Extracting a functional representation from a dictionary for non-rigid shape matching

Shape matching is a fundamental problem in computer graphics with many applications. Functional maps translate the point-wise shape-matching problem into its functional counterpart and have inspired numerous solutions over the last decade. Nearly all the solutions based on functional maps rely on the eigenfunctions of the Laplace-Beltrami Operator (LB) to describe the functional spaces defined on the surfaces and then convert the functional correspondences into point-wise correspondences. However, this final step is often error-prone and inaccurate in tiny regions and protrusions, where the energy of LB does not uniformly cover the surface. We propose a new functional basis Principal Components of a Dictionary (PCD) to address such intrinsic limitation. PCD constructs an orthonormal basis from the Principal Component Analysis (PCA) of a dictionary of functions defined over the shape. These dictionaries can target specific properties of the final basis, such as achieving an even spreading of energy. Our experimental evaluation compares seven different dictionaries on established benchmarks, showing that PCD is suited to target different shape-matching scenarios, resulting in more accurate point-wise maps than the LB basis when used in the same pipeline. This evidence provides a promising alternative for improving correspondence estimation, confirming the power and flexibility of functional maps.

Class Distribution Monitoring for Concept Drift Detection

We introduce Class Distribution Monitoring (CDM), an effective concept-drift detection scheme that monitors the class-conditional distributions of a datastream. In particular, our solution leverages multiple instances of an online and nonparametric change-detection algorithm based on QuantTree. CDM reports a concept drift after detecting a distribution change in any class, thus identifying which classes are affected by the concept drift. This can be precious information for diagnostics and adaptation. Our experiments on synthetic and real-world datastreams show that when the concept drift affects a few classes, CDM outperforms algorithms monitoring the overall data distribution, while achieving similar detection delays when the drift affects all the classes. Moreover, CDM outperforms comparable approaches that monitor the classification error, particularly when the change is not very apparent. Finally, we demonstrate that CDM inherits the properties of the underlying change detector, yielding an effective control over the expected time before a false alarm, or Average Run Length (ARL$_0$).

Composite Layers for Deep Anomaly Detection on 3D Point Clouds

Deep neural networks require specific layers to process point clouds, as the scattered and irregular location of points prevents us from using convolutional filters. Here we introduce the composite layer, a new convolutional operator for point clouds. The peculiarity of our composite layer is that it extracts and compresses the spatial information from the position of points before combining it with their feature vectors. Compared to well-known point-convolutional layers such as those of ConvPoint and KPConv, our composite layer provides additional regularization and guarantees greater flexibility in terms of design and number of parameters. To demonstrate the design flexibility, we also define an aggregate composite layer that combines spatial information and features in a nonlinear manner, and we use these layers to implement a convolutional and an aggregate CompositeNet. We train our CompositeNets to perform classification and, most remarkably, unsupervised anomaly detection. Our experiments on synthetic and real-world datasets show that, in both tasks, our CompositeNets outperform ConvPoint and achieve similar results as KPConv despite having a much simpler architecture. Moreover, our CompositeNets substantially outperform existing solutions for anomaly detection on point clouds.

Deep Open-Set Recognition for Silicon Wafer Production Monitoring

The chips contained in any electronic device are manufactured over circular silicon wafers, which are monitored by inspection machines at different production stages. Inspection machines detect and locate any defect within the wafer and return a Wafer Defect Map (WDM), i.e., a list of the coordinates where defects lie, which can be considered a huge, sparse, and binary image. In normal conditions, wafers exhibit a small number of randomly distributed defects, while defects grouped in specific patterns might indicate known or novel categories of failures in the production line. Needless to say, a primary concern of semiconductor industries is to identify these patterns and intervene as soon as possible to restore normal production conditions. Here we address WDM monitoring as an open-set recognition problem to accurately classify WDM in known categories and promptly detect novel patterns. In particular, we propose a comprehensive pipeline for wafer monitoring based on a Submanifold Sparse Convolutional Network, a deep architecture designed to process sparse data at an arbitrary resolution, which is trained on the known classes. To detect novelties, we define an outlier detector based on a Gaussian Mixture Model fitted on the latent representation of the classifier. Our experiments on a real dataset of WDMs show that directly processing full-resolution WDMs by Submanifold Sparse Convolutions yields superior classification performance on known classes than traditional Convolutional Neural Networks, which require a preliminary binning to reduce the size of the binary images representing WDMs. Moreover, our solution outperforms state-of-the-art open-set recognition solutions in detecting novelties.

Deep Autoencoders for Anomaly Detection in Textured Images using CW-SSIM

Detecting anomalous regions in images is a frequently encountered problem in industrial monitoring. A relevant example is the analysis of tissues and other products that in normal conditions conform to a specific texture, while defects introduce changes in the normal pattern. We address the anomaly detection problem by training a deep autoencoder, and we show that adopting a loss function based on Complex Wavelet Structural Similarity (CW-SSIM) yields superior detection performance on this type of images compared to traditional autoencoder loss functions. Our experiments on well-known anomaly detection benchmarks show that a simple model trained with this loss function can achieve comparable or superior performance to state-of-the-art methods leveraging deeper, larger and more computationally demanding neural networks.

Nonparametric and Online Change Detection in Multivariate Datastreams using QuantTree

We address the problem of online change detection in multivariate datastreams, and we introduce QuantTree Exponentially Weighted Moving Average (QT-EWMA), a nonparametric change-detection algorithm that can control the expected time before a false alarm, yielding a desired Average Run Length (ARL$_0$). Controlling false alarms is crucial in many applications and is rarely guaranteed by online change-detection algorithms that can monitor multivariate datastreams without knowing the data distribution. Like many change-detection algorithms, QT-EWMA builds a model of the data distribution, in our case a QuantTree histogram, from a stationary training set. To monitor datastreams even when the training set is extremely small, we propose QT-EWMA-update, which incrementally updates the QuantTree histogram during monitoring, always keeping the ARL$_0$ under control. Our experiments, performed on synthetic and real-world datastreams, demonstrate that QT-EWMA and QT-EWMA-update control the ARL$_0$ and the false alarm rate better than state-of-the-art methods operating in similar conditions, achieving lower or comparable detection delays.

Perception Visualization: Seeing Through the Eyes of a DNN

Artificial intelligence (AI) systems power the world we live in. Deep neural networks (DNNs) are able to solve tasks in an ever-expanding landscape of scenarios, but our eagerness to apply these powerful models leads us to focus on their performance and deprioritises our ability to understand them. Current research in the field of explainable AI tries to bridge this gap by developing various perturbation or gradient-based explanation techniques. For images, these techniques fail to fully capture and convey the semantic information needed to elucidate why the model makes the predictions it does. In this work, we develop a new form of explanation that is radically different in nature from current explanation methods, such as Grad-CAM. Perception visualization provides a visual representation of what the DNN perceives in the input image by depicting what visual patterns the latent representation corresponds to. Visualizations are obtained through a reconstruction model that inverts the encoded features, such that the parameters and predictions of the original models are not modified. Results of our user study demonstrate that humans can better understand and predict the system's decisions when perception visualizations are available, thus easing the debugging and deployment of deep models as trusted systems.

Adversarial Scratches: Deployable Attacks to CNN Classifiers

A growing body of work has shown that deep neural networks are susceptible to adversarial examples. These take the form of small perturbations applied to the model's input which lead to incorrect predictions. Unfortunately, most literature focuses on visually imperceivable perturbations to be applied to digital images that often are, by design, impossible to be deployed to physical targets. We present Adversarial Scratches: a novel L0 black-box attack, which takes the form of scratches in images, and which possesses much greater deployability than other state-of-the-art attacks. Adversarial Scratches leverage B\'ezier Curves to reduce the dimension of the search space and possibly constrain the attack to a specific location. We test Adversarial Scratches in several scenarios, including a publicly available API and images of traffic signs. Results show that, often, our attack achieves higher fooling rate than other deployable state-of-the-art methods, while requiring significantly fewer queries and modifying very few pixels.

Change Detection in Multivariate Datastreams: Likelihood and Detectability Loss

We address the problem of detecting changes in multivariate datastreams, and we investigate the intrinsic difficulty that change-detection methods have to face when the data dimension scales. In particular, we consider a general approach where changes are detected by comparing the distribution of the log-likelihood of the datastream over different time windows. Despite the fact that this approach constitutes the frame of several change-detection methods, its effectiveness when data dimension scales has never been investigated, which is indeed the goal of our paper. We show that the magnitude of the change can be naturally measured by the symmetric Kullback-Leibler divergence between the pre- and post-change distributions, and that the detectability of a change of a given magnitude worsens when the data dimension increases. This problem, which we refer to as \emph{detectability loss}, is due to the linear relationship between the variance of the log-likelihood and the data dimension. We analytically derive the detectability loss on Gaussian-distributed datastreams, and empirically demonstrate that this problem holds also on real-world datasets and that can be harmful even at low data-dimensions (say, 10).