In this paper we propose an edge-direct visual odometry algorithm that efficiently utilizes edge pixels to find the relative pose that minimizes the photometric error between images. Prior work on exploiting edge pixels instead treats edges as features and employ various techniques to match edge lines or pixels, which adds unnecessary complexity. Direct methods typically operate on all pixel intensities, which proves to be highly redundant. In contrast our method builds on direct visual odometry methods naturally with minimal added computation. It is not only more efficient than direct dense methods since we iterate with a fraction of the pixels, but also more accurate. We achieve high accuracy and efficiency by extracting edges from only one image, and utilize robust Gauss-Newton to minimize the photometric error of these edge pixels. This simultaneously finds the edge pixels in the reference image, as well as the relative camera pose that minimizes the photometric error. We test various edge detectors, including learned edges, and determine that the optimal edge detector for this method is the Canny edge detection algorithm using automatic thresholding. We highlight key differences between our edge direct method and direct dense methods, in particular how higher levels of image pyramids can lead to significant aliasing effects and result in incorrect solution convergence. We show experimentally that reducing the photometric error of edge pixels also reduces the photometric error of all pixels, and we show through an ablation study the increase in accuracy obtained by optimizing edge pixels only. We evaluate our method on the RGB-D TUM benchmark on which we achieve state-of-the-art performance.
The extension of direct methods using edge pixels is a logical direction, yet to the best of our knowledge no work has solely used edge pixels in a direct method minimizing the photometric error. @cite_18 the authors reduce a Euclidean geometric error using the distance transform on edges which does not utilize all information available in the scene. @cite_0 the authors minimize a joint error function combining photometric error over all pixels along with geometric error over edge pixels. Minimizing a joint error function always suffers from the decision on how best to weight each function, and the weighting can have significant effect on the final converged solution. @cite_10 , the authors threshold by gradients, which does not guarantee edges due to noise. They additionally select texture-less regions as well.
@cite_0 @cite_18 @cite_10
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Most visual odometry algorithm for a monocular camera focuses on points, either by feature matching, or direct alignment of pixel intensity, while ignoring a common but important geometry entity: edges. In this paper, we propose an odometry algorithm that combines points and edges to benefit from the advantages of both direct and feature based methods. It works better in texture-less environments and is also more robust to lighting changes and fast motion by increasing the convergence basin. We maintain a depth map for the keyframe then in the tracking part, the camera pose is recovered by minimizing both the photometric error and geometric error to the matched edge in a probabilistic framework. In the mapping part, edge is used to speed up and increase stereo matching accuracy. On various public datasets, our algorithm achieves better or comparable performance than state-of-the-art monocular odometry methods. In some challenging texture-less environments, our algorithm reduces the state estimation error over 50 . Direct Sparse Odometry (DSO) is a visual odometry method based on a novel, highly accurate sparse and direct structure and motion formulation. It combines a fully direct probabilistic model (minimizing a photometric error) with consistent, joint optimization of all model parameters, including geometry-represented as inverse depth in a reference frame-and camera motion. This is achieved in real time by omitting the smoothness prior used in other direct methods and instead sampling pixels evenly throughout the images. Since our method does not depend on keypoint detectors or descriptors, it can naturally sample pixels from across all image regions that have intensity gradient, including edges or smooth intensity variations on essentially featureless walls. The proposed model integrates a full photometric calibration, accounting for exposure time, lens vignetting, and non-linear response functions. We thoroughly evaluate our method on three different datasets comprising several hours of video. The experiments show that the presented approach significantly outperforms state-of-the-art direct and indirect methods in a variety of real-world settings, both in terms of tracking accuracy and robustness. Change detection is one of the most important applications of remote sensing technology. It is a challenging task due to the obvious variations in the radiometric value of spectral signature and the limited capability of utilizing spectral information. In this paper, an improved sparse coding method for change detection is proposed. The intuition of the proposed method is that unchanged pixels in different images can be well reconstructed by the joint dictionary, which corresponds to knowledge of unchanged pixels, while changed pixels cannot. First, a query image pair is projected onto the joint dictionary to constitute the knowledge of unchanged pixels. Then reconstruction error is obtained to discriminate between the changed and unchanged pixels in the different images. To select the proper thresholds for determining changed regions, an automatic threshold selection strategy is presented by minimizing the reconstruction errors of the changed pixels. Adequate experiments on multispectral data have been tested, and the experimental results compared with the state-of-the-art methods prove the superiority of the proposed method. Contributions of the proposed method can be summarized as follows: 1) joint dictionary learning is proposed to explore the intrinsic information of different images for change detection. In this case, change detection can be transformed as a sparse representation problem. To the authors’ knowledge, few publications utilize joint learning dictionary in change detection; 2) an automatic threshold selection strategy is presented, which minimizes the reconstruction errors of the changed pixels without the prior assumption of the spectral signature. As a result, the threshold value provided by the proposed method can adapt to different data due to the characteristic of joint dictionary learning; and 3) the proposed method makes no prior assumption of the modeling and the handling of the spectral signature, which can be adapted to different data. We propose a scheme to introduce directionality in the random walker algorithm for image segmentation. In particular, we extend the optimization framework of this algorithm to combinatorial graphs with directed edges. Our scheme is interactive and requires the user to label a few pixels that are representative of a foreground object and of the background. These labeled pixels are used to learn intensity models for the object and the background, which allow us to automatically set the weights of the directed edges. These weights are chosen so that they bias the direction of the object boundary gradients to flow from regions that agree well with the learned object intensity model to regions that do not agree well. We use these weights to define an energy function that associates asymmetric quadratic penalties with the edges in the graph. We show that this energy function is convex, hence it has a unique minimizer. We propose a provably convergent iterative algorithm for minimizing this energy function. We also describe the construction of an equivalent electrical network with diodes and resistors that solves the same segmentation problem as our framework. Finally, our experiments on a database of 69 images show that the use of directional information does improve the segmenting power of the random Walker algorithm. In this paper, we propose a dense visual SLAM method for RGB-D cameras that minimizes both the photometric and the depth error over all pixels. In contrast to sparse, feature-based methods, this allows us to better exploit the available information in the image data which leads to higher pose accuracy. Furthermore, we propose an entropy-based similarity measure for keyframe selection and loop closure detection. From all successful matches, we build up a graph that we optimize using the g2o framework. We evaluated our approach extensively on publicly available benchmark datasets, and found that it performs well in scenes with low texture as well as low structure. In direct comparison to several state-of-the-art methods, our approach yields a significantly lower trajectory error. We release our software as open-source. Preserving edge structures is a challenge to image interpolation algorithms that reconstruct a high-resolution image from a low-resolution counterpart. We propose a new edge-guided nonlinear interpolation technique through directional filtering and data fusion. For a pixel to be interpolated, two observation sets are defined in two orthogonal directions, and each set produces an estimate of the pixel value. These directional estimates, modeled as different noisy measurements of the missing pixel are fused by the linear minimum mean square-error estimation (LMMSE) technique into a more robust estimate, using the statistics of the two observation sets. We also present a simplified version of the LMMSE-based interpolation algorithm to reduce computational cost without sacrificing much the interpolation performance. Experiments show that the new interpolation techniques can preserve edge sharpness and reduce ringing artifacts The paper addresses the problem of camera tracking, which denotes the continuous image-based computation of a camera’s position and orientation with respect to a reference frame. The method aims at regular cameras, which means that 3D-3D registration methods applicable to RGB-D cameras are not an option. The tracked frame contains only 2D information, thus requiring a solution to the absolute pose or 2D-3D registration problem. While traditional solutions to camera tracking [3] rely on sparse feature correspondences, the community has recently seen a number of direct photometric registration methods such as [8] and [1]. [1] is conceptually similar to [8], however gains computational efficiency by reducing the computation from dense to semi-dense regions that correspond to a thresholded edge-map of the image. Photometric methods have the more general advantage of compensating for appearance variations caused by perspective view-point changes, whereas classical sparse methods often rely on static feature descriptors only (providing at most rotation and scale invariant properties [5, 6]). However, photometric registration techniques inherently suffer from the disability to overcome large disparities, where large sometimes means even just a couple of pixels [7]. Many photometric registration techniques therefore depend on pyramidal subsampling schemes in order to alleviate this problem. The goal of the present paper is a novel 2D-3D registration paradigm for semi-dense depth maps that relies on the Iterative Closest Point (ICP) technique, and thus a reintroduction of geometric error minimization as a valid alternative for real-time monocular camera tracking in the case of semi-dense features. An example semi-dense depth map is indicated in Figure 1. In comparison to photometric registration techniques, our ICP technique has the conceptual advantage of requiring neither isotropic enlargement of the employed semi-dense regions, nor pyramidal subsampling. The work is in line with [2], Tomono [9], and Klein and Murray [4], which already attempt curve or edge registration in 2D using ICP. Based on a hypothesized relative pose, the basic idea consists of warping a reference curve into the tracked image based on a prior 3D model or depth (in our case semi-dense) inside a reference frame. From a mathematical point of view, our idea may be formulated as follows. Let Traditional differential-based edge detection suffers from abrupt degradation in performance when images are corrupted by impulse noises. The morphological operators such as the median filters and weighted median filters possess the intrinsic ability to counteract impulse noise. In this paper, by combining the biwindow configuration with weighted median filters, anisotropic morphological directional derivatives (AMDDs) robust to impulse noise are proposed to measure the local grayscale variation around a pixel. For ideal step edges, the AMDD spatial response and directional representation are derived. The characteristics and edge resolution of two kinds of typical biwindows are analyzed thoroughly. In terms of the AMDD spatial response and directional representation of ideal step edges, the spatial matched filter is used to extract the edge strength map (ESM) from the AMDDs of an image. The spatial and directional matched filters are used to extract the edge direction map (EDM). Embedding the extracted ESM and EDM into the standard route of the differential-based edge detection, an anti-impulse-noise AMDD-based edge detector is constructed. It is compared with the existing state-of-the-art detectors on a recognized image dataset for edge detection evaluation. The results show that it attains competitive performance in noise-free and Gaussian noise cases and the best performance in impulse noise cases. We present two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms.The first algorithm solves the APSP problem for weighted directed graphs in which the edge weights are integers of small absolute value in O(n2+μ) time, where μ satisfies the equation ω(1, μ, 1) = 1 + 2μ and ω(1, μ, 1) is the exponent of the multiplication of an n × nμ matrix by an nμ × n matrix. Currently, the best available bounds on ω(1, μ, 1), obtained by Coppersmith, imply that μ 0 is an error parameter and W is the largest edge weight in the graph, after the edge weights are scaled so that the smallest non-zero edge weight in the graph is 1. It returns estimates of all the distances in the graph with a stretch of at most 1 + e. Corresponding paths can also be found efficiently. We describe a method to automatically find gradient thresholds to separate edge from nonedge pixels. A statistical model that is the weighted sum of two gamma densities corresponding to edge and nonedge pixels is used to identify a threshold. Results closely match human perceptual thresholds even under low signal-to-noise ratio (SNR) levels. This paper proposes a novel approach called Semantic Visual Odometry (SemVO) which incorporates class-level consistency priors into the problem of 6-DoF Visual Odometry. Dense class-level labels are learnt for each pixel of the image using a CNN trained for semantic segmentation. A semantic error is formulated penalising the sum of squared differences (SSD) on class-level feature maps extracted from the decoder of a RefineNet. It will be shown how the proposed approach allows dense RGB-D camera tracking using solely a semantic error term. SemVO is evaluated on the ScanNet dataset and the results demonstrate how the number of classes affects performance. Results are also provided showing how best to fuse the new error function with classic dense photometric and geometric methods. Finally, it is demonstrated that SemVO improves over standard approaches for large camera motion applications. In this paper, we propose a super-resolution image reconstruction algorithm to moderate-resolution imaging spectroradiometer (MODIS) remote sensing images. This algorithm consists of two parts: registration and reconstruction. In the registration part, a truncated quadratic cost function is used to exclude the outlier pixels, which strongly deviate from the registration model. Accurate photometric and geometric registration parameters can be obtained simultaneously. In the reconstruction part, the L1 norm data fidelity term is chosen to reduce the effects of inevitable registration error, and a Huber prior is used as regularization to preserve sharp edges in the reconstructed image. In this process, the outliers are excluded again to enhance the robustness of the algorithm. The proposed algorithm has been tested using real MODIS band-4 images, which were captured in different dates. The experimental results and comparative analyses verify the effectiveness of this algorithm. We present VI-DSO, a novel approach for visual-inertial odometry, which jointly estimates camera poses and sparse scene geometry by minimizing photometric and IMU measurement errors in a combined energy functional. The visual part of the system performs a bundle-adjustment like optimization on a sparse set of points, but unlike key-point based systems it directly minimizes a photometric error. This makes it possible for the system to track not only corners, but any pixels with large enough intensity gradients. IMU information is accumulated between several frames using measurement preintegration, and is inserted into the optimization as an additional constraint between keyframes. We explicitly include scale and gravity direction into our model and jointly optimize them together with other variables such as poses. As the scale is often not immediately observable using IMU data this allows us to initialize our visual-inertial system with an arbitrary scale instead of having to delay the initialization until everything is observable. We perform partial marginalization of old variables so that updates can be computed in a reasonable time. In order to keep the system consistent we propose a novel strategy which we call "dynamic marginalization". This technique allows us to use partial marginalization even in cases where the initial scale estimate is far from the optimum. We evaluate our method on the challenging EuRoC dataset, showing that VI-DSO outperforms the state of the art. Direct methods for visual odometry (VO) have gained popularity for their capability to exploit information from all intensity gradients in the image. However, low computational speed as well as missing guarantees for optimality and consistency are limiting factors of direct methods, in which established feature-based methods succeed instead. Based on these considerations, we propose a semidirect VO (SVO) that uses direct methods to track and triangulate pixels that are characterized by high image gradients, but relies on proven feature-based methods for joint optimization of structure and motion. Together with a robust probabilistic depth estimation algorithm, this enables us to efficiently track pixels lying on weak corners and edges in environments with little or high-frequency texture. We further demonstrate that the algorithm can easily be extended to multiple cameras, to track edges, to include motion priors, and to enable the use of very large field of view cameras, such as fisheye and catadioptric ones. Experimental evaluation on benchmark datasets shows that the algorithm is significantly faster than the state of the art while achieving highly competitive accuracy. Edge-aware operations, such as edge-preserving smoothing and edge-aware interpolation, require assessing the degree of similarity between pairs of pixels, typically defined as a simple monotonic function of the Euclidean distance between pixel values in some feature space. In this work we introduce the idea of replacing these Euclidean distances with diffusion distances, which better account for the global distribution of pixels in their feature space. These distances are approximated using diffusion maps: a set of the dominant eigenvectors of a large affinity matrix, which may be computed efficiently by sampling a small number of matrix columns (the Nystrom method). We demonstrate the benefits of using diffusion distances in a variety of image editing contexts, and explore the use of diffusion maps as a tool for facilitating the creation of complex selection masks. Finally, we present a new analysis that establishes a connection between the spatial interaction range between two pixels, and the number of samples necessary for accurate Nystrom approximations. This paper proposes an edge-based robust RGB-D visual odometry (VO)using 2-D edge divergence minimization. Our approach focuses on enabling the VO to operate in more general environments subject to low texture and changing brightness, by employing image edge regions and their image gradient vectors within the iterative closest points (ICP)framework. For more robust and stable ICP-based optimization, we propose a robust edge matching criterion with image gradient vectors. In addition, to reduce a bad effect of outlier residuals, we propose an improved edge registration problem of 2-D edge divergence minimization in the manner of an iterative reweight least squares (IRLS)motion estimation. To accelerate the proposed approach, a pixel sub-sampling method is employed. We evaluate estimation performance of our method in changing brightness conditions and low-textured scenes. Our approach shows more robust motion estimation than state-of-the-art methods while maintaining comparable accuracy in challenging image sequences at real-time (25 Hz)operation. Learning to reconstruct depths in a single image by watching unlabeled videos via deep convolutional network (DCN) is attracting significant attention in recent years. In this paper, we introduce a surface normal representation for unsupervised depth estimation framework. Our estimated depths are constrained to be compatible with predicted normals, yielding more robust geometry results. Specifically, we formulate an edge-aware depth-normal consistency term, and solve it by constructing a depth-to-normal layer and a normal-to-depth layer inside of the DCN. The depth-to-normal layer takes estimated depths as input, and computes normal directions using cross production based on neighboring pixels. Then given the estimated normals, the normal-to-depth layer outputs a regularized depth map through local planar smoothness. Both layers are computed with awareness of edges inside the image to help address the issue of depth normal discontinuity and preserve sharp edges. Finally, to train the network, we apply the photometric error and gradient smoothness for both depth and normal predictions. We conducted experiments on both outdoor (KITTI) and indoor (NYUv2) datasets, and show that our algorithm vastly outperforms state of the art, which demonstrates the benefits from our approach. We present a novel image resizing method which attempts to ensure that important local regions undergo a geometric similarity transformation, and at the same time, to preserve image edge structure. To accomplish this, we define handles to describe both local regions and image edges, and assign a weight for each handle based on an importance map for the source image. Inspired by conformal energy, which is widely used in geometry processing, we construct a novel quadratic distortion energy to measure the shape distortion for each handle. The resizing result is obtained by minimizing the weighted sum of the quadratic distortion energies of all handles. Compared to previous methods, our method allows distortion to be diffused better in all directions, and important image edges are well-preserved. The method is efficient, and offers a closed form solution. Recent advances in technology have enabled the combination of positron emission tomography (PET) with magnetic resonance imaging (MRI). These PET-MRI scanners simultaneously acquire functional PET and anatomical or functional MRI data. As function and anatomy are not independent of one another the images to be reconstructed are likely to have shared structures. We aim to exploit this inherent structural similarity by reconstructing from both modalities in a joint reconstruction framework. The structural similarity between two modalities can be modelled in two different ways: edges are more likely to be at similar positions and or to have similar orientations. We analyse the diffusion process generated by minimizing priors that encapsulate these different models. It turns out that the class of parallel level set priors always corresponds to anisotropic diffusion which is sometimes forward and sometimes backward diffusion. We perform numerical experiments where we jointly reconstruct from blurred Radon data with Poisson noise (PET) and under-sampled Fourier data with Gaussian noise (MRI). Our results show that both modalities benefit from each other in areas of shared edge information. The joint reconstructions have less artefacts and sharper edges compared to separate reconstructions and the l2-error can be reduced in all of the considered cases of under-sampling. This paper presents a new method for linearly combining multiple neural network classifiers based on the statistical pattern recognition theory. In our approach, several neural networks are first selected based on which works best for each class in terms of minimizing classification errors. Then, they are linearly combined to form an ideal classifier that exploits the strengths of the individual classifiers. In this approach, the minimum classification error criterion is utilized to estimate the optimal linear weights. In this formulation, because the classification decision rule is incorporated into the cost function, a more suitable better combination of weights for the classification objective could be obtained. Experimental results using artificial and real data sets show that the proposed method can construct a better combined classifier that outperforms the best single classifier in terms of overall classification errors for test data.