend to be costly. We present a new image registration technique that makes use of the spatial intensity gradient of the images to find a good match using a type of Newton-Raphson iteration. Our technique is faster because it examines far fewer potential matches between the images than existing techniques. Furthermore, this registration technique can be generalized to handle rotation, scaling and shearing. We show show our technique can be adapted for use in a stereo vision system.

Normalized Cuts and Image Segmentation <=SEP=> w e propose Q novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the amage data, our approach aims a t extracting the global impression of an image. We treat image segmentation QS (I graph partitioning problem and propose Q novel global criterion, the normalized cut, for segmenting the graph. The normalized cut craterion measures both the total dissimilarity between the different groups QS well as the total similarity within the groups. We show that an eficient computational technique based on a generaked eigenvalue problem can be used to optimize this criterion. w e have applied this approach to segmenting static images and found results very enco u raging.

A Computational Approach to Edge Detection <=SEP=> This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge.

A First Look at a Telepresence System with Room-Sized Real-Time 3 D Capture and Life-Sized Tracked Display Wall <=SEP=> This paper provides a first look at a telepresence system offering room-sized, fully dynamic real-time 3D scene capture and continuous-viewpoint head-tracked display on a life-sized tiled display wall. The system is an expansion of a previous system, based an array of commodity depth sensors. We describe adjustments and improvements made to camera calibration, sensor data processing, data merger, rendering, and display, as required to scale the earlier system to room-sized.

Weighted extreme learning machine for imbalance learning <=SEP=> Extreme learning machine (ELM) is a competitive machine learning technique, which is simple in theory and fast in implementation. The network types are ‘‘generalized’’ single hidden layer feedforward networks, which are quite diversified in the form of variety in feature mapping functions or kernels. To deal with data with imbalanced class distribution, a weighted ELM is proposed which is able (1) it is simple in theory and convenient in implementation; (2) a wide type of feature mapping functions or kernels are available for the proposed framework; (3) the proposed method can be applied directly into multiclass classification tasks. In addition, after integrating with the weighting scheme, (1) the weighted ELM is able to deal with data with imbalanced class distribution while maintain the good performance on well balanced data as unweighted ELM; (2) by assigning different weights for each example according to users’ needs, the weighted ELM can be generalized to cost sensitive learning. & 2012 Elsevier B.V. All rights reserved.

Robust motion detection using histogram of oriented gradients for illumination variations <=SEP=> This paper proposes a robust motion detection method for illumination variations which uses histogram of oriented gradients. The detection process is divided into two phases: coarse detection and refinement. In the coarse detection phase, first, a texture-based background model is built which implements a group of adaptive histograms of oriented gradients; then, by comparing the histogram of oriented gradients of each pixel between current frame and background model, a foreground is segmented based on texture feature which is not susceptible to illumination variations, whereas some missing foreground regions exist; finally, the result based on texture is optimized by combining the pixel-wise detection result produced by Gaussian Mixture Model (GMM) algorithm, which greatly improves the detection performance by incorporating efficient morphological operations. In the refinement phase, the above detection result is refined based on the distinction in color feature to eliminate errors like shadows, noises, redundant contour, etc. Experimental results show the effectiveness and robustness of our approach in detecting moving objects in varying illumination conditions.

Renewable energy strategies for sustainable development <=SEP=> This paper discusses the perspective of renewable energy (wind, solar, wave and biomass) in the making of strategies for a sustainable development. Such strategies typically involve three major technological changes: energy savings on the demand side, efficiency improvements in the energy production, and replacement of fossil fuels by various sources of renewable energy. Consequently, large-scale renewable energy implementation plans must include strategies of how to integrate the renewable sources in coherent energy systems influenced by energy savings and efficiency measures. Based on the case of Denmark, this paper discusses the problems and perspectives of converting present energy systems into a 100 percent renewable energy system. The conclusion is that such development will be possible. The necessary renewable energy sources are present, if further technological improvements of the energy system are achieved. Especially technologies of converting the transportation and the introduction of flexible energy system technologies are crucial.

DeepSynth : Synthesizing A Musical Instrument With Video <=SEP=> This paper introduces DeepSynth, an end-to-end neural network model for generating the sound of a musical instrument based on a silent video of it being played. We specifically focus on building a synthesizer for the piano, but the ideas proposed in this paper are applicable to a wide range of musical instruments. At a high level, the model consists of a convolutional neural network (CNN) to extract features from the raw video frames and two stacked neural autoregressive models, one to encode the spatiotemporal features of the video and the other to generate the raw audio waveform.

Implementation of page rank algorithm in Hadoop MapReduce framework <=SEP=> One of the most popular algorithm in processing internet data i.e. webpages is page rank algorithm which is intended to decide the importance of a webpage by assigning a weighting value based on any incoming link to those webpage. However, the large amount of internet data may lead into computational burden in processing those page rank algorithm. To take into account those burden, in this paper we present a page rank processing algorithm over distributed system using Hadoop MapReduce framework called MR PageRank. Our algorithm can be decomposed into three processes, each of which is implemented in one Map and Reduce job. We first parse the raw webpage input to produce title of page and its outgoing links as key and value pair, respectively, as well as total dangling node's weight and total amount of pages. We next calculate the probability of each page and distribute this probability to each of outgoing link evenly. Each of the outgoing weight is shuffled and aggregated based on similarity of page title to update a new weighting value of each page. Notice that in the calculation we consider the dangling node and jumping factor. In the end, all of the page are descendingly sorted based on their weighting values. From the experimental result, we show that our implementation has output with reasonable ordering result. This electronic document is a “live” template and already defines the components of your paper.

Big Data Analytics with Spark <=SEP=> What’s more, Big Data Analytics with Spark provides an introduction to other big data technologies that are commonly used along with Spark, such as HDFS, Avro, Parquet, Ka a, Cassandra, HBase, Mesos, and so on. It also provides an introduction to machine learning and graph concepts. So the book is self-suffi cient; all the technologies that you need to know to use Spark are covered. The only thing that you are expected to have is some programming knowledge in any language.

Variation in the impact of social network characteristics on physical functioning in elderly persons: MacArthur Studies of Successful Aging. <=SEP=> OBJECTIVES
Social support and social networks have been shown to exert significant effects on health and functioning among elderly persons. Although theorists have speculated that the strength of these effects may differ as a function of sociodemographic characteristics and prior health status, few studies have directly tested the moderating effects of these variables.


METHODS
Longitudinal data from the MacArthur Study of Successful Aging were used to examine the effects of structural and functional social support on changes in physical functioning over a 7-year period, measured by the Nagi scale, in a sample of initially high-functioning men and women aged 70 to 79 years. Multiple regression analyses were used to test the main effects of social support and social network variables, as well as their interactions with gender, income, and baseline physical performance.


RESULTS
After controlling for potential confounding effects, respondents with more social ties showed less functional decline. The beneficial effects of social ties were stronger for respondents who were male or had lower levels of baseline physical performance.


DISCUSSION
The effects of social support and social networks may vary according to the individual's gender and baseline physical capabilities. Studies of functional decline among elderly persons should not ignore this population variation in the effects of social networks.

Design and Implementation of Autonomous Car using Raspberry Pi <=SEP=> The project aims to build a monocular vision autonomous car prototype using Raspberry Pi as a processing chip. An HD camera along with an ultrasonic sensor is used to provide necessary data from the real world to the car. The car is capable of reaching the given destination safely and intelligently thus avoiding the risk of human errors. Many existing algorithms like lane detection, obstacle detection are combined together to provide the necessary control to the car.

Routing and Wavelength Assignment in Optical WDM Networks <=SEP=> This article discusses the routing and wavelength assignment (RWA) problem in optical networks employing wavelenength division multiplexing (WDM) technology. Two variants of the problem are studied: static RWA, whereby the traffic requirements are known in advance, and dynamic RWA in which connection requests arrive in some random fashion. Both point-topoint and multicast traffic demands are considered.

Correcting a metacognitive error: feedback increases retention of low-confidence correct responses. <=SEP=> Previous studies investigating posttest feedback have generally conceptualized feedback as a method for correcting erroneous responses, giving virtually no consideration to how feedback might promote learning of correct responses. Here, the authors show that when correct responses are made with low confidence, feedback serves to correct this initial metacognitive error, enhancing retention of low-confidence correct responses. In 2 experiments, subjects took an initial multiple-choice test on general knowledge facts and made a confidence judgment after each response. Feedback was provided for half of the questions, and retention was assessed by a final cued-recall test. Taking the initial test improved retention relative to not testing, and feedback further enhanced performance. Consistent with prior research, feedback improved retention by allowing subjects to correct initially erroneous responses. Of more importance, feedback also doubled the retention of correct low-confidence responses, relative to providing no feedback. The function of feedback is to correct both memory errors and metacognitive errors.

Low-Power High-Efficiency Class D Audio Power Amplifiers <=SEP=> The architecture, design, and implementation of two clock-free analog class D audio power amplifiers using 0.5 ¿m CMOS standard technology are introduced. The amplifiers are designed to consume significantly less power than former implementations. Both designs operate with a 2.7 V single voltage supply and deliver a maximum output power of 250 mW into an 8 ¿ speaker. The two class-D amplifiers are based on a hysteretic sliding mode controller, which avoids the complex task of generating the highly linear triangle carrier signal used in conventional architectures. The first design generates a two-level modulated signal, known as binary modulated amplifier (BMA); the second topology implements a three-level modulated signal, also called ternary modulated amplifier (TMA). The architectures and implementations are simple and compact, providing very low quiescent power consumption. Experimental results of the BMA/TMA yield an efficiency of 89/90% and a total harmonic distortion plus noise (THD+N) of 0.02/0.03%, respectively. The efficiency and linearity is comparable to state-of-the-art amplifiers but the static power consumption is less than one tenth of previous proposed architectures. Both class D amplifiers achieve a power supply rejection ratio greater than 75 dB at 217 Hz, and a signal-to-noise ratio (SNR) higher than 90 dB within the whole audio band. Each amplifier occupies less than 1.5 mm2.

Incremental Clustering of Mobile Objects <=SEP=> Moving objects are becoming increasingly attractive to the data mining community due to continuous advances in technologies like GPS, mobile computers, and wireless communication devices. Mining spatio-temporal data can benefit many different functions: marketing team managers for identifying the right customers at the right time, cellular companies for optimizing the resources allocation, web site administrators for data allocation matters, animal migration researchers for understanding migration patterns, and meteorology experts for weather forecasting. In this research we use a compact representation of a mobile trajectory and define a new similarity measure between trajectories. We also propose an incremental clustering algorithm for finding evolving groups of similar mobile objects in spatio-temporal data. The algorithm is evaluated empirically by the quality of object clusters (using Dunn and Rand indexes), memory space efficiency, execution times, and scalability (run time vs. number of objects).

Filling Knowledge Base Gaps for Distant Supervision of Relation Extraction <=SEP=> Distant supervision has attracted recent interest for training information extraction systems because it does not require any human annotation but rather employs existing knowledge bases to heuristically label a training corpus. However, previous work has failed to address the problem of false negative training examples mislabeled due to the incompleteness of knowledge bases. To tackle this problem, we propose a simple yet novel framework that combines a passage retrieval model using coarse features into a state-of-the-art relation extractor using multi-instance learning with fine features. We adapt the information retrieval technique of pseudorelevance feedback to expand knowledge bases, assuming entity pairs in top-ranked passages are more likely to express a relation. Our proposed technique significantly improves the quality of distantly supervised relation extraction, boosting recall from 47.7% to 61.2% with a consistently high level of precision of around 93% in the experiments.

Common-Specific Multimodal Learning for Deep Belief Network <=SEP=> Multimodal Deep Belief Network has been widely used to extract representations for multimodal data by fusing the high-level features of each data modality into common representations. Such straightforward fusion strategy can benefit the classification and information retrieval tasks. However, it may introduce noise in case the high-level features are not naturally common hence non-fusable for different modalities. Intuitively, each modality may have its own specific features and corresponding representation capabilities thus should not be simply fused. Therefore, it is more reasonable to fuse only the common features and represent the multimodal data by both the fused features and the modality-specific features. To distinguish common features from modal-specific features is a challenging task for traditional DBN models where all features are crudely mixed. This paper proposes the Common-Specific Multimodal Deep Belief Network (CSDBN) to solve the problem. CS-DBN automatically separates common features from modal-specific features and fuses only the common ones for data representation. Experimental results demonstrate the superiority of CS-DBN for classification tasks compared with the baseline approaches.

Pastry: Scalable, distributed object location and routing for large-scale peer-to- <=SEP=> This paper presents the design and evaluation of Pastry, a sc al ble, distributed object location and routing scheme for wide-ar a peer-to-peer applications. Pastry performs application-level routing and ob ject location in a potentially very large overlay network of nodes connected via the Int rnet. It can be used to support a wide range of peer-to-peer applications li ke g obal data storage, global data sharing, and naming. An insert operation in Pastry stores an object at a user-defin ed number of diverse nodes within the Pastry network. A lookup operation reliabl y retrieves a copy of the requested object if one exists. Moreover, a lookup is usu ally routed to the node nearest the client issuing the lookup (by some measure of pro ximity), among the nodes storing the requested object. Pastry is completely de centralized, scalable, and self-configuring; it automatically adapts to the arriva l, departure and failure of nodes. Experimental results obtained with a prototype implementa tion on a simulated network of up to 100,000 nodes confirm Pastry’s scalability, its ability to selfconfigure and adapt to node failures, and its good network loc ality properties.

Face-to-face transfer of wafer-scale graphene films <=SEP=> Graphene has attracted worldwide interest since its experimental discovery, but the preparation of large-area, continuous graphene film on SiO2/Si wafers, free from growth-related morphological defects or transfer-induced cracks and folds, remains a formidable challenge. Growth of graphene by chemical vapour deposition on Cu foils has emerged as a powerful technique owing to its compatibility with industrial-scale roll-to-roll technology. However, the polycrystalline nature and microscopic roughness of Cu foils means that such roll-to-roll transferred films are not devoid of cracks and folds. High-fidelity transfer or direct growth of high-quality graphene films on arbitrary substrates is needed to enable wide-ranging applications in photonics or electronics, which include devices such as optoelectronic modulators, transistors, on-chip biosensors and tunnelling barriers. The direct growth of graphene film on an insulating substrate, such as a SiO2/Si wafer, would be useful for this purpose, but current research efforts remain grounded at the proof-of-concept stage, where only discontinuous, nanometre-sized islands can be obtained. Here we develop a face-to-face transfer method for wafer-scale graphene films that is so far the only known way to accomplish both the growth and transfer steps on one wafer. This spontaneous transfer method relies on nascent gas bubbles and capillary bridges between the graphene film and the underlying substrate during etching of the metal catalyst, which is analogous to the method used by tree frogs to remain attached to submerged leaves. In contrast to the previous wet or dry transfer results, the face-to-face transfer does not have to be done by hand and is compatible with any size and shape of substrate; this approach also enjoys the benefit of a much reduced density of transfer defects compared with the conventional transfer method. Most importantly, the direct growth and spontaneous attachment of graphene on the underlying substrate is amenable to batch processing in a semiconductor production line, and thus will speed up the technological application of graphene.

A Simple and Accurate Syntax-Agnostic Neural Model for Dependency-based Semantic Role Labeling <=SEP=> We introduce a simple and accurate neural model for dependency-based semantic role labeling. Our model predicts predicate-argument dependencies relying on states of a bidirectional LSTM encoder. The semantic role labeler achieves competitive performance on English, even without any kind of syntactic information and only using local inference. However, when automatically predicted partof-speech tags are provided as input, it substantially outperforms all previous local models and approaches the best reported results on the English CoNLL2009 dataset. We also consider Chinese, Czech and Spanish where our approach also achieves competitive results. Syntactic parsers are unreliable on out-of-domain data, so standard (i.e., syntactically-informed) SRL models are hindered when tested in this setting. Our syntax-agnostic model appears more robust, resulting in the best reported results on standard out-of-domain test sets.

Memristor-Based Material Implication (IMPLY) Logic: Design Principles and Methodologies <=SEP=> Memristors are novel devices, useful as memory at all hierarchies. These devices can also behave as logic circuits. In this paper, the IMPLY logic gate, a memristor-based logic circuit, is described. In this memristive logic family, each memristor is used as an input, output, computational logic element, and latch in different stages of the computing process. The logical state is determined by the resistance of the memristor. This logic family can be integrated within a memristor-based crossbar, commonly used for memory. In this paper, a methodology for designing this logic family is proposed. The design methodology is based on a general design flow, suitable for all deterministic memristive logic families, and includes some additional design constraints to support the IMPLY logic family. An IMPLY 8-bit full adder based on this design methodology is presented as a case study.

Video Super-Resolution via Bidirectional Recurrent Convolutional Networks <=SEP=> Super resolving a low-resolution video, namely video super-resolution (SR), is usually handled by either single-image SR or multi-frame SR. Single-Image SR deals with each video frame independently, and ignores intrinsic temporal dependency of video frames which actually plays a very important role in video SR. Multi-Frame SR generally extracts motion information, e.g., optical flow, to model the temporal dependency, but often shows high computational cost. Considering that recurrent neural networks (RNNs) can model long-term temporal dependency of video sequences well, we propose a fully convolutional RNN named bidirectional recurrent convolutional network for efficient multi-frame SR. Different from vanilla RNNs, 1) the commonly-used full feedforward and recurrent connections are replaced with weight-sharing convolutional connections. So they can greatly reduce the large number of network parameters and well model the temporal dependency in a finer level, i.e., patch-based rather than frame-based, and 2) connections from input layers at previous timesteps to the current hidden layer are added by 3D feedforward convolutions, which aim to capture discriminate spatio-temporal patterns for short-term fast-varying motions in local adjacent frames. Due to the cheap convolutional operations, our model has a low computational complexity and runs orders of magnitude faster than other multi-frame SR methods. With the powerful temporal dependency modeling, our model can super resolve videos with complex motions and achieve well performance.

Semi-supervised time series classification <=SEP=> The problem of time series classification has attracted great interest in the last decade. However current research assumes the existence of large amounts of labeled training data. In reality, such data may be very difficult or expensive to obtain. For example, it may require the time and expertise of cardiologists, space launch technicians, or other domain specialists. As in many other domains, there are often copious amounts of unlabeled data available. For example, the PhysioBank archive contains gigabytes of ECG data. In this work we propose a semi-supervised technique for building time series classifiers. While such algorithms are well known in text domains, we will show that special considerations must be made to make them both efficient and effective for the time series domain. We evaluate our work with a comprehensive set of experiments on diverse data sources including electrocardiograms, handwritten documents, and video datasets. The experimental results demonstrate that our approach requires only a handful of labeled examples to construct accurate classifiers.

Directly Fabricating Soft Robotic Actuators With an Open-Source 3-D Printer <=SEP=> 3-D printing silicone has been a long sought for goal by roboticists. Fused deposition manufacturing (FDM) is a readily accessible and simple 3-D printing scheme that could hold the key to printing silicone. This study details an approach to 3-D print silicone elastomer through use of a thickening additive and heat curing techniques. We fabricated an identical control actuator using molding and 3-D printing techniques for comparison. By comparing the free space elongation and fixed length force of both actuators, we were able to evaluate the quality of the print. We observed that the 3-D printed linear actuator was able to perform similarly to the molded actuator, with an average error of 5.08% in actuator response, establishing the feasibility of such a system. We envision that further development of this system would contribute to the way soft robotic systems are fabricated.

Luhn Revisited: Significant Words Language Models <=SEP=> Users tend to articulate their complex information needs in only a few keywords, making underspecified statements of request the main bottleneck for retrieval effectiveness. Taking advantage of feedback information is one of the best ways to enrich the query representation, but can also lead to loss of query focus and harm performance in particular when the initial query retrieves only little relevant information when overfitting to accidental features of the particular observed feedback documents. Inspired by the early work of Luhn [23], we propose significant words language models of feedback documents that capture all, and only, the significant shared terms from feedback documents. We adjust the weights of common terms that are already well explained by the document collection as well as the weight of rare terms that are only explained by specific feedback documents, which eventually results in having only the significant terms left in the feedback model.
 Our main contributions are the following. First, we present significant words language models as the effective models capturing the essential terms and their probabilities. Second, we apply the resulting models to the relevance feedback task, and see a better performance over the state-of-the-art methods. Third, we see that the estimation method is remarkably robust making the models in- sensitive to noisy non-relevant terms in feedback documents. Our general observation is that the significant words language models more accurately capture relevance by excluding general terms and feedback document specific terms.

Performance Engineering for Microservices: Research Challenges and Directions <=SEP=> Microservices complement approaches like DevOps and continuous delivery in terms of software architecture. Along with this architectural style, several important deployment technologies, such as container-based virtualization and container orchestration solutions, have emerged. These technologies allow to efficiently exploit cloud platforms, providing a high degree of scalability, availability, and portability for microservices.
 Despite the obvious importance of a sufficient level of performance, there is still a lack of performance engineering approaches explicitly taking into account the particularities of microservices. In this paper, we argue why new solutions to performance engineering for microservices are needed. Furthermore, we identify open issues and outline possible research directions with regard to performance-aware testing, monitoring, and modeling of microservices.

ABF + + : Fast and Robust Angle Based Flattening Temporary version-In print <=SEP=> Conformal parameterization of mesh models has numerous applications in geometry processing. Conformality is desirable for remeshing, surface reconstruction, and many other mesh processing applications. Subject to the conformality requirement, these applications typically bene t from parameterizations with smaller stretch. The Angle Based Flattening (ABF) method, presented a few years ago, generates provably valid conformal parameterizations with low stretch. However, it is quite time consuming and becomes error prone for large meshes due to numerical error accumulation. This work presents ABF++, a highly e cient extension of the ABF method that overcomes these drawbacks, while maintaining all the advantages of ABF. ABF++ robustly parameterizes meshes of hundreds of thousands and millions of triangles within minutes. It is based on two main components: (1) a new numerical solution technique that dramatically reduces the dimension of the linear systems solved at each iteration, speeding up the solution; (2) an e cient hierarchical solution technique. The speedup with (1) does not come at the expense of greater distortion. The hierarchical technique (2) enables parameterization of models with millions of faces in seconds, at the expense of a minor increase in parametric distortion. The parameterization computed by ABF++ are provably valid, i.e. they contain no ipped triangles. As a result of these extensions, the ABF++ method is extremely suitable for robustly and e ciently parameterizing models for geometry processing applications.