The Conditional Lucas & Kanade Algorithm

The Lucas & Kanade (LK) algorithm is the method of choice for efficient dense image and object alignment. The approach is efficient as it attempts to model the connection between appearance and geometric displacement through a linear relationship that assumes independence across pixel coordinates. A drawback of the approach, however, is its generative nature. Specifically, its performance is tightly coupled with how well the linear model can synthesize appearance from geometric displacement, even though the alignment task itself is associated with the inverse problem. In this paper, we present a new approach, referred to as the Conditional LK algorithm, which: (i) directly learns linear models that predict geometric displacement as a function of appearance, and (ii) employs a novel strategy for ensuring that the generative pixel independence assumption can still be taken advantage of. We demonstrate that our approach exhibits superior performance to classical generative forms of the LK algorithm. Furthermore, we demonstrate its comparable performance to state-of-the-art methods such as the Supervised Descent Method with substantially less training examples, as well as the unique ability to "swap" geometric warp functions without having to retrain from scratch. Finally, from a theoretical perspective, our approach hints at possible redundancies that exist in current state-of-the-art methods for alignment that could be leveraged in vision systems of the future.Comment: 17 pages, 11 figure

A geometric proof of the equality between entanglement and edge spectra

The bulk-edge correspondence for topological quantum liquids states that the spectrum of the reduced density matrix of a large subregion reproduces the thermal spectrum of a physical edge. This correspondence suggests an intricate connection between ground state entanglement and physical edge dynamics. We give a simple geometric proof of the bulk-edge correspondence for a wide variety of physical systems. Our unified proof relies on geometric techniques available in Lorentz invariant and conformally invariant quantum field theories. These methods were originally developed in part to understand the physics of black holes, and we now apply them to determine the local structure of entanglement in quantum many-body systems.Comment: 7 pages, 3 figure

Loops and Knots as Topoi of Substance. Spinoza Revisited

The relationship between modern philosophy and physics is discussed. It is shown that the latter develops some need for a modernized metaphysics which shows up as an ultima philosophia of considerable heuristic value, rather than as the prima philosophia in the Aristotelian sense as it had been intended, in the first place. It is shown then, that it is the philosophy of Spinoza in fact, that can still serve as a paradigm for such an approach. In particular, Spinoza's concept of infinite substance is compared with the philosophical implications of the foundational aspects of modern physical theory. Various connotations of sub-stance are discussed within pre-geometric theories, especially with a view to the role of spin networks within quantum gravity. It is found to be useful to intro-duce a separation into physics then, so as to differ between foundational and empirical theories, respectively. This leads to a straightforward connection bet-ween foundational theories and speculative philosophy on the one hand, and between empirical theories and sceptical philosophy on the other. This might help in the end, to clarify some recent problems, such as the absence of time and causality at a fundamental level. It is implied that recent results relating to topos theory might open the way towards eventually deriving logic from physics, and also towards a possible transition from logic to hermeneutic.Comment: 42 page

Historic bim: A new repository for structural health monitoring

Recent developments in Building Information Modelling (BIM) technologies are facilitating the management of historic complex structures using new applications. This paper proposes a generative method combining the morphological and typological aspects of the historic buildings (H-BIM), with a set of monitoring information. This combination of 3D digital survey, parametric modelling and monitoring datasets allows for the development of a system for archiving and visualizing structural health monitoring (SHM) data (Fig. 1). The availability of a BIM database allows one to integrate a different kind of data stored in different ways (e.g. reports, tables, graphs, etc.) with a representation directly connected to the 3D model of the structure with appropriate levels of detail (LoD). Data can be interactively accessed by selecting specific objects of the BIM, i.e. connecting the 3D position of the sensors installed with additional digital documentation. Such innovative BIM objects, which form a new BIM family for SHM, can be then reused in other projects, facilitating data archiving and exploitation of data acquired and processed. The application of advanced modeling techniques allows for the reduction of time and costs of the generation process, and support cooperation between different disciplines using a central workspace. However, it also reveals new challenges for parametric software and exchange formats. The case study presented is the medieval bridge Azzone Visconti in Lecco (Italy), in which multi-Temporal vertical movements during load testing were integrated into H-BIM

DeepICP: An End-to-End Deep Neural Network for 3D Point Cloud Registration

We present DeepICP - a novel end-to-end learning-based 3D point cloud registration framework that achieves comparable registration accuracy to prior state-of-the-art geometric methods. Different from other keypoint based methods where a RANSAC procedure is usually needed, we implement the use of various deep neural network structures to establish an end-to-end trainable network. Our keypoint detector is trained through this end-to-end structure and enables the system to avoid the inference of dynamic objects, leverages the help of sufficiently salient features on stationary objects, and as a result, achieves high robustness. Rather than searching the corresponding points among existing points, the key contribution is that we innovatively generate them based on learned matching probabilities among a group of candidates, which can boost the registration accuracy. Our loss function incorporates both the local similarity and the global geometric constraints to ensure all above network designs can converge towards the right direction. We comprehensively validate the effectiveness of our approach using both the KITTI dataset and the Apollo-SouthBay dataset. Results demonstrate that our method achieves comparable or better performance than the state-of-the-art geometry-based methods. Detailed ablation and visualization analysis are included to further illustrate the behavior and insights of our network. The low registration error and high robustness of our method makes it attractive for substantial applications relying on the point cloud registration task.Comment: 10 pages, 6 figures, 3 tables, typos corrected, experimental results updated, accepted by ICCV 201