Evaluation Framework of Superpixel Methods with a Global Regularity Measure

In the superpixel literature, the comparison of state-of-the-art methods can be biased by the non-robustness of some metrics to decomposition aspects, such as the superpixel scale. Moreover, most recent decomposition methods allow to set a shape regularity parameter, which can have a substantial impact on the measured performances. In this paper, we introduce an evaluation framework, that aims to unify the comparison process of superpixel methods. We investigate the limitations of existing metrics, and propose to evaluate each of the three core decomposition aspects: color homogeneity, respect of image objects and shape regularity. To measure the regularity aspect, we propose a new global regularity measure (GR), which addresses the non-robustness of state-of-the-art metrics. We evaluate recent superpixel methods with these criteria, at several superpixel scales and regularity levels. The proposed framework reduces the bias in the comparison process of state-of-the-art superpixel methods. Finally, we demonstrate that the proposed GR measure is correlated with the performances of various applications.

SCALP: Superpixels with Contour Adherence using Linear Path

Superpixel decomposition methods are generally used as a pre-processing step to speed up image processing tasks. They group the pixels of an image into homogeneous regions while trying to respect existing contours. For all state-of-the-art superpixel decomposition methods, a trade-off is made between 1) computational time, 2) adherence to image contours and 3) regularity and compactness of the decomposition. In this paper, we propose a fast method to compute Superpixels with Contour Adherence using Linear Path (SCALP) in an iterative clustering framework. The distance computed when trying to associate a pixel to a superpixel during the clustering is enhanced by considering the linear path to the superpixel barycenter. The proposed framework produces regular and compact superpixels that adhere to the image contours. We provide a detailed evaluation of SCALP on the standard Berkeley Segmentation Dataset. The obtained results outperform state-of-the-art methods in terms of standard superpixel and contour detection metrics.

Robust Shape Regularity Criteria for Superpixel Evaluation

Regular decompositions are necessary for most superpixel-based object recognition or tracking applications. So far in the literature, the regularity or compactness of a superpixel shape is mainly measured by its circularity. In this work, we first demonstrate that such measure is not adapted for superpixel evaluation, since it does not directly express regularity but circular appearance. Then, we propose a new metric that considers several shape regularity aspects: convexity, balanced repartition, and contour smoothness. Finally, we demonstrate that our measure is robust to scale and noise and enables to more relevantly compare superpixel methods.

Superpixel-based Color Transfer

In this work, we propose a fast superpixel-based color transfer method (SCT) between two images. Superpixels enable to decrease the image dimension and to extract a reduced set of color candidates. We propose to use a fast approximate nearest neighbor matching algorithm in which we enforce the match diversity by limiting the selection of the same superpixels. A fusion framework is designed to transfer the matched colors, and we demonstrate the improvement obtained over exact matching results. Finally, we show that SCT is visually competitive compared to state-of-the-art methods.

Texture-Aware Superpixel Segmentation

Most superpixel algorithms compute a trade-off between spatial and color features at the pixel level. Hence, they may need fine parameter tuning to balance the two measures, and highly fail to group pixels with similar local texture properties. In this paper, we address these issues with a new Texture-Aware SuperPixel (TASP) method. To accurately segment textured and smooth areas, TASP automatically adjusts its spatial constraint according to the local feature variance. Then, to ensure texture homogeneity within superpixels, a new pixel to superpixel patch-based distance is proposed. TASP outperforms the segmentation accuracy of the state-of-the-art methods on texture and also natural color image datasets.

Semi-supervised Learning with Graphs: Covariance Based Superpixels For Hyperspectral Image Classification

In this paper, we present a graph-based semi-supervised framework for hyperspectral image classification. We first introduce a novel superpixel algorithm based on the spectral covariance matrix representation of pixels to provide a better representation of our data. We then construct a superpixel graph, based on carefully considered feature vectors, before performing classification. We demonstrate, through a set of experimental results using two benchmarking datasets, that our approach outperforms three state-of-the-art classification frameworks, especially when an extremely small amount of labelled data is used.

Regularized Optimal Transport and the Rot Mover's Distance

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences. Our framework thus naturally generalizes a previously proposed regularization based on the Boltzmann-Shannon entropy related to the Kullback-Leibler divergence, and solved with the Sinkhorn-Knopp algorithm. We call the regularized optimal transport distance the rot mover's distance in reference to the classical earth mover's distance. We develop two generic schemes that we respectively call the alternate scaling algorithm and the non-negative alternate scaling algorithm, to compute efficiently the regularized optimal plans depending on whether the domain of the regularizer lies within the non-negative orthant or not. These schemes are based on Dykstra's algorithm with alternate Bregman projections, and further exploit the Newton-Raphson method when applied to separable divergences. We enhance the separable case with a sparse extension to deal with high data dimensions. We also instantiate our proposed framework and discuss the inherent specificities for well-known regularizers and statistical divergences in the machine learning and information geometry communities. Finally, we demonstrate the merits of our methods with experiments using synthetic data to illustrate the effect of different regularizers and penalties on the solutions, as well as real-world data for a pattern recognition application to audio scene classification.

Parameter Estimation in Finite Mixture Models by Regularized Optimal Transport: A Unified Framework for Hard and Soft Clustering

In this short paper, we formulate parameter estimation for finite mixture models in the context of discrete optimal transportation with convex regularization. The proposed framework unifies hard and soft clustering methods for general mixture models. It also generalizes the celebrated $k$\nobreakdash-means and expectation-maximization algorithms in relation to associated Bregman divergences when applied to exponential family mixture models.

Characterizing the maximum parameter of the total-variation denoising through the pseudo-inverse of the divergence

We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated in details for the total-variation. Though, it is of importance when tuning the regularization parameter as it allows fixing an upper-bound on the grid for which the optimal parameter is sought. We establish a closed form expression for the one-dimensional case, as well as an upper-bound for the two-dimensional case, that appears reasonably tight in practice. This problem is directly linked to the computation of the pseudo-inverse of the divergence, which can be quickly obtained by performing convolutions in the Fourier domain.

Convex Histogram-Based Joint Image Segmentation with Regularized Optimal Transport Cost

We investigate in this work a versatile convex framework for multiple image segmentation, relying on the regularized optimal mass transport theory. In this setting, several transport cost functions are considered and used to match statistical distributions of features. In practice, global multidimensional histograms are estimated from the segmented image regions, and are compared to referring models that are either fixed histograms given a priori, or directly inferred in the non-supervised case. The different convex problems studied are solved efficiently using primal-dual algorithms. The proposed approach is generic and enables multi-phase segmentation as well as co-segmentation of multiple images.