Vibrating quantum billiards on Riemannian manifolds

Quantum billiards provide an excellent forum for the analysis of quantum chaos. Toward this end, we consider quantum billiards with time-varying surfaces, which provide an important example of quantum chaos that does not require the semiclassical ($\hbar \longrightarrow 0$) or high quantum-number limits. We analyze vibrating quantum billiards using the framework of Riemannian geometry. First, we derive a theorem detailing necessary conditions for the existence of chaos in vibrating quantum billiards on Riemannian manifolds. Numerical observations suggest that these conditions are also sufficient. We prove the aforementioned theorem in full generality for one degree-of-freedom boundary vibrations and briefly discuss a generalization to billiards with two or more degrees-of-vibrations. The requisite conditions are direct consequences of the separability of the Helmholtz equation in a given orthogonal coordinate frame, and they arise from orthogonality relations satisfied by solutions of the Helmholtz equation. We then state and prove a second theorem that provides a general form for the coupled ordinary differential equations that describe quantum billiards with one degree-of-vibration boundaries. This set of equations may be used to illustrate KAM theory and also provides a simple example of semiquantum chaos. Moreover, vibrating quantum billiards may be used as models for quantum-well nanostructures, so this study has both theoretical and practical applications.Comment: 23 pages, 6 figures, a few typos corrected. To appear in International Journal of Bifurcation and Chaos (9/01

Bayesian segnet: Model uncertainty in deep convolutional encoder-decoder architectures for scene understanding

We present a deep learning framework for probabilistic pixel-wise semantic segmentation, which we term Bayesian SegNet. Semantic segmentation is an important tool for visual scene understanding and a meaningful measure of uncertainty is essential for decision making. Our contribution is a practical system which is able to predict pixel-wise class labels with a measure of model uncertainty. We achieve this by Monte Carlo sampling with dropout at test time to generate a posterior distribution of pixel class labels. In addition, we show that modelling uncertainty improves segmentation performance by 2-3% across a number of state of the art architectures such as SegNet, FCN and Dilation Network, with no additional parametrisation. We also observe a significant improvement in performance for smaller datasets where modelling uncertainty is more effective. We benchmark Bayesian SegNet on the indoor SUN Scene Understanding and outdoor CamVid driving scenes datasets.Toyota Corporatio

Knowledge Distillation for Multi-task Learning

Multi-task learning (MTL) is to learn one single model that performs multiple tasks for achieving good performance on all tasks and lower cost on computation. Learning such a model requires to jointly optimize losses of a set of tasks with different difficulty levels, magnitudes, and characteristics (e.g. cross-entropy, Euclidean loss), leading to the imbalance problem in multi-task learning. To address the imbalance problem, we propose a knowledge distillation based method in this work. We first learn a task-specific model for each task. We then learn the multi-task model for minimizing task-specific loss and for producing the same feature with task-specific models. As the task-specific network encodes different features, we introduce small task-specific adaptors to project multi-task features to the task-specific features. In this way, the adaptors align the task-specific feature and the multi-task feature, which enables a balanced parameter sharing across tasks. Extensive experimental results demonstrate that our method can optimize a multi-task learning model in a more balanced way and achieve better overall performance.Comment: We propose a knowledge distillation method for addressing the imbalance problem in multi-task learnin

Geometry meets semantics for semi-supervised monocular depth estimation

Depth estimation from a single image represents a very exciting challenge in computer vision. While other image-based depth sensing techniques leverage on the geometry between different viewpoints (e.g., stereo or structure from motion), the lack of these cues within a single image renders ill-posed the monocular depth estimation task. For inference, state-of-the-art encoder-decoder architectures for monocular depth estimation rely on effective feature representations learned at training time. For unsupervised training of these models, geometry has been effectively exploited by suitable images warping losses computed from views acquired by a stereo rig or a moving camera. In this paper, we make a further step forward showing that learning semantic information from images enables to improve effectively monocular depth estimation as well. In particular, by leveraging on semantically labeled images together with unsupervised signals gained by geometry through an image warping loss, we propose a deep learning approach aimed at joint semantic segmentation and depth estimation. Our overall learning framework is semi-supervised, as we deploy groundtruth data only in the semantic domain. At training time, our network learns a common feature representation for both tasks and a novel cross-task loss function is proposed. The experimental findings show how, jointly tackling depth prediction and semantic segmentation, allows to improve depth estimation accuracy. In particular, on the KITTI dataset our network outperforms state-of-the-art methods for monocular depth estimation.Comment: 16 pages, Accepted to ACCV 201

Estimating Depth from RGB and Sparse Sensing

We present a deep model that can accurately produce dense depth maps given an RGB image with known depth at a very sparse set of pixels. The model works simultaneously for both indoor/outdoor scenes and produces state-of-the-art dense depth maps at nearly real-time speeds on both the NYUv2 and KITTI datasets. We surpass the state-of-the-art for monocular depth estimation even with depth values for only 1 out of every ~10000 image pixels, and we outperform other sparse-to-dense depth methods at all sparsity levels. With depth values for 1/256 of the image pixels, we achieve a mean absolute error of less than 1% of actual depth on indoor scenes, comparable to the performance of consumer-grade depth sensor hardware. Our experiments demonstrate that it would indeed be possible to efficiently transform sparse depth measurements obtained using e.g. lower-power depth sensors or SLAM systems into high-quality dense depth maps.Comment: European Conference on Computer Vision (ECCV) 2018. Updated to camera-ready version with additional experiment

Classical and Quantum Chaos in a quantum dot in time-periodic magnetic fields

We investigate the classical and quantum dynamics of an electron confined to a circular quantum dot in the presence of homogeneous $B_{dc}+B_{ac}$ magnetic fields. The classical motion shows a transition to chaotic behavior depending on the ratio $\epsilon=B_{ac}/B_{dc}$ of field magnitudes and the cyclotron frequency ${\tilde\omega_c}$ in units of the drive frequency. We determine a phase boundary between regular and chaotic classical behavior in the $\epsilon$ vs ${\tilde\omega_c}$ plane. In the quantum regime we evaluate the quasi-energy spectrum of the time-evolution operator. We show that the nearest neighbor quasi-energy eigenvalues show a transition from level clustering to level repulsion as one moves from the regular to chaotic regime in the $(\epsilon,{\tilde\omega_c})$ plane. The $\Delta_3$ statistic confirms this transition. In the chaotic regime, the eigenfunction statistics coincides with the Porter-Thomas prediction. Finally, we explicitly establish the phase space correspondence between the classical and quantum solutions via the Husimi phase space distributions of the model. Possible experimentally feasible conditions to see these effects are discussed.Comment: 26 pages and 17 PstScript figures, two large ones can be obtained from the Author

Deep Depth From Focus

Depth from focus (DFF) is one of the classical ill-posed inverse problems in computer vision. Most approaches recover the depth at each pixel based on the focal setting which exhibits maximal sharpness. Yet, it is not obvious how to reliably estimate the sharpness level, particularly in low-textured areas. In this paper, we propose `Deep Depth From Focus (DDFF)' as the first end-to-end learning approach to this problem. One of the main challenges we face is the hunger for data of deep neural networks. In order to obtain a significant amount of focal stacks with corresponding groundtruth depth, we propose to leverage a light-field camera with a co-calibrated RGB-D sensor. This allows us to digitally create focal stacks of varying sizes. Compared to existing benchmarks our dataset is 25 times larger, enabling the use of machine learning for this inverse problem. We compare our results with state-of-the-art DFF methods and we also analyze the effect of several key deep architectural components. These experiments show that our proposed method `DDFFNet' achieves state-of-the-art performance in all scenes, reducing depth error by more than 75% compared to the classical DFF methods.Comment: accepted to Asian Conference on Computer Vision (ACCV) 201

Pauli principle and chaos in a magnetized disk

We present results of a detailed quantum mechanical study of a gas of $N$ noninteracting electrons confined to a circular boundary and subject to homogeneous dc plus ac magnetic fields $(B=B_{dc}+B_{ac}f(t)$, with $f(t+2\pi/\omega_0)=f(t)$). We earlier found a one-particle {\it classical} phase diagram of the (scaled) Larmor frequency $\tilde\omega_c=omega_c/\omega_0$ {\rm vs} $\epsilon=B_{ac}/B_{dc}$ that separates regular from chaotic regimes. We also showed that the quantum spectrum statistics changed from Poisson to Gaussian orthogonal ensembles in the transition from classically integrable to chaotic dynamics. Here we find that, as a function of $N$ and $(\epsilon,\tilde\omega_c)$, there are clear quantum signatures in the magnetic response, when going from the single-particle classically regular to chaotic regimes. In the quasi-integrable regime the magnetization non-monotonically oscillates between diamagnetic and paramagnetic as a function of $N$. We quantitatively understand this behavior from a perturbation theory analysis. In the chaotic regime, however, we find that the magnetization oscillates as a function of $N$ but it is {\it always} diamagnetic. Equivalent results are also presented for the orbital currents. We also find that the time-averaged energy grows like $N^2$ in the quasi-integrable regime but changes to a linear $N$ dependence in the chaotic regime. In contrast, the results with Bose statistics are akin to the single-particle case and thus different from the fermionic case. We also give an estimate of possible experimental parameters were our results may be seen in semiconductor quantum dot billiards.Comment: 22 pages, 7 GIF figures, Phys. Rev. E. (1999

Self-supervised Depth Estimation to Regularise Semantic Segmentation in Knee Arthroscopy

Intra-operative automatic semantic segmentation of knee joint structures can assist surgeons during knee arthroscopy in terms of situational awareness. However, due to poor imaging conditions (e.g., low texture, overexposure, etc.), automatic semantic segmentation is a challenging scenario, which justifies the scarce literature on this topic. In this paper, we propose a novel self-supervised monocular depth estimation to regularise the training of the semantic segmentation in knee arthroscopy. To further regularise the depth estimation, we propose the use of clean training images captured by the stereo arthroscope of routine objects (presenting none of the poor imaging conditions and with rich texture information) to pre-train the model. We fine-tune such model to produce both the semantic segmentation and self-supervised monocular depth using stereo arthroscopic images taken from inside the knee. Using a data set containing 3868 arthroscopic images captured during cadaveric knee arthroscopy with semantic segmentation annotations, 2000 stereo image pairs of cadaveric knee arthroscopy, and 2150 stereo image pairs of routine objects, we show that our semantic segmentation regularised by self-supervised depth estimation produces a more accurate segmentation than a state-of-the-art semantic segmentation approach modeled exclusively with semantic segmentation annotation.Comment: 10 pages, 6 figure

Understanding Real World Indoor Scenes With Synthetic Data

Scene understanding is a prerequisite to many high level tasks for any automated intelligent machine operating in real world environments. Recent attempts with supervised learning have shown promise in this direction but also highlighted the need for enormous quantity of supervised data- performance increases in proportion to the amount of data used. However, this quickly becomes prohibitive when considering the manual labour needed to collect such data. In this work, we focus our attention on depth based semantic per-pixel labelling as a scene understanding problem and show the potential of computer graphics to generate virtually unlimited labelled data from synthetic 3D scenes. By carefully synthesizing training data with appropriate noise models we show comparable performance to state-of-the-art RGBD systems on NYUv2 dataset despite using only depth data as input and set a benchmark on depth-based segmentation on SUN RGB-D dataset