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We innovatively propose a flexible and consistent face alignment framework,LDDMM-Face, the key contribution of which is a deformation layer that naturallyembeds facial geometry in a diffeomorphic way. Instead of predicting faciallandmarks via heatmap or coordinate regression, we formulate this task in adiffeomorphic registration manner and predict momenta that uniquelyparameterize the deformation between initial boundary and true boundary, andthen perform large deformation diffeomorphic metric mapping (LDDMM)simultaneously for curve and landmark to localize the facial landmarks. Due tothe embedding of LDDMM into a deep network, LDDMM-Face can consistentlyannotate facial landmarks without ambiguity and flexibly handle variousannotation schemes, and can even predict dense annotations from sparse ones.Our method can be easily integrated into various face alignment networks. Weextensively evaluate LDDMM-Face on four benchmark datasets: 300W, WFLW, HELENand COFW-68. LDDMM-Face is comparable or superior to state-of-the-art methodsfor traditional within-dataset and same-annotation settings, but trulydistinguishes itself with outstanding performance when dealing withweakly-supervised learning (partial-to-full), challenging cases (e.g., occludedfaces), and different training and prediction datasets. In addition, LDDMM-Faceshows promising results on the most challenging task of predicting acrossdatasets with different annotation schemes.

LDDMM-Face: Large Deformation Diffeomorphic Metric Learning for Flexible and Consistent Face Alignment