I present a new focal-plane analog very-large-scale-integrated (aVLSI) sensor that estimates optical flow in two visual dimensions. Its computational architecture consists of a two-layer network of locally connected motion units that collectively estimate the optimal optical flow field. The applied gradient-based optical flow model assumes visual motion to be translational and smooth, and is formulated as a convex optimization problem. The model also guarantees that the estimation problem is well-posed regardless of the visual input by imposing a bias towards a preferred motion under ambiguous or noisy visual conditions. Model parameters can be globally adjusted, leading to a rich output behavior. Varying the smoothness strength, for example, can provide a continuous spectrum of motion estimates, ranging from normal to global optical flow. The non-linear network conductances improve the resulting optical flow estimate because they reduce spatial smoothing across large velocity differences and minimize the bias for reliable stimuli. Extended characterization and recorded optical flow fields from a 30 × 30 array prototype sensor demonstrate the validity of the optical flow model and the robustness and functionality of the computational architecture and its implementation.The ability to estimate motion using visual information is important for any natural and artificial agent behaving in a dynamical visual environment. Knowing the relative motions between different objects as well as between objects and the agent is crucial for a cognitive perception of the environment and thus a prerequisite for intelligent behavior. However, the demand for real-time processing and the limited resources available on freely behaving agents impose severe constraints that require efficient computational systems in terms of processing speed, energy consumption, and physical dimensions. These requirements favor parallel computational architectures. Implementations of such architectures become particularly appealing when image sensing and motion estimation circuitry can be combined within a single sensor. Furthermore, a sensor architecture that consists of a topographically uniform array of identical processing units (pixels) has the advantage that processing power scales with array size, thus keeping processing speed independent of spatial array resolution. Analog VLSI circuits are particularly suited for such architectures because they require significantly less power and silicon area than digital circuits for computational tasks of comparable complexity [1]. Furthermore, timecontinuous analog processing matches the continuous nature of visual motion information. Temporal aliasing artifacts do not occur while they can be a significant problem in clocked, sequential circuit implementations, in particular when limited to low frame-rates [2].Visual information is -in general -locally ambiguous and noisy, and often does not allow a unique estimation of visual motion. A prominent ambiguity, commonly referred to as the "aperture problem" [3]...