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Image vectorization converts raster images into vector graphics composed of regions separated by curves. Typical vectorization methods first define the regions by grouping similar colored regions via color quantization, then approximate their boundaries by Bezier curves. In that way, the raster input is converted into an SVG format parameterizing the regions' colors and the Bezier control points. This compact representation has many graphical applications thanks to its universality and resolution-independence. In this paper, we remark that image vectorization is nothing but an image segmentation, and that it can be built by fine to coarse region merging. Our analysis of the problem leads us to propose a vectorization method alternating region merging and curve smoothing. We formalize the method by alternate operations on the dual and primal graph induced from any domain partition. In that way, we address a limitation of current vectorization methods, which separate the update of regional information from curve approximation. We formalize region merging methods by associating them with various gain functionals, including the classic Beaulieu-Goldberg and Mumford-Shah functionals. More generally, we introduce and compare region merging criteria involving region number, scale, area, and internal standard deviation. We also show that the curve smoothing, implicit in all vectorization methods, can be performed by the shape-preserving affine scale space. We extend this flow to a network of curves and give a sufficient condition for the topological preservation of the segmentation. The general vectorization method that follows from this analysis shows explainable behaviors, explicitly controlled by a few intuitive parameters. It is experimentally compared to state-of-the-art software and proved to have comparable or superior fidelity and cost efficiency.

MIMO (multiple input, multiple output) approaches are a recent trend in neural network architectures for video restoration problems, where each network evaluation produces multiple output frames. The video is split into non-overlapping stacks of frames that are processed independently, resulting in a very appealing trade-off between output quality and computational cost. In this work we focus on the low-latency setting by limiting the number of available future frames. We find that MIMO architectures suffer from problems that have received little attention so far, namely (1) the performance drops significantly due to the reduced temporal receptive field, particularly for frames at the borders of the stack, (2) there are strong temporal discontinuities at stack transitions which induce a step-wise motion artifact. We propose two simple solutions to alleviate these problems: recurrence across MIMO stacks to boost the output quality by implicitly increasing the temporal receptive field, and overlapping of the output stacks to smooth the temporal discontinuity at stack transitions. These modifications can be applied to any MIMO architecture. We test them on three state-of-the-art video denoising networks with different computational cost. The proposed contributions result in a new state-of-the-art for low-latency networks, both in terms of reconstruction error and temporal consistency. As an additional contribution, we introduce a new benchmark consisting of drone footage that highlights temporal consistency issues that are not apparent in the standard benchmarks., Comment: See the project web page to download the associated videos

Image demosaicing and denoising play a critical role in the raw imaging pipeline. These processes have often been treated as independent, without considering their interactions. Indeed, most classic denoising methods handle noisy RGB images, not raw images. Conversely, most demosaicing methods address the demosaicing of noise free images. The real problem is to jointly denoise and demosaic noisy raw images. But the question of how to proceed is still not yet clarified. In this paper, we carry-out extensive experiments and a mathematical analysis to tackle this problem by low complexity algorithms. Indeed, both problems have been only addressed jointly by end-to-end heavy weight convolutional neural networks (CNNs), which are currently incompatible with low power portable imaging devices and remain by nature domain (or device) dependent. Our study leads us to conclude that, with moderate noise, demosaicing should be applied first, followed by denoising. This requires a simple adaptation of classic denoising algorithms to demosaiced noise, which we justify and specify. Although our main conclusion is ``demosaic first, then denoise'', we also discover that for high noise, there is a moderate PSNR gain by a more complex strategy: partial CFA denoising followed by demosaicing, and by a second denoising on the RGB image. These surprising results are obtained by a black-box optimization of the pipeline, which could be applied to any other pipeline. We validate our results on simulated and real noisy CFA images obtained from several benchmarks., Comment: This paper was accepted by Inverse Problems and Imaging on October, 2023

The goal of this paper is to perform object detection in satellite imagery with only a few examples, thus enabling users to specify any object class with minimal annotation. To this end, we explore recent methods and ideas from open-vocabulary detection for the remote sensing domain. We develop a few-shot object detector based on a traditional two-stage architecture, where the classification block is replaced by a prototype-based classifier. A large-scale pre-trained model is used to build class-reference embeddings or prototypes, which are compared to region proposal contents for label prediction. In addition, we propose to fine-tune prototypes on available training images to boost performance and learn differences between similar classes, such as aircraft types. We perform extensive evaluations on two remote sensing datasets containing challenging and rare objects. Moreover, we study the performance of both visual and image-text features, namely DINOv2 and CLIP, including two CLIP models specifically tailored for remote sensing applications. Results indicate that visual features are largely superior to vision-language models, as the latter lack the necessary domain-specific vocabulary. Lastly, the developed detector outperforms fully supervised and few-shot methods evaluated on the SIMD and DIOR datasets, despite minimal training parameters.

With the widespread application of convolutional neural networks (CNNs), the traditional model based denoising algorithms are now outperformed. However, CNNs face two problems. First, they are computationally demanding, which makes their deployment especially difficult for mobile terminals. Second, experimental evidence shows that CNNs often over-smooth regular textures present in images, in contrast to traditional non-local models. In this letter, we propose a solution to both issues by combining a nonlocal algorithm with a lightweight residual CNN. This solution gives full latitude to the advantages of both models. We apply this framework to two GPU implementations of classic nonlocal algorithms (NLM and BM3D) and observe a substantial gain in both cases, performing better than the state-of-the-art with low computational requirements. Our solution is between 10 and 20 times faster than CNNs with equivalent performance and attains higher PSNR. In addition the final method shows a notable gain on images containing complex textures like the ones of the MIT Moire dataset., Comment: 5 pages. This paper was accepted by IEEE Signal Processing Letters on July 1, 2021

Detecting relevant changes is a fundamental problem of video surveillance. Because of the high variability of data and the difficulty of properly annotating changes, unsupervised methods dominate the field. Arguably one of the most critical issues to make them practical is to reduce their false alarm rate. In this work, we develop a method-agnostic weakly supervised a-contrario validation process, based on high dimensional statistical modeling of deep features, to reduce the number of false alarms of any change detection algorithm. We also raise the insufficiency of the conventionally used pixel-wise evaluation, as it fails to precisely capture the performance needs of most real applications. For this reason, we complement pixel-wise metrics with object-wise metrics and evaluate the impact of our approach at both pixel and object levels, on six methods and several sequences from different datasets. Experimental results reveal that the proposed a-contrario validation is able to largely reduce the number of false alarms at both pixel and object levels.

Even though data annotation is extremely important for interpretability, research and development of artificial intelligence solutions, most research efforts such as active learning or few-shot learning focus on the sample efficiency problem. This paper studies the neglected complementary problem of getting annotated data given a predictor. For the simple binary classification setting, we present the spectrum ranging from optimal general solutions to practical efficient methods. The problem is framed as the full annotation of a binary classification dataset with the minimal number of yes/no questions when a predictor is available. For the case of general binary questions the solution is found in coding theory, where the optimal questioning strategy is given by the Huffman encoding of the possible labelings. However, this approach is computationally intractable even for small dataset sizes. We propose an alternative practical solution based on several heuristics and lookahead minimization of proxy cost functions. The proposed solution is analysed, compared with optimal solutions and evaluated on several synthetic and real-world datasets. On these datasets, the method allows a significant improvement ($23-86\%$) in annotation efficiency., Comment: 8 pages + references + appendix

We propose SING (StabIlized and Normalized Gradient), a plug-and-play technique that improves the stability and generalization of the Adam(W) optimizer. SING is straightforward to implement and has minimal computational overhead, requiring only a layer-wise standardization of the gradients fed to Adam(W) without introducing additional hyper-parameters. We support the effectiveness and practicality of the proposed approach by showing improved results on a wide range of architectures, problems (such as image classification, depth estimation, and natural language processing), and in combination with other optimizers. We provide a theoretical analysis of the convergence of the method, and we show that by virtue of the standardization, SING can escape local minima narrower than a threshold that is inversely proportional to the network's depth.

Blurry images usually exhibit similar blur at various locations across the image domain, a property barely captured in nowadays blind deblurring neural networks. We show that when extracting patches of similar underlying blur is possible, jointly processing the stack of patches yields superior accuracy than handling them separately. Our collaborative scheme is implemented in a neural architecture with a pooling layer on the stack dimension. We present three practical patch extraction strategies for image sharpening, camera shake removal and optical aberration correction, and validate the proposed approach on both synthetic and real-world benchmarks. For each blur instance, the proposed collaborative strategy yields significant quantitative and qualitative improvements., Comment: 23 pages, 14 figures

Neural style transfer (NST) is a deep learning technique that produces an unprecedentedly rich style transfer from a style image to a content image. It is particularly impressive when it comes to transferring style from a painting to an image. NST was originally achieved by solving an optimization problem to match the global statistics of the style image while preserving the local geometric features of the content image. The two main drawbacks of this original approach is that it is computationally expensive and that the resolution of the output images is limited by high GPU memory requirements. Many solutions have been proposed to both accelerate NST and produce images with larger size. However, our investigation shows that these accelerated methods all compromise the quality of the produced images in the context of painting style transfer. Indeed, transferring the style of a painting is a complex task involving features at different scales, from the color palette and compositional style to the fine brushstrokes and texture of the canvas. This paper provides a solution to solve the original global optimization for ultra-high resolution (UHR) images, enabling multiscale NST at unprecedented image sizes. This is achieved by spatially localizing the computation of each forward and backward passes through the VGG network. Extensive qualitative and quantitative comparisons, as well as a \textcolor{coverletter}{perceptual study}, show that our method produces style transfer of unmatched quality for such high-resolution painting styles. By a careful comparison, we show that state-of-the-art fast methods are still prone to artifacts, thus suggesting that fast painting style transfer remains an open problem. Source code is available at https://github.com/bgalerne/scaling_painting_style_transfer., Comment: 14 pages, 9 figures, 4 tables, accepted at EGSR 2024

Neural networks trained on large datasets by minimizing a loss have become the state-of-the-art approach for resolving data science problems, particularly in computer vision, image processing and natural language processing. In spite of their striking results, our theoretical understanding about how neural networks operate is limited. In particular, what are the interpolation capabilities of trained neural networks? In this paper we discuss a theorem of Domingos stating that "every machine learned by continuous gradient descent is approximately a kernel machine". According to Domingos, this fact leads to conclude that all machines trained on data are mere kernel machines. We first extend Domingo's result in the discrete case and to networks with vector-valued output. We then study its relevance and significance on simple examples. We find that in simple cases, the "neural tangent kernel" arising in Domingos' theorem does provide understanding of the networks' predictions. Furthermore, when the task given to the network grows in complexity, the interpolation capability of the network can be effectively explained by Domingos' theorem, and therefore is limited. We illustrate this fact on a classic perception theory problem: recovering a shape from its boundary.

The optics of any camera degrades the sharpness of photographs, which is a key visual quality criterion. This degradation is characterized by the point-spread function (PSF), which depends on the wavelengths of light and is variable across the imaging field. In this paper, we propose a two-step scheme to correct optical aberrations in a single raw or JPEG image, i.e., without any prior information on the camera or lens. First, we estimate local Gaussian blur kernels for overlapping patches and sharpen them with a non-blind deblurring technique. Based on the measurements of the PSFs of dozens of lenses, these blur kernels are modeled as RGB Gaussians defined by seven parameters. Second, we remove the remaining lateral chromatic aberrations (not contemplated in the first step) with a convolutional neural network, trained to minimize the red/green and blue/green residual images. Experiments on both synthetic and real images show that the combination of these two stages yields a fast state-of-the-art blind optical aberration compensation technique that competes with commercial non-blind algorithms., Comment: 28 pages, 20 figures, accepted at ECCV'22 as a poster

Recent years have seen the emergence of many new neural network structures (architectures and layers). To solve a given task, a network requires a certain set of abilities reflected in its structure. The required abilities depend on each task. There is so far no systematic study of the real capacities of the proposed neural structures. The question of what each structure can and cannot achieve is only partially answered by its performance on common benchmarks. Indeed, natural data contain complex unknown statistical cues. It is therefore impossible to know what cues a given neural structure is taking advantage of in such data. In this work, we sketch a methodology to measure the effect of each structure on a network's ability, by designing ad hoc synthetic datasets. Each dataset is tailored to assess a given ability and is reduced to its simplest form: each input contains exactly the amount of information needed to solve the task. We illustrate our methodology by building three datasets to evaluate each of the three following network properties: a) the ability to link local cues to distant inferences, b) the translation covariance and c) the ability to group pixels with the same characteristics and share information among them. Using a first simplified depth estimation dataset, we pinpoint a serious nonlocal deficit of the U-Net. We then evaluate how to resolve this limitation by embedding its structure with nonlocal layers, which allow computing complex features with long-range dependencies. Using a second dataset, we compare different positional encoding methods and use the results to further improve the U-Net on the depth estimation task. The third introduced dataset serves to demonstrate the need for self-attention-like mechanisms for resolving more realistic depth estimation tasks., Comment: Accepted at the VDU2022 workshop hosted at CVPR2022

Methane (CH4) emissions estimates from top-down studies over oil and gas basins have revealed systematic under-estimation of CH4 emissions in current national inventories. Sparse but extremely large amounts of CH4 from oil and gas production activities have been detected across the globe, resulting in a significant increase of the overall O&G contribution. However, attribution to specific facilities remains a major challenge unless high-resolution images provide the sufficient granularity within O&G basin. In this paper, we monitor known oil-and-gas infrastructures across the globe using recurrent Sentinel-2 imagery to detect and quantify more than 800 CH4 emissions. In combination with emissions estimates from airborne and Sentinel-5P measurements, we demonstrate the robustness of the fit to a power law from 0.1 tCH4/hr to 600 tCH4/hr. We conclude here that the prevalence of ultra-emitters (> 25tCH4/hr) detected globally by Sentinel-5P directly relates to emission occurrences below its detection threshold. Similar power law coefficients arise from several major oil and gas producers but noticeable differences in emissions magnitudes suggest large differences in maintenance practices and infrastructures across countries., Comment: Preprint version of https://pubs.acs.org/doi/abs/10.1021/acs.est.1c08575

With the aim of evaluating image forensics tools, we propose a methodology to create forgeries traces, leaving intact the semantics of the image. Thus, the only forgery cues left are the specific alterations of one or several aspects of the image formation pipeline. This methodology creates automatically forged images that are challenging to detect for forensic tools and overcomes the problem of creating convincing semantic forgeries. Based on this methodology, we create the Trace database and conduct an evaluation of the main state-of-the-art image forensics tools.

The Rational Polynomial Camera (RPC) model can be used to describe a variety of image acquisition systems in remote sensing, notably optical and Synthetic Aperture Radar (SAR) sensors. RPC functions relate 3D to 2D coordinates and vice versa, regardless of physical sensor specificities, which has made them an essential tool to harness satellite images in a generic way. This article describes a terrain-independent algorithm to accurately derive a RPC model from a set of 3D-2D point correspondences based on a regularized least squares fit. The performance of the method is assessed by varying the point correspondences and the size of the area that they cover. We test the algorithm on SAR and optical data, to derive RPCs from physical sensor models or from other RPC models after composition with corrective functions.

Image demosaicking and denoising are the first two key steps of the color image production pipeline. The classical processing sequence has for a long time consisted of applying denoising first, and then demosaicking. Applying the operations in this order leads to oversmoothing and checkerboard effects. Yet, it was difficult to change this order, because once the image is demosaicked, the statistical properties of the noise are dramatically changed and hard to handle by traditional denoising models. In this paper, we address this problem by a hybrid machine learning method. We invert the traditional color filter array (CFA) processing pipeline by first demosaicking and then denoising. Our demosaicking algorithm, trained on noiseless images, combines a traditional method and a residual convolutional neural network (CNN). This first stage retains all known information, which is the key point to obtain faithful final results. The noisy demosaicked image is then passed through a second CNN restoring a noiseless full-color image. This pipeline order completely avoids checkerboard effects and restores fine image detail. Although CNNs can be trained to solve jointly demosaicking-denoising end-to-end, we find that this two-stage training performs better and is less prone to failure. It is shown experimentally to improve on the state of the art, both quantitatively and in terms of visual quality., Comment: 28 pages, 40 figures

Silhouettes or 2D planar shapes are extremely important in human communication, which involves many logos, graphics symbols and fonts in vector form. Many more shapes can be extracted from image by binarization or segmentation, thus in raster form that requires a vectorization. There is a need for disposing of a mathematically well defined and justified shape vectorization process, which in addition provides a minimal set of control points with geometric meaning. In this paper we propose a silhouette vectorization method which extracts the outline of a 2D shape from a raster binary image, and converts it to a combination of cubic B\'{e}zier polygons and perfect circles. Starting from the boundary curvature extrema computed at sub-pixel level, we identify a set of control points based on the affine scale-space induced by the outline. These control points capture similarity invariant geometric features of the given silhouette and give precise locations of the shape's corners.of the given silhouette. Then, piecewise B\'{e}zier cubics are computed by least-square fitting combined with an adaptive splitting to guarantee a predefined accuracy. When there are no curvature extrema identified, either the outline is recognized as a circle using the isoperimetric inequality, or a pair of the most distant outline points are chosen to initiate the fitting. Given their construction, most of our control points are geometrically stable under affine transformations. By comparing with other feature detectors, we show that our method can be used as a reliable feature point detector for silhouettes. Compared to state-of-the-art image vectorization software, our algorithm demonstrates superior reduction on the number of control points, while maintaining high accuracy.

Image denoising and demosaicking are the most important early stages in digital camera pipelines. They constitute a severely ill-posed problem that aims at reconstructing a full color image from a noisy color filter array (CFA) image. In most of the literature, denoising and demosaicking are treated as two independent problems, without considering their interaction, or asking which should be applied first. Several recent works have started addressing them jointly in works that involve heavy weight CNNs, thus incompatible with low power portable imaging devices. Hence, the question of how to combine denoising and demosaicking to reconstruct full color images remains very relevant: Is denoising to be applied first, or should that be demosaicking first? In this paper, we review the main variants of these strategies and carry-out an extensive evaluation to find the best way to reconstruct full color images from a noisy mosaic. We conclude that demosaicking should applied first, followed by denoising. Yet we prove that this requires an adaptation of classic denoising algorithms to demosaicked noise, which we justify and specify.

Anomaly detectors address the difficult problem of detecting automatically exceptions in an arbitrary background image. Detection methods have been proposed by the thousands because each problem requires a different background model. By analyzing the existing approaches, we show that the problem can be reduced to detecting anomalies in residual images (extracted from the target image) in which noise and anomalies prevail. Hence, the general and impossible background modeling problem is replaced by simpler noise modeling, and allows the calculation of rigorous thresholds based on the a contrario detection theory. Our approach is therefore unsupervised and works on arbitrary images., Comment: ICIP 2018

Modeling the processing chain that has produced a video is a difficult reverse engineering task, even when the camera is available. This makes model based video processing a still more complex task. In this paper we propose a fully blind video denoising method, with two versions off-line and on-line. This is achieved by fine-tuning a pre-trained AWGN denoising network to the video with a novel frame-to-frame training strategy. Our denoiser can be used without knowledge of the origin of the video or burst and the post processing steps applied from the camera sensor. The on-line process only requires a couple of frames before achieving visually-pleasing results for a wide range of perturbations. It nonetheless reaches state of the art performance for standard Gaussian noise, and can be used off-line with still better performance., Comment: CVPR 2019

Non-local patch based methods were until recently state-of-the-art for image denoising but are now outperformed by CNNs. Yet they are still the state-of-the-art for video denoising, as video redundancy is a key factor to attain high denoising performance. The problem is that CNN architectures are hardly compatible with the search for self-similarities. In this work we propose a new and efficient way to feed video self-similarities to a CNN. The non-locality is incorporated into the network via a first non-trainable layer which finds for each patch in the input image its most similar patches in a search region. The central values of these patches are then gathered in a feature vector which is assigned to each image pixel. This information is presented to a CNN which is trained to predict the clean image. We apply the proposed architecture to image and video denoising. For the latter patches are searched for in a 3D spatio-temporal volume. The proposed architecture achieves state-of-the-art results. To the best of our knowledge, this is the first successful application of a CNN to video denoising., Comment: A shorter version of this work has been accepted at ICIP 2019 (A NON-LOCAL CNN FOR VIDEO DENOISING). The results of v2 were improved compared to v1 and the code was updated accordingly. Code is available at: https://github.com/axeldavy/vnlnet

This paper introduces a quantitative evaluation of filters that seek to separate an image into its large-scale variations, the base layer, and its fine-scale variations, the detail layer. Such methods have proliferated with the development of HDR imaging and the proposition of many new tone-mapping operators. We argue that an objective quality measurement for all methods can be based on their artifacts. To this aim, the four main recurrent artifacts are described and mathematically characterized. Among them two are classic, the luminance halo and the staircase effect, but we show the relevance of two more, the contrast halo and the compartmentalization effect. For each of these artifacts we design a test-pattern and its attached measurement formula. Then we fuse these measurements into a single quality mark, and obtain in that way a ranking method valid for all filters performing a base+detail decomposition. This synthetic ranking is applied to seven filters representative of the literature and shown to agree with expert artifact rejection criteria., Comment: 12 pages; 11 figures; 2 tables; supplementary material available (link given in the paper)

We review the broad variety of methods that have been proposed for anomaly detection in images. Most methods found in the literature have in mind a particular application. Yet we show that the methods can be classified mainly by the structural assumption they make on the "normal" image. Five different structural assumptions emerge. Our analysis leads us to reformulate the best representative algorithms by attaching to them an a contrario detection that controls the number of false positives and thus derive universal detection thresholds. By combining the most general structural assumptions expressing the background's normality with the best proposed statistical detection tools, we end up proposing generic algorithms that seem to generalize or reconcile most methods. We compare the six best representatives of our proposed classes of algorithms on anomalous images taken from classic papers on the subject, and on a synthetic database. Our conclusion is that it is possible to perform automatic anomaly detection on a single image., Comment: Thibaud Ehret and Axel Davy contributed equally to this work

Many psychophysical studies are dedicated to the evaluation of the human gestalt detection on dot or Gabor patterns, and to model its dependence on the pattern and background parameters. Nevertheless, even for these constrained percepts, psychophysics have not yet reached the challenging prediction stage, where human detection would be quantitatively predicted by a (generic) model. On the other hand, Computer Vision has attempted at defining automatic detection thresholds. This chapter sketches a procedure to confront these two methodologies inspired in gestaltism. Using a computational quantitative version of the non-accidentalness principle, we raise the possibility that the psychophysical and the (older) gestaltist setups, both applicable on dot or Gabor patterns, find a useful complement in a Turing test. In our perceptual Turing test, human performance is compared by the scientist to the detection result given by a computer. This confrontation permits to revive the abandoned method of gestaltic games. We sketch the elaboration of such a game, where the subjects of the experiment are confronted to an alignment detection algorithm, and are invited to draw examples that will fool it. We show that in that way a more precise definition of the alignment gestalt and of its computational formulation seems to emerge. Detection algorithms might also be relevant to more classic psychophysical setups, where they can again play the role of a Turing test. To a visual experiment where subjects were invited to detect alignments in Gabor patterns, we associated a single function measuring the alignment detectability in the form of a number of false alarms (NFA). The first results indicate that the values of the NFA, as a function of all simulation parameters, are highly correlated to the human detection. This fact, that we intend to support by further experiments , might end up confirming that human alignment detection is the result of a single mechanism.

Exemplar-based texture synthesis is the process of generating, from an input sample, new texture images of arbitrary size and which are perceptually equivalent to the sample. The two main approaches are statistics-based methods and patch re-arrangement methods. In the first class, a texture is characterized by a statistical signature; then, a random sampling conditioned to this signature produces genuinely different texture images. The second class boils down to a clever "copy-paste" procedure, which stitches together large regions of the sample. Hybrid methods try to combine ideas from both approaches to avoid their hurdles. The recent approaches using convolutional neural networks fit to this classification, some being statistical and others performing patch re-arrangement in the feature space. They produce impressive synthesis on various kinds of textures. Nevertheless, we found that most real textures are organized at multiple scales, with global structures revealed at coarse scales and highly varying details at finer ones. Thus, when confronted with large natural images of textures the results of state-of-the-art methods degrade rapidly, and the problem of modeling them remains wide open., Comment: v2: Added comments and typos fixes. New section added to describe FRAME. New method presented: CNNMRF

We reconsider the classic problem of estimating accurately a 2D transformation from point matches between images containing outliers. RANSAC discriminates outliers by randomly generating minimalistic sampled hypotheses and verifying their consensus over the input data. Its response is based on the single hypothesis that obtained the largest inlier support. In this article we show that the resulting accuracy can be improved by aggregating all generated hypotheses. This yields RANSAAC, a framework that improves systematically over RANSAC and its state-of-the-art variants by statistically aggregating hypotheses. To this end, we introduce a simple strategy that allows to rapidly average 2D transformations, leading to an almost negligible extra computational cost. We give practical applications on projective transforms and homography+distortion models and demonstrate a significant performance gain in both cases.

In this paper, we reconsider the early computer vision bottom-up program, according to which higher level features (geometric structures) in an image could be built up recursively from elementary features by simple grouping principles coming from Gestalt theory. Taking advantage of the (recent) advances in reliable line segment detectors, we propose three feature detectors that constitute one step up in this bottom up pyramid. For any digital image, our unsupervised algorithm computes three classic Gestalts from the set of predetected line segments: good continuations, nonlocal alignments, and bars. The methodology is based on a common stochastic {\it a contrario model} yielding three simple detection formulas, characterized by their number of false alarms. This detection algorithm is illustrated on several digital images.

The most popular image matching algorithm SIFT, introduced by D. Lowe a decade ago, has proven to be sufficiently scale invariant to be used in numerous applications. In practice, however, scale invariance may be weakened by various sources of error inherent to the SIFT implementation affecting the stability and accuracy of keypoint detection. The density of the sampling of the Gaussian scale-space and the level of blur in the input image are two of these sources. This article presents a numerical analysis of their impact on the extracted keypoints stability. Such an analysis has both methodological and practical implications, on how to compare feature detectors and on how to improve SIFT. We show that even with a significantly oversampled scale-space numerical errors prevent from achieving perfect stability. Usual strategies to filter out unstable detections are shown to be inefficient. We also prove that the effect of the error in the assumption on the initial blur is asymmetric and that the method is strongly degraded in presence of aliasing or without a correct assumption on the camera blur.

Most computer vision application rely on algorithms finding local correspondences between different images. These algorithms detect and compare stable local invariant descriptors centered at scale-invariant keypoints. Because of the importance of the problem, new keypoint detectors and descriptors are constantly being proposed, each one claiming to perform better (or to be complementary) to the preceding ones. This raises the question of a fair comparison between very diverse methods. This evaluation has been mainly based on a repeatability criterion of the keypoints under a series of image perturbations (blur, illumination, noise, rotations, homotheties, homographies, etc). In this paper, we argue that the classic repeatability criterion is biased towards algorithms producing redundant overlapped detections. To compensate this bias, we propose a variant of the repeatability rate taking into account the descriptors overlap. We apply this variant to revisit the popular benchmark by Mikolajczyk et al., on classic and new feature detectors. Experimental evidence shows that the hierarchy of these feature detectors is severely disrupted by the amended comparator., Comment: Fixed typo in affiliations