Variational Autoencoders (VAEs) have become a cornerstone in generative modeling and representation learning within machine learning. This paper explores a nuanced aspect of VAEs, focusing on interpreting the Kullback-Leibler (KL) Divergence, a critical component within the Evidence Lower Bound (ELBO) that governs the trade-off between reconstruction accuracy and regularization. Meanwhile, the KL Divergence enforces alignment between latent variable distributions and a prior imposing a structure on the overall latent space but leaves individual variable distributions unconstrained. The proposed method redefines the ELBO with a mixture of Gaussians for the posterior probability, introduces a regularization term to prevent variance collapse, and employs a PatchGAN discriminator to enhance texture realism. Implementation details involve ResNetV2 architectures for both the Encoder and Decoder. The experiments demonstrate the ability to generate realistic faces, offering a promising solution for enhancing VAE-based generative models.

The Hadamard Layer, a simple and computationally efficient way to improve results in semantic segmentation tasks, is presented. This layer has no free parameters that require to be trained. Therefore it does not increase the number of model parameters, and the extra computational cost is marginal. Experimental results show that the new Hadamard layer substantially improves the performance of the investigated models (variants of the Pix2Pix model). The performance’s improvement can be explained by the Hadamard layer forcing the network to produce an internal encoding of the classes so that all bins are active. Therefore, the network computation is more distributed. In a sort that the Hadamard layer requires that to change the predicted class, it is necessary to modify 2k−1bins, assuming k bins in the encoding. A specific loss function allows a stable and fast training convergence.

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the "HARDI reconstruction challenge" organized in the context of the "ISBI 2012" conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies.

We present a novel framework for image segmentation based on the maximum likelihood estimator. A common hypothesis for explaining the differences among image regions is that they are generated by sampling different likelihood functions called models. In this work, we construct on last hypothesis and, additionally, we assume that such samples come from independent and identically distributed random variables. Thus, the probability (likelihood) that a particular model generates the observed value (at a given pixel) is estimated by computing the likelihood of the sample composed with the surrounding pixels. This simple approach allows us to propose efficient segmentation methods able to deal with textured images. Our approach is naturally extended for combining different features. Experiments in interactive image segmentation, automatic stereo analysis and denoising of brain water diffusion multi-tensor fields demonstrate the capabilities of our approach.

We present a framework for image segmentation based on quadratic programming, i.e., by minimization of a quadratic regularized energy linearly constrained. In particular, we present a new variational derivation of the quadratic Markov measure field (QMMF) models, which can be understood as a procedure for regularizing model preferences (memberships or likelihoods). We also present efficient optimization algorithms. In the QMMFs, the uncertainty in the computed regularized probability measure field is controlled by penalizing Gini's coefficient, and hence, it affects the convexity of the quadratic programming problem. The convex case is reduced to the solution of a positive definite linear system, and for that case, an efficient Gauss-Seidel (GS) scheme is presented. On the other hand, we present an efficient projected GS with subspace minimization for optimizing the nonconvex case. We demonstrate the proposal capabilities by experiments and numerical comparisons with interactive two-class segmentation, as well as the simultaneous estimation of segmentation and (parametric and nonparametric) generative models. We present extensions to the original formulation for including color and texture clues, as well as imprecise user scribbles in an interactive framework.

Abstract We propose a general image and video editing method based on a Bayesian segmentation framework. In the first stage, classes are established from scribbles made by a user on the image. These scribbles can be considered as a multi‐map (multi‐label map) that defines the boundary conditions of a probability measure field to be computed for each pixel. In the second stage, the global minima of a positive definite quadratic cost function with linear constraints, is calculated to find the probability measure field. The components of such a probability measure field express the degree of each pixel belonging to spatially smooth classes. Finally, the computed probabilities (memberships) are used for defining the weights of a linear combination of user provided colours or effects associated to each class. The proposed method allows the application of different operators, selected interactively by the user, over part or the whole image without needing to recompute the memberships. We present applications to colourization, recolourization, editing and photomontage tasks.

Intravascular ultrasound (IVUS) is a catheter-based medical imaging technique that produces cross-sectional images of blood vessels and is particularly useful for studying atherosclerosis. In this paper, we present a probabilistic approach for the semi-automatic identification of the luminal border on IVUS images. Specifically, we parameterize the lumen contour using a mixture of Gaussian that is deformed by the minimization of a cost function formulated using a probabilistic approach. For the optimization of the cost function, we introduce a novel method that linearly combines the descent directions of the steepest descent and BFGS optimization methods within a trust region that improves convergence. Results of our proposed method on 20 MHz IVUS images are presented and discussed in order to demonstrate the effectiveness of our approach.

A quadratic programming formulation for multiclass image segmentation is investigated. It is proved that, in the convex case, the non-negativity constraint on the recent reported quadratic Markov measure field model can be neglected and the solution preserves the probability measure property. This allows one to design efficient optimization algorithms. Additionally, it is proposed a (free parameter) inter-pixel affinity measure which is more related with classes memberships than with color or gray gradient based standard methods. Moreover, it is introduced a formulation for computing the pixel likelihoods by taking into account local context and texture properties.

We propose a gray scale image colorization method based on a Bayesian segmentation framework in which the classes are established from scribbles made by a user on the image. These scribbles can be considered as a multimap (multilabels map) that defines the boundary conditions of a probability measure field to be computed in each pixel. The components of such a probability measure field express the degree of belonging of each pixel to spatially smooth classes. In a first step we obtain the probability measure field by computing the global minima of a positive definite quadratic cost function with linear constraints. Then color is introduced in a second step through a pixelwise operation. The computed probabilities (memberships) are used for defining the weights of a simple linear combination of user provided colors associated to each class. An advantage of our method is that it allows us to re-colorize part or the whole image in an easy way, without need of recomputing the memberships (or /sp alpha/-channels).

We present a Markov random field model for image binary segmentation that computes the probability that each pixel belongs to a given class. We show that the computation of a real valued field has noticeable computational and performance advantages with respect to the computation of binary valued field; the proposed energy function is efficiently minimized with standard fast linear order algorithms as conjugate gradient or multigrid Gauss-Seidel schemes. By providing a good initial guesses as starting point we avoid to construct from scratch a new solution, accelerating the computational process, and allow us to naturally implement efficient multigrid algorithms. For applications with limited computational time, a good partial solution can be obtained by stopping the iterations even if the global optimum is not yet reached. We present a meticulous comparison with state of the art methods: graph cut, random walker and GMMF The algorithms' performance are compared using a cross-validation procedure and an automatics algorithm for learning the parameter set.

We present a new Markov random field (MRF) based model for parametric image segmentation. Instead of directly computing a label map, our method computes the probability that the observed data at each pixel is generated by a particular intensity model. Prior information about segmentation smoothness and low entropy of the probability distribution maps is codified in the form of a MRF with quadratic potentials so that the optimal estimator is obtained by solving a quadratic cost function with linear constraints. Although, for segmentation purposes, the mode of the probability distribution at each pixel is naturally used as an optimal estimator, our method permits the use of other estimators, such as the mean or the median, which may be more appropriate for certain applications. Numerical experiments and comparisons with other published schemes are performed, using both synthetic images and real data of brain MRI for which expert hand-made segmentations are available. Finally, we show that the proposed methodology may be easily extended to other problems, such as stereo disparity estimation.

In this paper, we present a new formulation for recovering the fiber tract geometry within a voxel from diffusion weighted magnetic resonance imaging (MRI) data, in the presence of single or multiple neuronal fibers. To this end, we define a discrete set of diffusion basis functions. The intravoxel information is recovered at voxels containing fiber crossings or bifurcations via the use of a linear combination of the above mentioned basis functions. Then, the parametric representation of the intravoxel fiber geometry is a discrete mixture of Gaussians. Our synthetic experiments depict several advantages by using this discrete schema: the approach uses a small number of diffusion weighted images (23) and relatively small b values (1250 s/mm2), i.e., the intravoxel information can be inferred at a fraction of the acquisition time required for datasets involving a large number of diffusion gradient orientations. Moreover our method is robust in the presence of more than two fibers within a voxel, improving the state-of-the-art of such parametric models. We present two algorithmic solutions to our formulation: by solving a linear program or by minimizing a quadratic cost function (both with non-negativity constraints). Such minimizations are efficiently achieved with standard iterative deterministic algorithms. Finally, we present results of applying the algorithms to synthetic as well as real data.

We present a new general Bayesian formulation for simultaneously restoring and segmenting piecewise smooth images. This implies estimation of the associated parameters of the classes within an image, the class label for each image pixel and the number of classes. The intensity image is modelled by parametric models based on regularized networks. The method fits the regions (or classes) with complex spatial intensity distributions with an identifiable group of simple models. Prior information is introduced in form of a two-level Markov random field (MRF). The low--level MRF models the information required to recover piecewise restorations, while the high-level MRF constraints the segmentation. The high--level MRF supports a merging process of simple intensity models into classes.

We present a class of models, derived from classical discrete Markov random fields, that may be used for the solution of ill-posed problems in image processing and in computational vision. They lead to reconstruction algorithms that are flexible, computationally efficient, and biologically plausible. To illustrate their use, we present their application to the reconstruction of the dominant orientation and direction fields, to the classification of multiband images, and to image quantization and filtering.

In the last decade, several authors have proposed edge preserving regularization (EPR) methods for solving ill posed problems in image processing and computer vision. These EPR techniques are based on the minimization of non-quadratic and in some cases non-convex energy functionals. We introduce a new EPR technique that corresponds to an adaptive-rest condition spring system, meaning that at those places where we want an homogeneous smoothing, the rest condition of the springs is close to zero (as a homogeneous spring system), whereas at edges, the rest condition is equal to the size of the corresponding jump.