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  1. The success of image generative models has enabled us to build methods that can edit images based on text or other user input. However, these methods are bespoke, imprecise, require additional information, or are limited to only 2D image edits. We present GeoDiffuser, a zero-shot optimization-based method that unifies common 2D and 3D image-based object editing capabilities into a single method. Our key insight is to view image editing operations as geometric transformations. We show that these transformations can be directly incorporated into the attention layers in diffusion models to implicitly perform editing operations. Our training-free optimization method uses an objective function that seeks to preserve object style but generate plausible images, for instance with accurate lighting and shadows. It also inpaints disoccluded parts of the image where the object was originally located. Given a natural image and user input, we segment the foreground object using SAM and estimate a corresponding transform which is used by our optimization approach for editing. GeoDiffuser can perform common 2D and 3D edits like object translation, 3D rotation, and removal. We present quantitative results, including a perceptual study, that shows how our approach is better than existing methods. 
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  2. We present an implementation of a formally verified safety fallback controller for improved collision avoidance in an autonomous vehicle research platform. Our approach uses a primary trajectory planning system that aims for collision-free navigation in the presence of pedestrians and other vehicles, and a fallback controller that guards its behavior. The safety fallback controller excludes the possibility of collisions by accounting for nondeterministic uncertainty in the dynamics of the vehicle and moving obstacles, and takes over the primary controller as necessary. We demonstrate the system in an experimental set-up that includes simulations and real-world tests with a 1/5-scale vehicle. In stressing simulation scenarios, the safety fallback controller significantly reduces the number of collisions. 
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