A novel method for synthesizing synthetic aperture radar (SAR) sea-ice imagery named IceSynth II is presented. A Markov random field model is assumed, and a conditional sampling approach is used to learn local conditional posterior probability distributions on a regional basis. Synthetic SAR sea-ice images and the associated ground-truth segmentations are generated using a region-based posterior sampling approach. Experimental results using single-polarization RADARSAT-1 and dual-polarization RADARSAT-2 SAR sea-ice imagery provided by the Canadian Ice Service show that IceSynth II is capable of producing SAR sea-ice imagery that is more realistic than existing approaches. The synthesized images are well suited for performing systematic and reliable objective evaluation of SAR sea-ice image segmentation methods.
The focus of the paper is mainly on the existence of limit cycles of a planar system with third-degree polynomial functions. A previously developed perturbation technique for computing normal forms of differential equations is employed to calculate the focus values of the system near equilibrium points. Detailed studies have been provided for a number of cases with certain restrictions on system parameters, giving rise to a complete classification for the local dynamical behavior of the system. In particular, a sufficient condition is established for the existence of k small amplitude limit cycles in the neighborhood of a high degenerate critical point. The condition is then used to show that the system can have eight and ten small amplitude (local) limit cycles for a set of particular parameter values.
A key challenge in model-free category-level pose estimation is the extraction of contextual object features that generalize across varying instances within a specific category. Recent approaches leverage foundational features to capture semantic and geometry cues from data. However, these approaches fail under partial visibility. We overcome this with a first-complete-then-aggregate strategy for feature extraction utilizing class priors. In this paper, we present GCE-Pose, a method that enhances pose estimation for novel instances by integrating category-level global context prior. GCE-Pose performs semantic shape reconstruction with a proposed Semantic Shape Reconstruction (SSR) module. Given an unseen partial RGB-D object instance, our SSR module reconstructs the instance's global geometry and semantics by deforming category-specific 3D semantic prototypes through a learned deep Linear Shape Model. We further introduce a Global Context Enhanced (GCE) feature fusion module that effectively fuses features from partial RGB-D observations and the reconstructed global context. Extensive experiments validate the impact of our global context prior and the effectiveness of the GCE fusion module, demonstrating that GCE-Pose significantly outperforms existing methods on challenging real-world datasets HouseCat6D and NOCS-REAL275. Our project page is available at https://colin-de.github.io/GCE-Pose/.
Abstract The bifurcation and stability analysis of the non-autonomous system studied in a companion paper is extended to cases in which external resonance occurs. In particular, three representative resonance cases are studied. They are 1 : 1 primary resonance, 1 : 2 superharmonic resonance, and 2 : 1 subharmonic resonance cases. Again, the intrinsic harmonic balancing technique is used as the main method of analysis which is facilitated by MAPLE, a symbolic computer language
The benefits of augmenting Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) image data with Quick Scatterometer (QuikSCAT) image data for supervised sea ice classification in the Western Arctic region are investigated. Experiments compared the performance of a maximum likelihood classifier when used with the AMSR-E-only data set against using the combined data. The preferred number of bands to use for classification was examined, as well as whether principal component analysis (PCA) can be used to reduce the dimensionality of the data. The reliability of training data over time was also investigated. Adding QuikSCAT often improves classifier accuracy in a statistically significant manner and never decreases it significantly when a sufficient number of bands are used. Combining these data sets is beneficial for sea ice mapping. Using all available bands is recommended, data fusion with PCA does not offer any benefit for these data, and training data from a specific date remains reliable within 30 days.
Abstract The stability and bifurcation behaviour of a three dimensional, non-autonomous model of a molecular system is studied analytically. It is shown that quasi-periodic motions (on a torus) bifurcate from a periodic motion, and there exists a shift in the critical value of the parameter compared to that of the associated autonomous system which was studied earlier. The solutions and their stability are determined with the aid of the intrinsic harmonic balancing technique and MAPLE, a symbolic computer language
In this paper, we prove the existence of twelve small (local) limit cycles in a planar system with third-degree polynomial functions. The best result so far in literature for a cubic order planar system is eleven limit cycles. The system considered in this paper has a saddle point at the origin and two focus points which are symmetric about the origin. This system was studied by the authors and shown to exhibit ten small limit cycles: five around each of the focus points. It will be proved in this paper that the system can have twelve small limit cycles. The major tasks involved in the proof are to compute the focus values and solve coupled enormous large polynomial equations. A computationally efficient perturbation technique based on multiple scales is employed to calculate the focus values. Moreover, the focus values are perturbed to show that the system can exactly have twelve small limit cycles.
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