This paper explores visual motion-based invariants, resulting in a new instantaneous domain where: a) the stationary environment is perceived as unchanged, even as the 2D images undergo continuous changes due to camera motion, b) obstacles can be detected and potentially avoided in specific subspaces, and c) moving objects can potentially be detected. To achieve this, we make use of nonlinear functions derived from measurable optical flow, which are linked to geometric 3D invariants. We present simulations involving a camera that translates and rotates relative to a 3D object, capturing snapshots of the camera projected images. We show that the object appears unchanged in the new domain over time. We process real data from the KITTI dataset and demonstrate how to segment space to identify free navigational regions and detect obstacles within a predetermined subspace. Additionally, we present preliminary results, based on the KITTI dataset, on the identification and segmentation of moving objects, as well as the visualization of shape constancy. This representation is straightforward, relying on functions for the simple de-rotation of optical flow. This representation only requires a single camera, it is pixel-based, making it suitable for parallel processing, and it eliminates the necessity for 3D reconstruction techniques.
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