We innovatively propose a flexible and consistent face alignment framework, LDDMM-Face, the key contribution of which is a deformation layer that naturally embeds facial geometry in a diffeomorphic way. Instead of predicting facial landmarks via heatmap or coordinate regression, we formulate this task in a diffeomorphic registration manner and predict momenta that uniquely parameterize the deformation between initial boundary and true boundary, and then perform large deformation diffeomorphic metric mapping (LDDMM) simultaneously for curve and landmark to localize the facial landmarks. Due to the embedding of LDDMM into a deep network, LDDMM-Face can consistently annotate facial landmarks without ambiguity and flexibly handle various annotation schemes, and can even predict dense annotations from sparse ones. Our method can be easily integrated into various face alignment networks. We extensively evaluate LDDMM-Face on four benchmark datasets: 300W, WFLW, HELEN and COFW-68. LDDMM-Face is comparable or superior to state-of-the-art methods for traditional within-dataset and same-annotation settings, but truly distinguishes itself with outstanding performance when dealing with weakly-supervised learning (partial-to-full), challenging cases (e.g., occluded faces), and different training and prediction datasets. In addition, LDDMM-Face shows promising results on the most challenging task of predicting across datasets with different annotation schemes.
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