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In this letter, we extend the concept of level lines of scalar images to vector-valued data. Consistent with the scalar case, we define the level-lines of vector-valued images as the integral curves of the directions of minimal vectorial change. This direction, and the magnitude of the change, are computed using classical Riemannian geometry. As an example of the use of this new concept, we show how to visualize the basic geometry of vector-valued images with a scalar image.