Deep neural networks (DNNs) achieve remarkable performance in object recog- nition tasks. However, their robustness against realistic geometric perturbations, especially those induced by 3D viewpoint variations and projective transformations, remains limited. While most certification methods focus on additive pixel-wise perturbations, structured geo- metric attacks remain underexplored, particularly for contour classifiers. This paper presents a multimodal certification framework for object recognition combining image and contour representations under 3D–2D projective transformations. The proposed approach relies on abstract interpretation and extends the DeepPoly abstract domain to model projective at- tacks acting on planar contours through the group P SLp2, Cq. Furthermore, we introduce a comparative analysis of contour reparameterization strategies, demonstrating that affine reparameterization significantly reduces certification conservativeness under projective dis- tortions.
Smati et al. (Thu,) studied this question.