On top of Segment Anything Model (SAM), SAM 2 further extends its capability from image to video inputs through a memory bank mechanism and obtains a remarkable performance compared with previous methods, making it a foundation model for video segmentation task. In this paper, we aim at making SAM 2 much more efficient so that it even runs on mobile devices while maintaining a comparable performance. Despite several works optimizing SAM for better efficiency, we find they are not sufficient for SAM 2 because they all focus on compressing the image encoder, while our benchmark shows that the newly introduced memory attention blocks are also the latency bottleneck. Given this observation, we propose EdgeTAM, which leverages a novel 2D Spatial Perceiver to reduce the computational cost. In particular, the proposed 2D Spatial Perceiver encodes the densely stored frame-level memories with a lightweight Transformer that contains a fixed set of learnable queries. Given that video segmentation is a dense prediction task, we find preserving the spatial structure of the memories is essential so that the queries are split into global-level and patch-level groups. We also propose a distillation pipeline that further improves the performance without inference overhead. As a result, EdgeTAM achieves 87.7, 70.0, 72.3, and 71.7 ${\mathcal{J}}{{\& }}{\mathcal{F}}$ on DAVIS 2017, MOSE, SA-V val, and SA-V test, while running at 16 FPS on iPhone 15 Pro Max. The code and models are available here.

In this work, we propose Visual-Predictive Instruction Tuning (VPiT) - a simple and effective extension to visual instruction tuning that enables a pretrained LLM to quickly morph into an unified autoregressive model capable of generating both text and visual tokens. VPiT teaches an LLM to predict discrete text tokens and continuous visual tokens from any input sequence of image and text data curated in an instruction-following format. Our empirical investigation reveals several intriguing properties of VPiT: (1) visual generation ability emerges as a natural byproduct of improved visual understanding, and can be unlocked efficiently with a small amount of generation data; (2) while we find understanding and generation to be mutually beneficial, understanding data contributes to both capabilities more effectively than generation data. Building upon these findings, we train our MetaMorph model and achieve competitive performance on both visual understanding and generation. In visual generation, MetaMorph can leverage the world knowledge and reasoning abilities gained from LLM pretraining, and overcome common failure modes exhibited by other generation models. Our results suggest that LLMs may have strong "prior" vision capabilities that can be efficiently adapted to both visual understanding and generation with a relatively simple instruction tuning process.

Segment Anything Model 2 (SAM 2) has emerged as a powerful tool for video object segmentation and tracking anything. Key components of SAM 2 that drive the impressive video object segmentation performance include a large multistage image encoder for frame feature extraction and a memory mechanism that stores memory contexts from past frames to help current frame segmentation. The high computation complexity of multistage image encoder and memory module has limited its applications in real-world tasks, e.g., video object segmentation on mobile devices. To address this limitation, we propose EfficientTAMs, lightweight track anything models that produce high-quality results with low latency and model size. Our idea is based on revisiting the plain, nonhierarchical Vision Transformer (ViT) as an image encoder for video object segmentation, and introducing an efficient memory module, which reduces the complexity for both frame feature extraction and memory computation for current frame segmentation. We take vanilla lightweight ViTs and efficient memory module to build EfficientTAMs, and train the models on SA-1B and SA-V datasets for video object segmentation and track anything tasks. We evaluate on multiple video segmentation benchmarks including semi-supervised VOS and promptable video segmentation, and find that our proposed EfficientTAM with vanilla ViT perform comparably to SAM 2 model (HieraB+SAM 2) with ~2x speedup on A100 and ~2.4x parameter reduction. On segment anything image tasks, our EfficientTAMs also perform favorably over original SAM with ~20x speedup on A100 and ~20x parameter reduction. On mobile devices such as iPhone 15 Pro Max, our EfficientTAMs can run at ~10 FPS for performing video object segmentation with reasonable quality, highlighting the capability of small models for on-device video object segmentation applications.

Multimodal Large Language Models (MLLMs) have shown promising progress in understanding and analyzing video content. However, processing long videos remains a significant challenge constrained by LLM's context size. To address this limitation, we propose \textbf{LongVU}, a spatiotemporal adaptive compression mechanism that reduces the number of video tokens while preserving visual details of long videos. Our idea is based on leveraging cross-modal query and inter-frame dependencies to adaptively reduce temporal and spatial redundancy in videos. Specifically, we leverage DINOv2 features to remove redundant frames that exhibit high similarity. Then we utilize text-guided cross-modal query for selective frame feature reduction. Further, we perform spatial token reduction across frames based on their temporal dependencies. Our adaptive compression strategy effectively processes a large number of frames with little visual information loss within given context length. Our LongVU consistently surpass existing methods across a variety of video understanding benchmarks, especially on hour-long video understanding tasks such as VideoMME and MLVU. Given a light-weight LLM, our LongVU also scales effectively into a smaller size with state-of-the-art video understanding performance.

Contemporary evaluation techniques are inadequate for agentic systems. These approaches either focus exclusively on final outcomes—ignoring the step-by-step nature of the thinking done by agentic systems—or require excessive manual labour. To address this, we introduce the Agent-as-a-Judge framework, wherein agentic systems are used to evaluate agentic systems. This is a natural extension of the LLM-as-a-Judge framework, incorporating agentic features that enable intermediate feedback for the entire task-solving processes for more precise evaluations. We apply the Agent-as-a-Judge framework to the task of code generation. To overcome issues with existing benchmarks and provide a proof-of-concept testbed for Agent-as-a-Judge, we present DevAI, a new benchmark of 55 realistic AI code generation tasks. DevAI includes rich manual annotations, like a total of 365 hierarchical solution requirements, which make it particularly suitable for an agentic evaluator. We benchmark three of the top code-generating agentic systems using Agent-as-a-Judge and find that our framework dramatically outperforms LLM-as-a-Judge and is as reliable as our human evaluation baseline. Altogether, we believe that this work represents a concrete step towards enabling vastly more sophisticated agentic systems. To help that, our dataset and the full implementation of Agent-as-a-Judge will be publically available at https://github.com/metauto-ai/agent-as-a-judge

The optimal bit-width for achieving the best trade-off between quantized model size and accuracy has been a subject of ongoing debate. While some advocate for 4-bit quantization, others propose that 1.58-bit offers superior results. However, the lack of a cohesive framework for different bits has left such conclusions relatively tenuous. We present ParetoQ, the first unified framework that facilitates rigorous comparisons across 1-bit, 1.58-bit, 2-bit, 3-bit, and 4-bit quantization settings. Our findings reveal a notable learning transition between 2 and 3 bits: For 3-bits and above, the fine-tuned models stay close to their original pre-trained distributions, whereas for learning 2-bit networks or below, the representations change drastically. By optimizing training schemes and refining quantization functions, ParetoQ surpasses all previous methods tailored to specific bit widths. Remarkably, our ParetoQ ternary 600M-parameter model even outperforms the previous SoTA ternary 3B-parameter model in accuracy, using only one-fifth of the parameters. Extensive experimentation shows that ternary, 2-bit, and 3-bit quantization maintains comparable performance in the size-accuracy trade-off and generally exceeds 4-bit and binary quantization. Considering hardware constraints, 2-bit quantization offers promising potential for memory reduction and speedup.

Fusing 3D LiDAR features with 2D camera features is a promising technique for enhancing the accuracy of 3D detection, thanks to their complementary physical properties. While most of the existing methods focus on directly fusing camera features with raw LiDAR point clouds or shallow-level 3D features, it is observed that directly combining 2D and 3D features in deeper layers actually leads to a decrease in accuracy due to feature misalignment. The misalignment, which stems from the aggregation of features learned from large receptive fields, becomes increasingly more severe as we delve into deeper layers. In this paper, we propose PathFusion as a solution to enable the alignment of semantically coherent LiDAR-camera deep feature fusion. PathFusion introduces a path consistency loss at multiple stages within the network, encouraging the 2D backbone and its fusion path to transform 2D features in a way that aligns semantically with the transformation of the 3D backbone. This ensures semantic consistency between 2D and 3D features, even in deeper layers, and amplifies the usage of the network’s learning capacity. We apply PathFusion to improve a prior-art fusion baseline, Focals Conv, and observe an improvement of over 1.2% in mAP on the nuScenes test split consistently with and without testing-time data augmentations, and moreover, PathFusion also improves KITTI AP3D(R11) by about 0.6% on the moderate level.

Segment Anything Model (SAM) has emerged as a powerful tool for numerous vision applications. A key component that drives the impressive performance for zero-shot trans-fer and high versatility is a super large Transformer model trained on the extensive high-quality SA -1 B dataset. While beneficial, the huge computation cost of SAM model has limited its applications to wider real-world applications. To address this limitation, we propose EfficientSAMs, light-weight SAM models that exhibits decent performance with largely reduced complexity. Our idea is based on leveraging masked image pretraining, SAMI, which learns to reconstruct features from SAM image encoder for effective visual representation learning. Further, we take SAMI-pretrained light-weight image encoders and mask decoder to build Effi-cientSAMs, and finetune the models on SA -1B for segment anything task. We perform evaluations on multiple vision tasks including image classification, object detection, in-stance segmentation, and semantic segmentation, and find that our proposed pretraining method, SAMI, consistently outperforms other masked image pretraining methods. On segment anything task such as zero-shot instance segmentation, our EfficientSAMs with SAMI-pretrained lightweight image encoders perform favorably with a significant gain (e.g., rv4 AP on COCOILVIS) over other fast SAM models. Our EfficientSAM code and models are available at here.

This paper addresses the growing need for efficient large language models (LLMs) on mobile devices, driven by increasing cloud costs and latency concerns. We focus on designing top-quality LLMs with fewer than a billion parameters, a practical choice for mobile deployment. Contrary to prevailing belief emphasizing the pivotal role of data and parameter quantity in determining model quality, our investigation underscores the significance of model architecture for sub-billion scale LLMs. Leveraging deep and thin architectures, coupled with embedding sharing and grouped-query attention mechanisms, we establish a strong baseline network denoted as MobileLLM, which attains a remarkable 2.7%/4.3% accuracy boost over preceding 125M/350M state-of-the-art models. Additionally, we propose an immediate block-wise weight-sharing approach with no increase in model size and only marginal latency overhead. The resultant models, denoted as MobileLLM-LS, demonstrate a further accuracy enhancement of 0.7%/0.8% than MobileLLM 125M/350M. Moreover, MobileLLM model family shows significant improvements compared to previous sub-billion models on chat benchmarks, and demonstrates close correctness to LLaMA-v2 7B in API calling tasks, highlighting the capability of small models for common on-device use cases.

Flow matching has been successfully applied onto generative models, particularly in producing high-quality images and audio. However, the iterative sampling required for the ODE solver in flow matching-based approaches can be time-consuming. Reflow finetune, a technique derived from Rectified flow, offers a promising solution by transforming the ODE trajectory into a straight one, thereby reducing the number of sampling steps. In this paper, we focus on developing data-efficient flow-based approaches for text-to-audio generation. We found that directly applying reflow to the pre-trained flow matching-based audio generation models is typically computationally expensive. It requires over 50,000 training iterations and five times the amount of training data to achieve satisfactory results. To address this issue, we introduce a novel data-efficient reflow (DEreflow) method. This method modifies the reflow data pairs and trajectory to align with the flow matching distribution. As a result of this alignment, our approach requires significantly fewer steps (8,000 compared to 50,000) and data pairs $(0.5$ times the scale of training data compared to 5 times). Results show that the proposed DEreflow consistently outperforms the original reflow method on the text-to-audio generation task.

Transformers have shown superior performance on various computer vision tasks with their capabilities to capture long-range dependencies. Despite the success, it is challenging to directly apply Transformers on point clouds due to their quadratic cost in the number of points. In this paper, we present a Self-Positioning point-based Transformer (SPoTr), which is designed to capture both local and global shape contexts with reduced complexity. Specifically, this architecture consists of local self-attention and self-positioning point-based global cross-attention. The self-positioning points, adaptively located based on the input shape, consider both spatial and semantic information with disentangled attention to improve expressive power. With the self-positioning points, we propose a novel global cross-attention mechanism for point clouds, which improves the scalability of global self-attention by allowing the attention module to compute attention weights with only a small set of self-positioning points. Experiments show the effectiveness of SPoTr on three point cloud tasks such as shape classification, part segmentation, and scene segmentation. In particular, our proposed model achieves an accuracy gain of 2.6% over the previous best models on shape classification with ScanObjectNN. We also provide qualitative analyses to demonstrate the interpretability of self-positioning points. The code of SPoTr is available at https://github.com/mlvlab/SPoTr.

Diffusion models have emerged as a powerful tool for point cloud generation. A key component that drives the impressive performance for generating high-quality samples from noise is iteratively denoise for thousands of steps. While beneficial, the complexity of learning steps has limited its applications to many 3D real-world. To address this limitation, we propose Point Straight Flow (PSF), a model that exhibits impressive performance using one step. Our idea is based on the reformulation of the standard diffusion model, which optimizes the curvy learning trajectory into a straight path. Further, we develop a distillation strategy to shorten the straight path into one step without a performance loss, enabling applications to 3D real-world with latency constraints. We perform evaluations on multiple 3D tasks and find that our PSF performs comparably to the standard diffusion model, outperforming other efficient 3D point cloud generation methods. On real-world applications such as point cloud completion and training-free text-guided generation in a low-latency setup, PSF performs favorably.

Vision Transformers (ViTs) have shown impressive per-formance but still require a high computation cost as compared to convolutional neural networks (CNNs), one rea-son is that ViTs' attention measures global similarities and thus has a quadratic complexity with the number of in-put tokens. Existing efficient ViTs adopt local attention or linear attention, which sacrifice ViTs' capabilities of capturing either global or local context. In this work, we ask an important research question: Can ViTs learn both global and local context while being more efficient during inference? To this end, we propose a framework called Castling- ViT, which trains ViTs using both linear-angular attention and masked softmax-based quadratic attention, but then switches to having only linear-angular attention during inference. Our Castling- ViT leverages angular ker-nels to measure the similarities between queries and keys via spectral angles. And we further simplify it with two techniques: (1) a novel linear-angular attention mechanism: we decompose the angular kernels into linear terms and high-order residuals, and only keep the linear terms; and (2) we adopt two parameterized modules to approximate high-order residuals: a depthwise convolution and an aux-iliary masked softmax attention to help learn global and lo-cal information, where the masks for softmax attention are regularized to gradually become zeros and thus incur no overhead during inference. Extensive experiments validate the effectiveness of our Castling- ViT, e.g., achieving up to a 1.8% higher accuracy or 40% MACs reduction on classification and 1.2 higher mAP on detection under comparable FLOPs, as compared to ViTs with vanilla softmax-based at-tentions. Project page is available at here.

Data augmentation is key to improving the generalization ability of deep learning models. Mixup is a simple and widely-used data augmentation technique that has proven effective in alleviating the problems of overfitting and data scarcity. Also, recent studies of saliency-aware Mixup in the image domain show that preserving discriminative parts is beneficial to improving the generalization performance. However, these Mixup-based data augmentations are underexplored in 3D vision, especially in point clouds. In this paper, we propose SageMix, a saliency-guided Mixup for point clouds to preserve salient local structures. Specifically, we extract salient regions from two point clouds and smoothly combine them into one continuous shape. With a simple sequential sampling by re-weighted saliency scores, SageMix preserves the local structure of salient regions. Extensive experiments demonstrate that the proposed method consistently outperforms existing Mixup methods in various benchmark point cloud datasets. With PointNet++, our method achieves an accuracy gain of 2.6% and 4.0% over standard training in ModelNet40 and ScanObjectNN, respectively. In addition to generalization performance, SageMix improves robustness and uncertainty calibration. Moreover, when adopting our method to various tasks including part segmentation and standard image classification, our method achieves competitive performance. Code is available at https://github.com/mlvlab/SageMix.

Generative adversarial networks (GANs) have emerged as a powerful generative model in computer vision. Given their impressive abilities in generating highly realistic images, they are also being used in novel ways in applications in the life sciences. This raises an interesting question when GANs are used in scientific or biomedical studies. Consider the setting where we are restricted to only using the samples from a trained GAN for downstream group difference analysis (and do not have direct access to the real data). Will we obtain similar conclusions? In this work, we explore if "generated" data, i.e., sampled from such GANs can be used for performing statistical group difference tests in cases versus controls studies, common across many scientific disciplines. We provide a detailed analysis describing regimes where this may be feasible. We complement the technical results with an empirical study focused on the analysis of cortical thickness on brain mesh surfaces in an Alzheimer's disease dataset. To exploit the geometric nature of the data, we use simple ideas from spectral graph theory to show how adjustments to existing GANs can yield improvements. We also give a generalization error bound by extending recent results on Neural Network Distance. To our knowledge, our work offers the first analysis assessing whether the Null distribution in "healthy versus diseased subjects" type statistical testing using data generated from the GANs coincides with the one obtained from the same analysis with real data. The code is available at https://github.com/yyxiongzju/GLapGAN.

Transformers have emerged as a powerful tool for a broad range of natural language processing tasks. A key component that drives the impressive performance of Transformers is the self-attention mechanism that encodes the influence or dependence of other tokens on each specific token. While beneficial, the quadratic complexity of self-attention on the input sequence length has limited its application to longer sequences - a topic being actively studied in the community. To address this limitation, we propose Nyströmformer - a model that exhibits favorable scalability as a function of sequence length. Our idea is based on adapting the Nyström method to approximate standard self-attention with O(n) complexity. The scalability of Nyströmformer enables application to longer sequences with thousands of tokens. We perform evaluations on multiple downstream tasks on the GLUE benchmark and IMDB reviews with standard sequence length, and find that our Nyströmformer performs comparably, or in a few cases, even slightly better, than standard self-attention. On longer sequence tasks in the Long Range Arena (LRA) benchmark, Nyströmformer performs favorably relative to other efficient self-attention methods. Our code is available at https://github.com/mlpen/Nystromformer.

Inverted bottleneck layers, which are built upon depth-wise convolutions, have been the predominant building blocks in state-of-the-art object detection models on mobile devices. In this work, we investigate the optimality of this design pattern over a broad range of mobile accelerators by revisiting the usefulness of regular convolutions. We discover that regular convolutions are a potent component to boost the latency-accuracy trade-off for object detection on accelerators, provided that they are placed strategically in the network via neural architecture search. By incorporating regular convolutions in the search space and directly optimizing the network architectures for object detection, we obtain a family of object detection models, MobileDets, that achieve state-of-the-art results across mobile accelerators. On the COCO object detection task, MobileDets outperform MobileNetV3+SSDLite by 1.7 mAP at comparable mobile CPU inference latencies. MobileDets also outperform MobileNetV2+SSDLite by 1.9 mAP on mobile CPUs, 3.7 mAP on Google EdgeTPU, 3.4 mAP on Qualcomm Hexagon DSP and 2.7 mAP on Nvidia Jetson GPU without increasing latency. Moreover, MobileDets are comparable with the state-of-the-art MnasFPN on mobile CPUs even without using the feature pyramid, and achieve better mAP scores on both EdgeTPUs and DSPs with up to 2× speedup. Code and models are available in the TensorFlow Object Detection API [16]: https://github.com/tensorflow/models/tree/master/research/object_detection.

Transformer-based models are widely used in natural language processing (NLP). Central to the transformer model is the self-attention mechanism, which captures the interactions of token pairs in the input sequences and depends quadratically on the sequence length. Training such models on longer sequences is expensive. In this paper, we show that a Bernoulli sampling attention mechanism based on Locality Sensitive Hashing (LSH), decreases the quadratic complexity of such models to linear. We bypass the quadratic cost by considering self-attention as a sum of individual tokens associated with Bernoulli random variables that can, in principle, be sampled at once by a single hash (although in practice, this number may be a small constant). This leads to an efficient sampling scheme to estimate self-attention which relies on specific modifications of LSH (to enable deployment on GPU architectures). We evaluate our algorithm on the GLUE benchmark with standard 512 sequence length where we see favorable performance relative to a standard pretrained Transformer. On the Long Range Arena (LRA) benchmark, for evaluating performance on long sequences, our method achieves results consistent with softmax self-attention but with sizable speed-ups and memory savings and often outperforms other efficient self-attention methods. Our code is available at https://github.com/mlpen/YOSO.

There is much interest in computer vision to utilize commodity hardware for gaze estimation. A number of papers have shown that algorithms based on deep convolutional architectures are approaching accuracies where streaming data from mass-market devices can offer good gaze tracking performance, although a gap still remains between what is possible and the performance users will expect in real deployments. We observe that one obvious avenue for improvement relates to a gap between some basic technical assumptions behind most existing approaches and the statistical properties of the data used for training. Specifically, most training datasets involve tens of users with a few hundreds (or more) repeated acquisitions per user. The non i.i.d. nature of this data suggests better estimation may be possible if the model explicitly made use of such “repeated measurements” from each user as is commonly done in classical statistical analysis using so-called mixed effects models. The goal of this paper is to adapt these “mixed effects” ideas from statistics within a deep neural network architecture for gaze estimation, based on eye images. Such a formulation seeks to specifically utilize information regarding the hierarchical structure of the training data - each node in the hierarchy is a user who provides tens or hundreds of repeated samples. This modification yields an architecture that offers state of the art performance on various publicly available datasets improving results by 10-20%.

Modern deep networks have proven to be very effective for analyzing real world images. However, their application in medical imaging is still in its early stages, primarily due to the large size of three-dimensional images, requiring enormous convolutional or fully connected layers - if we treat an image (and not image patches) as a sample. These issues only compound when the focus moves towards longitudinal analysis of 3D image volumes through recurrent structures, and when a point estimate of model parameters is insufficient in scientific applications where a reliability measure is necessary. Using insights from differential geometry, we adapt the tensor train decomposition to construct networks with significantly fewer parameters, allowing us to train powerful recurrent networks on whole brain image volume sequences. We describe the "orthogonal" tensor train, and demonstrate its ability to express a standard network layer both theoretically and empirically. We show its ability to effectively reconstruct whole brain volumes with faster convergence and stronger confidence intervals compared to the standard tensor train decomposition. We provide code and show experiments on the ADNI dataset using image sequences to regress on a cognition related outcome.

The design of neural network architectures is frequently either based on human expertise using trial/error and empirical feedback or tackled via large scale reinforcement learning strategies performed over distinct discrete architecture choices. In the latter case, the optimization is often non-differentiable and also not very amenable to derivative-free optimization methods. Most methods in use today require sizable computational resources. And if we want networks that additionally satisfy resource constraints, the above challenges are exacerbated because the search must now balance accuracy with certain budget constraints on resources. We formulate this problem as the optimization of a set function -- we find that the empirical behavior of this set function often (but not always) satisfies marginal gain and monotonicity principles -- properties central to the idea of submodularity. Based on this observation, we adapt algorithms within discrete optimization to obtain heuristic schemes for neural network architecture search, where we have resource constraints on the architecture. This simple scheme when applied on CIFAR-100 and ImageNet, identifies resource-constrained architectures with quantifiably better performance than current state-of-the-art models designed for mobile devices. Specifically, we find high-performing architectures with fewer parameters and computations by a search method that is much faster.

This paper is inspired by a relatively recent work of Seitz and Baker which introduced the so-called Filter Flow model. Filter flow finds the transformation relating a pair of (or multiple) images by identifying a large set of local linear filters, imposing additional constraints on certain structural properties of these filters enables Filter Flow to serve as a general one stop construction for a spectrum of problems in vision: from optical flow to defocus to stereo to affine alignment. The idea is beautiful yet the benefits are not borne out in practice because of significant computational challenges. This issue makes most (if not all) deployments for practical vision problems out of reach. The key thrust of our work is to identify mathematically (near) equivalent reformulations of this model that can eliminate this serious limitation. We demonstrate via a detailed optimization-focused development that Filter Flow can indeed be solved fairly efficiently for a wide range of instantiations. We derive efficient algorithms, perform extensive theoretical analysis focused on convergence and parallelization and show how results competitive with the state of the art for many applications can be achieved with negligible application specific adjustments or post-processing. The actual numerical scheme is easy to understand and, implement (30 lines in Matlab) - this development will enable Filter Flow to be a viable general solver and testbed for numerous applications in the community, going forward.

Because the B-spline surface intersection is a fundamental operation in geometric design software, it is important to make the surface intersection operation robust and efficient. As is well known, affine arithmetic is robust for calculating the surface intersection because it is able to not only find every branch of the intersection, but also deal with some singular cases, such as surface tangency. However, the classical affine arithmetic is defined only for the globally supported polynomials, and its computation is very time consuming, thus hampering its usefulness in practical applications, especially in geometric design. In this paper, we extend affine arithmetic to calculate the range of recursively and locally defined B-spline basis functions, and we accelerate the affine arithmetic-based surface intersection algorithm by using a GPU. Moreover, we develop efficient methods to thin the strip-shaped intersection regions produced by the affine arithmetic-based intersection algorithm, calculate the intersection points, and further improve their accuracy. The many examples presented in this paper demonstrate the robustness and efficiency of this method.