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Intra-operative 2D-3D registration of X-ray images with pre-operatively acquired CT scans is a crucial procedure in orthopedic surgeries. Anatomical landmarks pre-annotated in the CT volume can be detected in X-ray images to establish 2D-3D correspondences, which are then utilized for registration. However, registration often fails in certain view angles due to poor landmark visibility. We propose a novel method to address this issue by detecting arbitrary landmark points in X-ray images. Our approach represents 3D points as distinct subspaces, formed by feature vectors (referred to as ray embeddings) corresponding to intersecting rays. Establishing 2D-3D correspondences then becomes a task of finding ray embeddings that are close to a given subspace, essentially performing an intersection test. Unlike conventional methods for landmark estimation, our approach eliminates the need for manually annotating fixed landmarks. We trained our model using the synthetic images generated from CTPelvic1K CLINIC dataset, which contains 103 CT volumes, and evaluated it on the DeepFluoro dataset, comprising real X-ray images. Experimental results demonstrate the superiority of our method over conventional methods. The code is available at https://github.com/Pragyanstha/rayemb., Comment: Accepted as an oral presentation at ACCV 2024

This paper proposes a method to reconstruct the neural radiance field with equirectangular omnidirectional images. Implicit neural scene representation with a radiance field can reconstruct the 3D shape of a scene continuously within a limited spatial area. However, training a fully implicit representation on commercial PC hardware requires a lot of time and computing resources (15 $\sim$ 20 hours per scene). Therefore, we propose a method to accelerate this process significantly (20 $\sim$ 40 minutes per scene). Instead of using a fully implicit representation of rays for radiance field reconstruction, we adopt feature voxels that contain density and color features in tensors. Considering omnidirectional equirectangular input and the camera layout, we use spherical voxelization for representation instead of cubic representation. Our voxelization method could balance the reconstruction quality of the inner scene and outer scene. In addition, we adopt the axis-aligned positional encoding method on the color features to increase the total image quality. Our method achieves satisfying empirical performance on synthetic datasets with random camera poses. Moreover, we test our method with real scenes which contain complex geometries and also achieve state-of-the-art performance. Our code and complete dataset will be released at the same time as the paper publication., Comment: will be appeared in GCCE 2022

Rate-induced tipping (R-tipping) occurs when time-variation of input parameters of a dynamical system interacts with system timescales to give genuine nonautonomous instabilities. Such instabilities appear as the input varies at some critical rates and cannot, in general, be understood in terms of autonomous bifurcations in the frozen system with a fixed-in-time input. This paper develops an accessible mathematical framework for R-tipping in multidimensional nonautonomous dynamical systems with an autonomous future limit. We focus on R-tipping via loss of tracking of base attractors that are equilibria in the frozen system, due to crossing what we call regular thresholds. These thresholds are associated with regular edge states: compact hyperbolic invariant sets with one unstable direction and orientable stable manifold, that lie on a basin boundary in the frozen system. We define R-tipping and critical rates for the nonautonomous system in terms of special solutions that limit to a compact invariant set of the future limit system that is not an attractor. We focus on the case when the limit set is a regular edge state, which we call the regular R-tipping edge state that anchors the associated regular R-tipping threshold at infinity. We introduce the concept of edge tails to rigorously classify R-tipping into reversible, irreversible, and degenerate cases. The main idea is to compactify the problem and use regular edge states of the future limit system to analyse R-tipping in the nonautonomous system. This allows us to give sufficient conditions for the occurrence of R-tipping in terms of easily testable properties of the frozen system and input variation, and necessary and sufficient conditions for the occurrence of reversible and irreversible R-tipping in terms of computationally verifiable (heteroclinic) connections to regular R-tipping edge states in the compactified system.

We develop a general compactification framework to facilitate analysis of nonlinear nonautonomous ODEs where nonautonomous terms decay asymptotically. The strategy is to compactify the problem: the phase space is augmented with a bounded but open dimension and then extended at one or both ends by gluing in flow-invariant subspaces that carry autonomous dynamics of the limit systems from infinity. We derive the weakest decay conditions possible for the compactified system to be continuously differentiable on the extended phase space. This enables us to use equilibria and other compact invariant sets of the limit systems from infinity to analyse the original nonautonomous problem in the spirit of dynamical systems theory. Specifically, we prove that solutions of interest are contained in unique invariant manifolds of saddles for the limit systems when embedded in the extended phase space. The uniqueness holds in the general case, that is even if the compactification gives rise to a centre direction and the manifolds become centre or centre-stable manifolds. A wide range of problems including pullback attractors, rate-induced critical transitions (R-tipping) and nonlinear wave solutions fit naturally into our framework.

We report a ground X-ray calibration of two X-ray telescope prototypes at the PANTER X-ray Test Facility, of the Max-Planck-Institute for Extraterrestrial Physics, in Neuried, Germany. The X-ray telescope prototypes were developed by the Institute of Precision Optical Engineering (IPOE) of Tongji University, in a conical Wolter-I configuration, using thermal glass slumping technology. Prototype #1 with 3 layers and Prototype #2 with 21 layers were tested to assess the prototypes' on-axis imaging performance. The measurement of Prototype #1 indicates a Half Power Diameter (HPD) of 82" at 1.49 keV. As for Prototype #2, we performed more comprehensive measurements of on-axis angular resolution and effective area at several energies ranging from 0.5-10 keV. The HPD and effective area are 111" and 39 cm^2 at 1.49 keV, respectively, at which energy the on-axis performance of the prototypes is our greatest concern., Comment: 11 pages, 9 figures