Photometric invariance is used in many computer vision applications. The advantage of photometric invariance is the robustness against shadows, shading, and illumination conditions. However, the drawbacks of photometric invariance is the loss of discriminative power and the inherent instabilities caused by the non-linear transformations to compute the invariants. In this paper, we propose a new class of derivatives which we refer to as photometric quasi-invariants. These quasi-invariants share with full invariants the nice property that they are robust against photometric edges, such as shadows or specular edges. Further, these quasi-invariants do not have the inherent instabilities of full photometric invariants. We will apply these quasi-invariant derivatives in the context of photometric invariant edge detection and classification. Experiments show that the quasi-invariant derivatives are stable and they significantly outperform the full invariant derivatives in discriminative power.