In general

two or more images of a single scene are related by the so-called epipolar geometry. Since the epipolar geometry contains all geometric information that is necessary for establishing correspondence

it is commonly used for the extraction of three-dimensional information in computer vision

photogrammetry and remote sensing. The epipolar geometry means that a point （a） in the image is mapped to the point on the known linear line （epipolar line） or non-linear curve （epipolar curve） in the other image. In case of aerial and perspective imagery

the epipolar geometry is mathematically well founded and widely used in computer vision and aerial photogrammetry. It is told that the epipolar geometry of the linear push-broom sensor is different from that of the perspective one and that the epipolar geometry of perspective imagery cannot be applied to linear push-broom imagery. This paper addresses the epipolar geometry of linear push-broom imagery. Compared with the epipolar geometry of frame perspective images

we qualitatively analyze the epipolarity model of perspective and aerial imagery and propose an epipolarity model of linear push-broom sensor images. The proposed epipolarity model is a non-linear hyperbola curve

based on the approach of track of projection and depends on the sensor model of collinear equation. We discuss the pro- perties of epipolar curves of linear push-broom sensor images

experiment with a kind of classical linear push-broom sensor images: SPOT

draw a conclusion about the epipolar geometry of linear push-broom sensor images

and build the theoretical basis for the application of epipolar curves.