StEik: Stabilizing the Optimization of Neural Signed Distance Functions and Finer Shape Representation

We present new insights and a novel paradigm (StEik) for learning implicit neural representations (INR) of shapes. In particular, we shed light on the popular eikonal loss used for imposing a signed distance function constraint in INR. We show analytically that as the representation power of the network increases, the optimization approaches a partial differential equation (PDE) in the continuum limit that is unstable. We show that this instability can manifest in existing network optimization, leading to irregularities in the reconstructed surface and/or convergence to sub-optimal local minima, and thus fails to capture fine geometric and topological structure. We show analytically how other terms added to the loss, currently used in the literature for other purposes, can actually eliminate these instabilities. However, such terms can over-regularize the surface, preventing the representation of fine shape detail. Based on a similar PDE theory for the continuum limit, we introduce a new regularization term that still counteracts the eikonal instability but without over-regularizing. Furthermore, since stability is now guaranteed in the continuum limit, this stabilization also allows for considering new network structures that are able to represent finer shape detail. We introduce such a structure based on quadratic layers. Experiments on multiple benchmark data sets show that our new regularization and network are able to capture more precise shape details and more accurate topology than existing state-of-the-art.

Image Reconstruction from Events. Why learn it?

Traditional cameras measure image intensity. Event cameras, by contrast, measure per-pixel temporal intensity changes asynchronously. Recovering intensity from events is a popular research topic since the reconstructed images inherit the high dynamic range (HDR) and high-speed properties of events; hence they can be used in many robotic vision applications and to generate slow-motion HDR videos. However, state-of-the-art methods tackle this problem by training an event-to-image recurrent neural network (RNN), which lacks explainability and is difficult to tune. In this work we show, for the first time, how tackling the joint problem of motion and intensity estimation leads us to model event-based image reconstruction as a linear inverse problem that can be solved without training an image reconstruction RNN. Instead, classical and learning-based image priors can be used to solve the problem and remove artifacts from the reconstructed images. The experiments show that the proposed approach generates images with visual quality on par with state-of-the-art methods despite only using data from a short time interval (i.e., without recurrent connections). Our method can also be used to improve the quality of images reconstructed by approaches that first estimate the image Laplacian; here our method can be interpreted as Poisson reconstruction guided by image priors.

Deep Learning 3D Dose Prediction for Conventional Lung IMRT Using Consistent/Unbiased Automated Plans

Deep learning (DL) 3D dose prediction has recently gained a lot of attention. However, the variability of plan quality in the training dataset, generated manually by planners with wide range of expertise, can dramatically effect the quality of the final predictions. Moreover, any changes in the clinical criteria requires a new set of manually generated plans by planners to build a new prediction model. In this work, we instead use consistent plans generated by our in-house automated planning system (named ``ECHO'') to train the DL model. ECHO (expedited constrained hierarchical optimization) generates consistent/unbiased plans by solving large-scale constrained optimization problems sequentially. If the clinical criteria changes, a new training data set can be easily generated offline using ECHO, with no or limited human intervention, making the DL-based prediction model easily adaptable to the changes in the clinical practice. We used 120 conventional lung patients (100 for training, 20 for testing) with different beam configurations and trained our DL-model using manually-generated as well as automated ECHO plans. We evaluated different inputs: (1) CT+(PTV/OAR)contours, and (2) CT+contours+beam configurations, and different loss functions: (1) MAE (mean absolute error), and (2) MAE+DVH (dose volume histograms). The quality of the predictions was compared using different DVH metrics as well as dose-score and DVH-score, recently introduced by the AAPM knowledge-based planning grand challenge. The best results were obtained using automated ECHO plans and CT+contours+beam as training inputs and MAE+DVH as loss function.

An Efficiently Coupled Shape and Appearance Prior for Active Contour Segmentation

This paper proposes a novel training model based on shape and appearance features for object segmentation in images and videos. Whereas most such models rely on two-dimensional appearance templates or a finite set of descriptors, our appearance-based feature is a one-dimensional function, which is efficiently coupled with the object's shape by integrating intensities along the object's iso-contours. Joint PCA training on these shape and appearance features further exploits shape-appearance correlations and the resulting training model is incorporated in an active-contour-type energy functional for recognition-segmentation tasks. Experiments on synthetic and infrared images demonstrate how this shape and appearance training model improves accuracy compared to methods based on the Chan-Vese energy.

Multitask 3D CBCT-to-CT Translation and Organs-at-Risk Segmentation Using Physics-Based Data Augmentation

Purpose: In current clinical practice, noisy and artifact-ridden weekly cone-beam computed tomography (CBCT) images are only used for patient setup during radiotherapy. Treatment planning is done once at the beginning of the treatment using high-quality planning CT (pCT) images and manual contours for organs-at-risk (OARs) structures. If the quality of the weekly CBCT images can be improved while simultaneously segmenting OAR structures, this can provide critical information for adapting radiotherapy mid-treatment as well as for deriving biomarkers for treatment response. Methods: Using a novel physics-based data augmentation strategy, we synthesize a large dataset of perfectly/inherently registered planning CT and synthetic-CBCT pairs for locally advanced lung cancer patient cohort, which are then used in a multitask 3D deep learning framework to simultaneously segment and translate real weekly CBCT images to high-quality planning CT-like images. Results: We compared the synthetic CT and OAR segmentations generated by the model to real planning CT and manual OAR segmentations and showed promising results. The real week 1 (baseline) CBCT images which had an average MAE of 162.77 HU compared to pCT images are translated to synthetic CT images that exhibit a drastically improved average MAE of 29.31 HU and average structural similarity of 92% with the pCT images. The average DICE scores of the 3D organs-at-risk segmentations are: lungs 0.96, heart 0.88, spinal cord 0.83 and esophagus 0.66. Conclusions: We demonstrate an approach to translate artifact-ridden CBCT images to high quality synthetic CT images while simultaneously generating good quality segmentation masks for different organs-at-risk. This approach could allow clinicians to adjust treatment plans using only the routine low-quality CBCT images, potentially improving patient outcomes.

Verifying the Causes of Adversarial Examples

The robustness of neural networks is challenged by adversarial examples that contain almost imperceptible perturbations to inputs, which mislead a classifier to incorrect outputs in high confidence. Limited by the extreme difficulty in examining a high-dimensional image space thoroughly, research on explaining and justifying the causes of adversarial examples falls behind studies on attacks and defenses. In this paper, we present a collection of potential causes of adversarial examples and verify (or partially verify) them through carefully-designed controlled experiments. The major causes of adversarial examples include model linearity, one-sum constraint, and geometry of the categories. To control the effect of those causes, multiple techniques are applied such as $L_2$ normalization, replacement of loss functions, construction of reference datasets, and novel models using multi-layer perceptron probabilistic neural networks (MLP-PNN) and density estimation (DE). Our experiment results show that geometric factors tend to be more direct causes and statistical factors magnify the phenomenon, especially for assigning high prediction confidence. We believe this paper will inspire more studies to rigorously investigate the root causes of adversarial examples, which in turn provide useful guidance on designing more robust models.

An Adaptive View of Adversarial Robustness from Test-time Smoothing Defense

The safety and robustness of learning-based decision-making systems are under threats from adversarial examples, as imperceptible perturbations can mislead neural networks to completely different outputs. In this paper, we present an adaptive view of the issue via evaluating various test-time smoothing defense against white-box untargeted adversarial examples. Through controlled experiments with pretrained ResNet-152 on ImageNet, we first illustrate the non-monotonic relation between adversarial attacks and smoothing defenses. Then at the dataset level, we observe large variance among samples and show that it is easy to inflate accuracy (even to 100%) or build large-scale (i.e., with size ~10^4) subsets on which a designated method outperforms others by a large margin. Finally at the sample level, as different adversarial examples require different degrees of defense, the potential advantages of iterative methods are also discussed. We hope this paper reveal useful behaviors of test-time defenses, which could help improve the evaluation process for adversarial robustness in the future.

An Interactive Control Approach to 3D Shape Reconstruction

The ability to accurately reconstruct the 3D facets of a scene is one of the key problems in robotic vision. However, even with recent advances with machine learning, there is no high-fidelity universal 3D reconstruction method for this optimization problem as schemes often cater to specific image modalities and are often biased by scene abnormalities. Simply put, there always remains an information gap due to the dynamic nature of real-world scenarios. To this end, we demonstrate a feedback control framework which invokes operator inputs (also prone to errors) in order to augment existing reconstruction schemes. For proof-of-concept, we choose a classical region-based stereoscopic reconstruction approach and show how an ill-posed model can be augmented with operator input to be much more robust to scene artifacts. We provide necessary conditions for stability via Lyapunov analysis and perhaps more importantly, we show that the stability depends on a notion of absolute curvature. Mathematically, this aligns with previous work that has shown Ricci curvature as proxy for functional robustness of dynamical networked systems. We conclude with results that show how our method can improve standalone reconstruction schemes.

Accelerated Optimization in the PDE Framework: Formulations for the Manifold of Diffeomorphisms

We consider the problem of optimization of cost functionals on the infinite-dimensional manifold of diffeomorphisms. We present a new class of optimization methods, valid for any optimization problem setup on the space of diffeomorphisms by generalizing Nesterov accelerated optimization to the manifold of diffeomorphisms. While our framework is general for infinite dimensional manifolds, we specifically treat the case of diffeomorphisms, motivated by optical flow problems in computer vision. This is accomplished by building on a recent variational approach to a general class of accelerated optimization methods by Wibisono, Wilson and Jordan, which applies in finite dimensions. We generalize that approach to infinite dimensional manifolds. We derive the surprisingly simple continuum evolution equations, which are partial differential equations, for accelerated gradient descent, and relate it to simple mechanical principles from fluid mechanics. Our approach has natural connections to the optimal mass transport problem. This is because one can think of our approach as an evolution of an infinite number of particles endowed with mass (represented with a mass density) that moves in an energy landscape. The mass evolves with the optimization variable, and endows the particles with dynamics. This is different than the finite dimensional case where only a single particle moves and hence the dynamics does not depend on the mass. We derive the theory, compute the PDEs for accelerated optimization, and illustrate the behavior of these new accelerated optimization schemes.

Towards an Understanding of Neural Networks in Natural-Image Spaces

Two major uncertainties, dataset bias and perturbation, prevail in state-of-the-art AI algorithms with deep neural networks. In this paper, we present an intuitive explanation for these issues as well as an interpretation of the performance of deep networks in a natural-image space. The explanation consists of two parts: the philosophy of neural networks and a hypothetic model of natural-image spaces. Following the explanation, we slightly improve the accuracy of a CIFAR-10 classifier by introducing an additional "random-noise" category during training. We hope this paper will stimulate discussion in the community regarding the topological and geometric properties of natural-image spaces to which deep networks are applied.