Subspace optimization

Building performance simulation can support parametric explorations of design option spaces. Resources available for modelling and computing often require the reduction of the descriptive information of a design solution at the level of design-space model rather than at that of building model. To obtain that reduction, two design-space models of different scope (for example, one full-scope and simplified, the other partial-scope and detailed) can be combined to make their responses usable as surrogates of those produced by a full-scope detailed inquiry. But aligning two building models of different scope can be difficult and sometimes impossible. This article presents a design-space 'grafting' technique supported by metamodelling that makes possible to hybridize two non-aligned design-space models so as to obtain a diffusely calibrated conjoint response. The strategy can be integrated into metamodelling and decomposition-based optimization to decrease the information costs entailed by parametric explorations.

In this article the most fundamental decomposition-based optimization method -block coordinate search, based on the sequential decomposition of problems in subproblems -and building performance simulation programs are used to reason about a building design process at micro-urban scale and strategies are defined to make the search more efficient. Cyclic overlapping block coordinate search is here considered in its double nature of optimization method and surrogate model (and metaphore) of a sequential design process. Heuristic indicators apt to support the design of search structures suited to that me thod are developed from building-simulation-assisted computational experiments, aimed to choose the form and position of a small building in a plot. Those indicators link the sharing of structure between subspaces ("commonality") to recursive recombination, measured as freshness of the search wake and novelty of the search moves. The aim of these indicators is to measure the relative effectiveness of decomposition-based design moves and create efficient block searches. Implications of a possible use of these indicators in genetic algorithms are also highlighted.

Principal component analysis (PCA) is essential for diminishing the number of dimensions across various fields, preserving data integrity while simplifying complexity. Eigenfaces, a notable application of PCA, illustrates the method's effectiveness in facial recognition. This paper introduces a novel PCA approximation technique based on maximizing distance and compares it with the traditional eigenfaces approach. We employ several image quality metrics including Euclidean distance, mean absolute error (MAE), peak signal-to-noise ratio (PSNR), signal-to-noise ratio (SNR), and structural similarity index measure (SSIM) for a quantitative assessment. Experiments conducted on the Brazilian FEI database reveal significant differences between the approximated and classical eigenfaces. Despite these differences, our approximation method demonstrates superior performance in retrieval and search tasks, offering faster and parallelizable implementation. The results underscore the practical advantages of our approach, particularly in scenarios requiring rapid processing and expansion capabilities.

This paper proposes accelerated subspace optimization methods in the context of image restoration. Subspace optimization methods belong to the class of iterative descent algorithms for unconstrained optimization. At each iteration of such methods, a stepsize vector allowing the best combination of several search directions is computed through a multi-dimensional search. It is usually obtained by an inner iterative second-order method ruled by a stopping criterion that guarantees the convergence of the outer algorithm. As an alternative, we propose an original multi-dimensional search strategy based on the majorize-minimize principle. It leads to a closed-form stepsize formula that ensures the convergence of the subspace algorithm whatever the number of inner iterations. The practical efficiency of the proposed scheme is illustrated in the context of edge-preserving image restoration.

This paper proposes accelerated subspace optimization methods in the context of image restoration. Subspace optimization methods belong to the class of iterative descent algorithms for unconstrained optimization. At each iteration of such methods, a stepsize vector allowing the best combination of several search directions is computed through a multi-dimensional search. It is usually obtained by an inner iterative second-order method ruled by a stopping criterion that guarantees the convergence of the outer algorithm. As an alternative, we propose an original multi-dimensional search strategy based on the majorize-minimize principle. It leads to a closed-form stepsize formula that ensures the convergence of the subspace algorithm whatever the number of inner iterations. The practical efficiency of the proposed scheme is illustrated in the context of edge-preserving image restoration.

A background model describes a scene without any foreground objects and has a number of applications, ranging from video surveillance to computational photography. Recent studies have introduced the method of Dynamic Mode Decomposition (DMD) for robustly separating video frames into a background model and foreground components. While the method introduced operates by converting color images to grayscale, we in this study propose a technique to obtain the background model in the color domain. The effectiveness of our technique is demonstrated using a publicly available Scene Background Initialisation (SBI) dataset. Our results both qualitatively and quantitatively show that DMD can successfully obtain a colored background model.

We propose a fast algorithm for solving the 1-regularized minimization problem min x∈R n μ x 1 + Ax − b 2 2 for recovering sparse solutions to an undetermined system of linear equations Ax = b. The algorithm is divided into two stages that are performed repeatedly. In the first stage a first-order iterative "shrinkage" method yields an estimate of the subset of components of x likely to be nonzero in an optimal solution. Restricting the decision variables x to this subset and fixing their signs at their current values reduces the 1-norm x 1 to a linear function of x. The resulting subspace problem, which involves the minimization of a smaller and smooth quadratic function, is solved in the second phase. Our code FPC AS embeds this basic two-stage algorithm in a continuation (homotopy) approach by assigning a decreasing sequence of values to μ. This code exhibits state-of-the-art performance in terms of both its speed and its ability to recover sparse signals.

We analyze an abridged version of the active-set algorithm FPC AS proposed in [18] for solving the l 1-regularized problem, i.e., a weighted sum of the l 1-norm x 1 and a smooth function f (x). The active set algorithm alternatively iterates between two stages. In the first "nonmonotone line search (NMLS)" stage, an iterative first-order method based on "shrinkage" is used to estimate the support at the solution. In the second "subspace optimization" stage, a smaller smooth problem is solved to recover the magnitudes of the nonzero components of x. We show that NMLS itself is globally convergent and the convergence rate is at least R-linearly. In particular, NMLS is able to identify of the zero components of a stationary point after a finite number of steps under some mild conditions. The global convergence of FPC AS is established based on the properties of NMLS.

Estimating the stationary background of a video sequence is useful in many applications like surveillance, segmentation, compression, inpainting, privacy protection, and computational photography. To perform this task, we introduce the LaBGen-P method based on the principles of LaBGen and the conclusions drawn in the corresponding paper. It combines a pixel-wise median filter and a pixel selection mechanism based on a motion detection performed by the frame difference algorithm. By working with pixels instead of patches, as originally done in LaBGen, it avoids some discontinuities between different spatial areas and generates better visual results. In this paper, we describe the LaBGen-P method, study its performance on the sequences of the SBMnet dataset, and compare it to that of LaBGen and other methods on the same dataset. Both algorithms emerged as the best ones during the IEEE Scene Background Modeling Contest (SBMC) organized in 2016. However, as there is not yet a good under...

Given a video of frames of size ℎ ×. Background components of a video are the elements matrix which relative constant over frames. In PCA (principal component analysis) method these elements are referred as "principal components". In video processing, background subtraction means excision of background component from the video. PCA method is used to get the background component. This method transforms 3 dimensions video (ℎ × ×) into 2 dimensions one (×), where is a linear array of size ℎ ×. The principal components are the dominant eigenvectors which are the basis of an eigenspace. The limited memory block Krylov subspace optimization then is proposed to improve performance the computation. Background estimation is obtained as the projection each input image (the first frame at each sequence image) onto space expanded principal component. The procedure was run for the standard dataset namely SBI (Scene Background Initialization) dataset consisting of 8 videos with interval resolution [146 150, 352 240], total frame [258,500]. The performances are shown with 8 metrics, especially (in average for 8 videos) percentage of error pixels (0.24%), the percentage of clustered error pixels (0.21%), multiscale structural similarity index (0.88 form maximum 1), and running time (61.68 seconds).