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This paper explores visual motion-based invariants, resulting in a newinstantaneous domain where: a) the stationary environment is perceived asunchanged, even as the 2D images undergo continuous changes due to cameramotion, b) obstacles can be detected and potentially avoided in specificsubspaces, and c) moving objects can potentially be detected. To achieve this,we make use of nonlinear functions derived from measurable optical flow, whichare linked to geometric 3D invariants.  We present simulations involving a camera that translates and rotatesrelative to a 3D object, capturing snapshots of the camera projected images. Weshow that the object appears unchanged in the new domain over time. We processreal data from the KITTI dataset and demonstrate how to segment space toidentify free navigational regions and detect obstacles within a predeterminedsubspace. Additionally, we present preliminary results, based on the KITTIdataset, on the identification and segmentation of moving objects, as well asthe visualization of shape constancy.  This representation is straightforward, relying on functions for the simplede-rotation of optical flow. This representation only requires a single camera,it is pixel-based, making it suitable for parallel processing, and iteliminates the necessity for 3D reconstruction techniques.

Invariant-based Mapping of Space During General Motion of an Observer