This work presents an information-theoretic examination of diffusion-based purification methods, the state-of-the-art adversarial defenses that utilize diffusion models to remove malicious perturbations in adversarial examples. By theoretically characterizing the inherent purification errors associated with the Markov-based diffusion purifications, we introduce LoRID, a novel Low-Rank Iterative Diffusion purification method designed to remove adversarial perturbation with low intrinsic purification errors. LoRID centers around a multi-stage purification process that leverages multiple rounds of diffusion-denoising loops at the early time-steps of the diffusion models, and the integration of Tucker decomposition, an extension of matrix factorization, to remove adversarial noise at high-noise regimes. Consequently, LoRID increases the effective diffusion time-steps and overcomes strong adversarial attacks, achieving superior robustness performance in CIFAR-10/100, CelebA-HQ, and ImageNet datasets under both white-box and grey-box settings.

We tackle the problem of analyzing and retrieving technical drawings. First, we introduce DeepPatent, a new large-scale dataset for recognition and retrieval of design patent drawings. The dataset provides more than 350,000 design patent drawings for the purpose of image retrieval. Unlike existing datasets, DeepPatent provides fine-grained image retrieval associations within the collection of drawings and does not rely on cross-domain associations for supervision. We develop a baseline deep learning model, named Patent-Net, based on best practices for training retrieval models for static images. We demonstrate the superior performance of PatentNet when trained on our fine-grained associations of DeepPatent against other deep learning approaches and classic computer vision descriptors. With the introduction of this new dataset, and benchmark algorithms, we demonstrate that the analysis and retrieval of technical drawings remains an open challenge in computer vision; and that patent drawing retrieval provides a real-world testbench to spur research.

In this investigation, we focus on the problem of mapping the ground reflectivity with multiple laser scanners mounted on mobile robots/vehicles. The problem originates because regions of the ground become populated with a varying number of reflectivity measurements, whose value depends on the observer and its corresponding perspective. Here, we propose a novel automatic, data-driven computational mapping framework specifically aimed at preserving edge sharpness in the map reconstruction process and that considers the sources of measurement variation. Our new formulation generates map-perspective gradients and applies sub-set selection fusion and de-noising operators to these through iterative algorithms that minimize an ℓ1sparse regularized least squares formulation. The reconstruction of the ground reflectivity is then carried out based on Poisson's formulation posed as an ℓ2term promoting consistency with the fused gradient of map-perspectives and a term that ensures equality constraints with reference measurement map data. We demonstrate that our new framework outperforms the capabilities of the existing ones with experiments realized on Ford's fleet of autonomous vehicles. For example, we show that we can achieve map enhancement (i.e., contrast enhancement), artifact removal, de-noising, and map-stitching without requiring an additional reflectivity adjustment to calibrate sensors to the specific mounting and robot/vehicle motion.

We present a new method for joint automatic extrinsic calibration and sensor fusion for a multimodal sensor system comprising a LIDAR and an optical camera. Our approach exploits the natural alignment of depth and intensity edges when the calibration parameters are correct. Thus, in contrast to a number of existing approaches, we do not require the presence or identification of known alignment targets. On the other hand, the characteristics of each sensor modality, such as sampling pattern and information measured, are significantly different, making direct edge alignment difficult. To overcome this difficulty, we jointly fuse the data and estimate the calibration parameters. In particular, the joint processing evaluates and optimizes both the quality of edge alignment and the performance of the fusion algorithm using a common cost function on the output. We demonstrate accurate calibration in practical configurations in which depth measurements are sparse and contain no reflectivity information. Experiments on synthetic and real data obtained with a three-dimensional LIDAR sensor demonstrate the effectiveness of our approach.

Third generation full-waveform (FW) LIDAR systems collect time-resolved 1D signals generated by laser pulses reflecting off of intercepted objects. From these signals, scene depth profiles along each pulse path can be readily constructed. Using the conventional sampling process, however, massive amounts of data are typically required in order to achieve acceptable depth and spatial resolutions, and this data must be stored, transmitted, and processed. We have previously shown that such signals can be sampled at sub-Nyquist rates by using a finite rate of innovations (FRI) model. That work, however, used LIDAR data for which ground-truth distances were not available and it was therefore not possible to fully evaluate the range precision of an FRI-based representation. Here, we apply the proposed methodology to carefully ground-truthed laboratory data in order to better characterize its capabilities and limitations.

Third-generation full-waveform (FW) light detection and ranging (LIDAR) systems collect time-resolved 1-D signals generated by laser pulses reflected off of intercepted objects. From these signals, scene depth profiles along each pulse path can be readily constructed. By emitting a series of pulses toward a scene using a predefined scanning pattern and with the appropriate sampling and processing, an image-like depth map can be generated. Unfortunately, massive amounts of data are typically acquired to achieve acceptable depth and spatial resolutions. The sampling systems acquiring this data, however, seldom take into account the underlying low-dimensional structure generally present in FW signals and, consequently, they sample very inefficiently. Our main goal and focus here is to develop efficient sampling models and processes to collect individual time-resolved FW LIDAR signals. Specifically, we study sub-Nyquist sampling of the continuous-time LIDAR FW reflected pulses, considering two different sampling mechanisms: 1) modeling FW signals as short-duration pulses with multiple band-limited echoes; and 2) modeling them as signals with finite rates of innovation.

Third generation LIDAR full-waveform (FW) based systems collect 1D temporal profiles of laser pulses reflected by the intercepted objects to construct depth profiles along each pulse path. By emitting a series of pulses towards a scene using a predefined scanning pattern, a 3D image containing spatial-depth information can be constructed. Achieving super-resolution to resolve finer spatial details is of great interest because the spatial resolution of a LIDAR system is typically limited by the size of the spot on the target. In this study, we consider the problem of resolving range maps to resolutions smaller than the size of the spot using overlapping spots. This overlap provides the additional information needed to locate multiple objects within a spot using sparse source separation, thus achieving super-resolution.

In this paper, we address the problem of sampling the LIDAR range map. The significance of this problem is based upon the fact that large datasets generated by sampling inefficiently impose storage, processing and transmission limitations. Current compression approaches addressing these issues rely on collecting large amounts of data to analyze and throw away the redundancies. Unfortunately, the sampling performed by these approaches is still inefficient. Our approach to compression consists instead, on using a random uniform impulsive scan sampling scheme with sampling densities depending on the surface complexity. Turns out that the number of scanned time-resolved waveforms required to achieve “good” approximations, needs to satisfy the bound equation, where equation is an estimator of the surface numerical rank. Such a bound allows one to sub-sample surfaces which are close to a low-rank space and update, on the fly, the sampling densities required to improve the quality of the approximation.

One of the major problems associated with LIDAR sensing is that significant amounts of data must be collected to obtain detailed topographical information about a region. Current efforts to solve this problem have focused on designing compression algorithms which operate on the collected data. These, however, require the collection of large amounts of data only to discard most of it in some transformed domain. Instead, compressive sensing has demonstrated that highly accurate signal reconstructions are achievable even when sampling below the Nyquist rate. Such sensing is clearly desirable for LIDAR range data compression if it can be achieved. One notes, however, that compressive sensing requires a priori knowledge of the sparsifying basis of the signal which is a major problem for LIDAR since that basis depends not only on the underlying scene complexity but also on the laser spot size and target distance. For these reasons, the goal of this research is to take the first steps in establishing a relationship between typical LIDAR scenes of varying complexity and the sparsity of the scene compressively sampled.