Plug&Play (PnP) diffusion models are state-of-the-art methods in computed tomography (CT) reconstruction. Such methods usually consider applications where the sinogram contains a sufficient amount of information for the posterior distribution to be concentrated around a single mode, and consequently are evaluated using image-to-image metrics such as PSNR/SSIM. Instead, we are interested in reconstructing compressible flow images from sinograms having a small number of projections, which results in a posterior distribution no longer concentrated or even multimodal. Thus, in this paper, we aim at evaluating the approximate posterior of PnP diffusion models and introduce two posterior evaluation properties. We quantitatively evaluate three PnP diffusion methods on three different datasets for several numbers of projections. We surprisingly find that, for each method, the approximate posterior deviates from the true posterior when the number of projections decreases.

Aerial or satellite imagery is a great source for land surface analysis, which might yield land-use maps or elevation models. In this letter, we present a neural network framework for learning semantics and local height together. We show how this joint multitask learning benefits to each task on the large data set of the 2018 Data Fusion Contest. Moreover, our framework also yields an uncertainty map that allows assessing the prediction of the model. Code is available at https://github.com/marcelampc/mtl_aerial_images.

This paper deals with efficient atom selection procedure in a continuous dictionary, as required for instance in a Frank-Wolfe approach within a BLASSO problem for the one-dimensional deconvolution problem. We show that efficient maximization of a correlation between any given vector and an atom sweeping a continuous dictionary can be performed through a particular piece-wise linear approximation of dictionaries: the polar approximation. We finally identify the polar approximation as being optimal in a mean square error sense for dictionaries with raised-cosine Toeplitz kernels.

Depth estimation from a single monocular image has reached great performances thanks to recent works based on deep networks. However, as various choices of losses, architectures and experimental conditions are proposed in the literature, it is difficult to establish their respective influence on the performances. In this paper we propose an in-depth study of various losses and experimental conditions for depth regression, on NYUv2 dataset. From this study we propose a new network for depth estimation combining an encoder-decoder architecture with an adversarial loss. This network reaches top scores in the competitive evaluation of NUYv2 dataset while being simpler to train in a single phase.

A new algorithm is proposed to detect small objects by background suppression. It relies on a modified version of the non-local means filter introduced by Buades et al. for background prediction. Background pixels are estimated by a weighted average depending on the similarity between neighborhoods pixels. For background suppression, the similarity criterion is modified to be less sensitive to point object presence. The resulting D-NLM filter better detects dim point objects than current detection filters. A straightforward spatio-temporal extension is also proposed, it has the advantage of not requiring prior accurate background motion compensation. Our method is well adapted to slow object velocity and large background motion contexts, where it outperforms significantly conventional spatio-temporal filters.

We present a new approach for spatially varying blur identification using a single image. Within each local patch in the image, the local blur is selected between a finite set of candidate PSFs by a maximum likelihood approach. We propose to work with a Generalized Likelihood to reduce the number of parameters and we use the Generalized Singular Value De- composition to limit the computing cost, while making proper image boundary hypotheses. The resulting method is fast and demonstrates good performance on simulated and real examples originating from applications such as motion blur identification and depth from defocus.

We consider the recovery of 1-D image features. Such features can be described by a noisy, blurred and undersampled image of a unique 1-D profile. The profile’s recovery is modeled as a 1-D continuous super-resolution (SR) problem. We adopt a functional estimation within a Tikhonov regularization framework. A linear closed-form solution is derived and applied to real data for bar code recovery from low-resolution video frames. Performance modeling in then considered. Thanks to a continuous stochastic model of the input profile, we define a quantitative performance measure which is a mean-square error averaged over a class of profiles with tunable regularity. As a result, an expected SR resolution enhancement ratio is computed, which depends on experimental parameters: SNR, number of input images, sampling rate. A good agreement is found between this theoretical study and empirical performance in experimental SR recovery of bar code profiles.

Robust estimation of the optical flow is addressed through a multiresolution energy minimization. It involves repeated evaluation of spatial and temporal gradients of image intensity which rely usually on bilinear interpolation and image filtering. We propose to base both computations on a single pyramidal cubic B-spline model of image intensity. We show empirically improvements in convergence speed and estimation error and validate the resulting algorithm on real test sequences.

Super-resolution (SR) techniques make use of subpixel shifts between frames in an image sequence to yield higher resolution images. We propose an original observation model devoted to the case of nonisometric inter-frame motion as required, for instance, in the context of airborne imaging sensors. First, we describe how the main observation models used in the SR literature deal with motion, and we explain why they are not suited for nonisometric motion. Then, we propose an extension of the observation model by Elad and Feuer adapted to affine motion. This model is based on a decomposition of affine transforms into successive shear transforms, each one efficiently implemented by row-by-row or column-by-column one-dimensional affine transforms. We demonstrate on synthetic and real sequences that our observation model incorporated in a SR reconstruction technique leads to better results in the case of variable scale motions and it provides equivalent results in the case of isometric motions.

We study dense optical flow estimation using iterative registration of local window, also known as iterative Lucas-Kanade (LK) [B. Lucas et al, 1981]. We show that the usual iterative-warping scheme encounters divergence problems and propose a modified scheme with better behavior. It yields good results with a much lower cost than the exact dense LK algorithm, on simulated and real sequences.

We are concerned with analysis of linear reconstruction-based super-resolution (SR) techniques. We propose a novel Fourier interpretation of an "archetype" linear SR algorithm and derive practical results on the expected performances of such techniques.

IRLS and RSD algorithms of robust statistics arise as special cases of half-quadratic schemes [1]. Here, we adopt a statistical framework and we show that both algorithms are instances of the EM algorithm. The augmented dataset respectively involves a scale and a location mixture of Gaussians. The su#cient conditions for the construction cover a broad class of already known robust statistics.

This paper provides a complete characterization of stationary Markov random fields on a finite rectangular (non-toroidal) lattice in the basic case of a second-order neighborhood system. Equivalently, it characterizes stationary Markov fields on Z/sup 2/ whose restrictions to finite rectangular subsets are still Markovian (i.e., even on the boundaries). Until now, Pickard random fields formed the only known class of such fields. First, we derive a necessary and sufficient condition for Markov random fields on a finite lattice to be stationary. It is shown that their joint distribution factors in terms of the marginal distribution on a generic (2/spl times/2) cell which must fulfil some consistency constraints. Second, we solve the consistency constraints and provide a complete characterization of such measures in three cases. Symmetric measures and Gaussian measures are shown to necessarily belong to the Pickard class, whereas binary measures belong either to the Pickard class, or to a new nontrivial class which is further studied. In particular, the corresponding fields admit a simple parameterization and may be simulated in a simple, although nonunilateral manner.

Because true maximum likelihood (ML) is too expensive, the dominant approach in Bernoulli-Gaussian (BG) myopic deconvolution consists in the joint maximization of a single generalized likelihood with respect to the input signal and the hyperparameters. This article assesses the theoretical properties of a related maximum generalized marginal likelihood (MGML) estimator in a simplified framework: the filter is reduced to identity, so that the output data is a mixture of Gaussian populations. Our results are three-fold: first, exact MGML estimates can be efficiently computed; second, this estimator performs better than ML in the short sample case whereas it is drastically less expensive; third, asymptotic estimates are significant although biased.