Active inference, grounded in the free energy principle, provides a powerful lens for understanding how agents balance exploration and goal-directed behavior in uncertain environments. Here, we propose a new planning framework that integrates Monte Carlo tree search (MCTS) with active inference objectives to systematically reduce epistemic uncertainty while pursuing extrinsic rewards. Our key insight is that MCTS, already renowned for its search efficiency, can be naturally extended to incorporate free energy minimization by blending expected rewards with information gain. Concretely, the cross-entropy method (CEM) is used to optimize action proposals at the root node, while tree expansions leverage reward modeling alongside intrinsic exploration bonuses. This synergy allows our planner to maintain coherent estimates of value and uncertainty throughout planning, without sacrificing computational tractability. Empirically, we benchmark our planner on a diverse set of continuous control tasks, where it demonstrates performance gains over both stand-alone CEM and MCTS with random rollouts.

In this work, we present a novel, theoretical approach to address one of the longstanding problems in computer vision: 2D and 3D affine invariant feature matching. Our proposed Grassmannian Graph (GrassGraph) framework employs a two stage procedure that is capable of robustly recovering correspondences between two unorganized, affinely related feature (point) sets. In the ideal case, the first stage maps the feature sets to an affine invariant Grassmannian representation, where the features are mapped into the same subspace. It turns out that coordinate representations extracted from the Grassmannian differ by an arbitrary orthonormal matrix. In the second stage, by approximating the Laplace-Beltrami operator (LBO) on these coordinates, this extra orthonormal factor is nullified, providing true affine invariant coordinates which we then utilize to recover correspondences via simple mutual nearest neighbor relations. Our validation benchmarks use large number of experimental trials performed on 2D and 3D datasets. Experimental results show that the proposed GrassGraph method successfully recovers large affine transformations.

This paper proposes a novel image-retargeting algorithm that can retarget images to a large family of non-rectangular shapes. Specifically, we study image retargeting from a broader perspective that includes the content as well as the shape of an image, and the proposed content and shape-aware image-retargeting (CASAIR) algorithm is driven by the dual objectives of image content preservation and image domain transformation, with the latter defined by an application-specific target shape. The algorithm is based on the idea of seam segment carving that successively removes low-cost seam segments from the image to simultaneously achieve the two objectives, with the selection of seam segments determined by a cost function incorporating inputs from image content and target shape. To provide a complete characterization of shapes that can be obtained using CASAIR, we introduce the notion of bhv-convex shapes, and we show that bhv-convex shapes are precisely the family of shapes that can be retargeted to by CASAIR. The proposed algorithm is simple in both its design and implementation, and in practice, it offers an efficient and effective retargeting platform that provides its users with considerable flexibility in choosing target shapes. To demonstrate the potential of CASAIR for broadening the application scope of image retargeting, this paper also proposes a smart camera-projector system that incorporates CASAIR. In the context of ubiquitous display, CASAIR equips the camera-projector system with the capability of retargeting images online in order to maximize the quality and fidelity of the displayed images whenever the situation demands.

The accelerated evolution and explosion of the Internet and social media is generating voluminous quantities of data (on zettabyte scales). Paramount amongst the desires to manipulate and extract actionable intelligence from vast big data volumes is the need for scalable, performance-conscious analytics algorithms. To directly address this need, we propose a novel MapReduce implementation of the exemplar-based clustering algorithm known as Affinity Propagation. Our parallelization strategy extends to the multilevel Hierarchical Affinity Propagation algorithm and enables tiered aggregation of unstructured data with minimal free parameters, in principle requiring only a similarity measure between data points. We detail the linear run-time complexity of our approach, overcoming the limiting quadratic complexity of the original algorithm. Experimental validation of our clustering methodology on a variety of synthetic and real data sets (e.g. images and point data) demonstrates our competitiveness against other state-of-the-art MapReduce clustering techniques.

Driven by desirable attributes such as topological characterization and invariance to isometric transformations, the use of the Laplace-Beltrami operator (LBO) and its associated spectrum have been widely adopted among the shape analysis community. Here we demonstrate a novel use of the LBO for shape matching and retrieval by estimating probability densities on its Eigen space, and subsequently using the intrinsic geometry of the density manifold to categorize similar shapes. In our framework, each 3D shape's rich geometric structure, as captured by the low order eigenvectors of its LBO, is robustly characterized via a nonparametric density estimated directly on these eigenvectors. By utilizing a probabilistic model where the square root of the density is expanded in a wavelet basis, the space of LBO-shape densities is identifiable with the unit hyper sphere. We leverage this simple geometry for retrieval by computing an intrinsic Karcher mean (on the hyper sphere of LBO-shape densities) for each shape category, and use the closed-form distance between a query shape and the means to classify shapes. Our method alleviates the need for superfluous feature extraction schemes-required for popular bag-of-features approaches-and experiments demonstrate it to be robust and competitive with the state-of-the-art in 3D shape retrieval algorithms.

The accelerated evolution and explosion of the Internet and social media is generating voluminous quantities of data (on zettabyte scales). Paramount amongst the desires to manipulate and extract actionable intelligence from vast big data volumes is the need for scalable, performance-conscious analytics algorithms. To directly address this need, we propose a novel MapReduce implementation of the exemplar-based clustering algorithm known as Affinity Propagation. Our parallelization strategy extends to the multilevel Hierarchical Affinity Propagation algorithm and enables tiered aggregation of unstructured data with minimal free parameters, in principle requiring only a similarity measure between data points. We detail the linear run-time complexity of our approach, overcoming the limiting quadratic complexity of the original algorithm. Experimental validation of our clustering methodology on a variety of synthetic and real data sets (e.g. images and point data) demonstrates our competitiveness against other state-of-the-art MapReduce clustering techniques.

This paper proposes a new affine registration algorithm for matching two point sets in IR2or IR3. The input point sets are represented as probability density functions, using either Gaussian mixture models or discrete density models, and the problem of registering the point sets is treated as aligning the two distributions. Since polynomials transform as symmetric tensors under an affine transformation, the distributions' moments, which are the expected values of polynomials, also transform accordingly. Therefore, instead of solving the harder problem of aligning the two distributions directly, we solve the softer problem of matching the distributions' moments. By formulating a least-squares problem for matching moments of the two distributions up to degree three, the resulting cost function is a polynomial that can be efficiently optimized using techniques originated from algebraic geometry: the global minimum of this polynomial can be determined by solving a system of polynomial equations. The algorithm is robust in the presence of noises and outliers, and we validate the proposed algorithm on a variety of point sets with varying degrees of deformation and noise.

Shape matching plays a prominent role in the comparison of similar structures. We present a unifying framework for shape matching that uses mixture models to couple both the shape representation and deformation. The theoretical foundation is drawn from information geometry wherein information matrices are used to establish intrinsic distances between parametric densities. When a parameterized probability density function is used to represent a landmark-based shape, the modes of deformation are automatically established through the information matrix of the density. We first show that given two shapes parameterized by Gaussian mixture models (GMMs), the well-known Fisher information matrix of the mixture model is also a Riemannian metric (actually, the Fisher-Rao Riemannian metric) and can therefore be used for computing shape geodesics. The Fisher-Rao metric has the advantage of being an intrinsic metric and invariant to reparameterization. The geodesicâcomputed using this metricâestablishes an intrinsic deformation between the shapes, thus unifying both shape representation and deformation. A fundamental drawback of the Fisher-Rao metric is that it is not available in closed form for the GMM. Consequently, shape comparisons are computationally very expensive. To address this, we develop a new Riemannian metric based on generalized \phi-entropy measures. In sharp contrast to the Fisher-Rao metric, the new metric is available in closed form. Geodesic computations using the new metric are considerably more efficient. We validate the performance and discriminative capabilities of these new information geometry-based metrics by pairwise matching of corpus callosum shapes. We also study the deformations of fish shapes that have various topological properties. A comprehensive comparative analysis is also provided using other landmark-based distances, including the Hausdorff distance, the Procrustes metric, landmark-based diffeomorphisms, and the bending energies of the thin-plate (TPS) and Wendland splines.

Shape representation and retrieval of stored shape models are becoming increasingly more prominent in fields such as medical imaging, molecular biology and remote sensing. We present a novel framework that directly addresses the necessity for a rich and compressible shape representation, while simultaneously providing an accurate method to index stored shapes. The core idea is to represent point-set shapes as the square root of probability densities expanded in a wavelet basis. We then use this representation to develop a natural similarity metric that respects the geometry of these probability distributions, i.e. under the wavelet expansion, densities are points on a unit hypersphere and the distance between densities is given by the separating arc length. The process uses a linear assignment solver for non-rigid alignment between densities prior to matching; this has the connotation of "sliding" wavelet coefficients akin to the sliding block puzzle L'Âne Rouge. We illustrate the utility of this framework by matching shapes from the MPEG-7 data set and provide comparisons to other similarity measures, such as Euclidean distance shape distributions.

Density estimation for observational data plays an integral role in a broad spectrum of applications, e.g., statistical data analysis and information-theoretic image registration. Of late, wavelet-based density estimators have gained in popularity due to their ability to approximate a large class of functions, adapting well to difficult situations such as when densities exhibit abrupt changes. The decision to work with wavelet density estimators brings along with it theoretical considerations (e.g., non-negativity, integrability) and empirical issues (e.g., computation of basis coefficients) that must be addressed in order to obtain a bona fide density. In this paper, we present a new method to accurately estimate a non-negative density which directly addresses many of the problems in practical wavelet density estimation. We cast the estimation procedure in a maximum likelihood framework which estimates the square root of the density radicalp, allowing us to obtain the natural non-negative density representation ( radicalp)(2). Analysis of this method will bring to light a remarkable theoretical connection with the Fisher information of the density and, consequently, lead to an efficient constrained optimization procedure to estimate the wavelet coefficients. We illustrate the effectiveness of the algorithm by evaluating its performance on mutual information-based image registration, shape point set alignment, and empirical comparisons to known densities. The present method is also compared to fixed and variable bandwidth kernel density estimators.

The use of independent component analysis (ICA) methods for blind source separation of signals and images has been demonstrated in many applications and publications. While many ICA based algorithms for source separation exist, few impose physical constraints on the recovered independent components and the mixing matrix. Of particular interest is the non-negativity of the recovered independent components and the recovered mixing matrix. Such constraints are important for example when trying to do subpixel demixing on hyperspectral images. In this article, we propose a constrained non-negative maximum-likelihood ICA (CNML-ICA) algorithm that tackles the limitations of some existing non-negative ICA methods.