Most deep neural network (DNN) verification research focuses on qualitative verification, which answers whether or not a DNN violates a safety/robustness property. This paper proposes an approach to convert qualitative verification into quantitative verification for neural networks. The resulting quantitative verification method not only can answer YES or NO questions but also can compute the probability of a property being violated. To do that, we introduce the concept of a probabilistic star (or shortly ProbStar), a new variant of the well-known star set, in which the predicate variables belong to a Gaussian distribution and propose an approach to compute the probability of a probabilistic star in high-dimensional space. Unlike existing works dealing with constrained input sets, our work considers the input set as a truncated multivariate normal (Gaussian) distribution, i.e., besides the constraints on the input variables, the input set has a probability of the constraints being satisfied. The input distribution is represented as a probabilistic star set and is propagated through a network to construct the output reachable set containing multiple ProbStars, which are used to verify the safety or robustness properties of the network. In case of a property is violated, the violation probability can be computed precisely by an exact verification algorithm or approximately by an overapproximate verification algorithm. The proposed approach is implemented in a tool named StarV and is evaluated using the well-known ACASXu networks and a rocket landing benchmark.

Over the past decade, a lot of researches have been done on the development of advanced driver assistance systems (ADAS). Most of these ADAS are now active and need to be tested and evaluated before large deployment. In these ADAS, the prototyping and the implementation of the control stages are risky stages and not so easy to carry out. Indeed, the prototyping and the test of such reactive algorithms need heavy hardware and software supports (dedicated vehicle, actuators, hardware architecture, software architecture, sensors). To achieve such active devices, additional developments and implementation of numerous expensive embedded devices are required. Therefore, in order to reduce both time and risk, in early design stage, it becomes necessary to have a very realistic simulation environment dedicated to the development and to the evaluation of these ADAS. For such virtual platform, it is mandatory to provide physics-driven road environments, virtual embedded sensors, and physics-based vehicle models. In this publication, we present a dedicated couple of platforms with their efficient interconnection for the prototyping of such ADAS. Initially, the SiVIC simulation platform has been developed to generate the virtual world (environments, sensors, actuators, vehicles). In order to improve the real time prototyping capabilities of SiVIC, an efficient interconnection of this first platform has been done with RTMaps platform. This second one is mainly dedicated to the multi-sensors data processing (data management, fusion, flow recording and replaying). In this paper we will show the interest of such bi-directionnal interconnected platforms to prototype complex and real time embedded ADAS. This interconnection can be done not only on one computer but also on a distributed and distant computers architecture. The relevance of this approach will be illustrated with an automatic parking application.

Abstract Accurate depth estimation is a challenging, yet essential step in the conversion of a 2D image sequence to a 3D stereo sequence. We present a novel approach to construct a temporally coherent depth map for each image in a sequence. The quality of the estimated depth is high enough for the purpose of2D to 3D stereo conversion. Our approach first combines the video sequence into a panoramic image. A user can scribble on this single panoramic image to specify depth information. The depth is then propagated to the remainder of the panoramic image. This depth map is then remapped to the original sequence and used as the initial guess for each individual depth map in the sequence. Our approach greatly simplifies the required user interaction during the assignment of the depth and allows for relatively free camera movement during the generation of a panoramic image. We demonstrate the effectiveness of our method by showing stereo converted sequences with various camera motions.

Abstract Computer graphics is one of the most efficient ways to create a stereoscopic image. The process of stereoscopic CG generation is, however, still very inefficient compared to that of monoscopic CG generation. Despite that stereo images are very similar to each other, they are rendered and manipulated independently. Additional requirements for disparity control specific to stereo images lead to even greater inefficiency. This paper proposes a method to reduce the inefficiency accompanied in the creation of a stereoscopic image. The system automatically generates an optimized single image representation of the entire visible area from both cameras. The single image can be easily manipulated with conventional techniques, as it is spatially smooth and maintains the original shapes of scene objects. In addition, a stereo image pair can be easily generated with an arbitrary disparity setting. These convenient and efficient features are achieved by the automatic generation of a stereo camera pair, robust occlusion detection with a pair of Z‐buffers, an optimization method for spatial smoothness, and stereo image pair generation with a non‐linear disparity adjustment. Experiments show that our technique dramatically improves the efficiency of stereoscopic image creation while preserving the quality of the results.