In　this　paper,　we　propose　a　novel　Dynamic　Geometrical　Image　Network　(DGIN)　for　automatic　4D　Facial　Expression　Recognition　(FER).　Given　a　3D　video　represented　as　a　sequence　of　face　scans,　we　first　estimate　their　differential　geometry　quantities　and　generate　geometrical　images,　including　Depth　Images　(DPI),　three　Normal　Component　Images　(NCI)　and　Shape　Index　Images　(SII).　These　geometrical　images　are　then　fed　into　DGIN　for　end-to-end　training　and　prediction.　DGIN　consists　of　a　short-term　temporal　pooling　layer　for　dynamic　geometric　image　generation,　several　repetitions　of　convolution+ReLU+pooling　layers　for　facial　spatial　feature　extraction,　and　a　long-term　temporal　pooling　layer　for　dynamic　feature　map　fusion,　followed　by　fully　connected　layers　and　a　joint　loss　layer.　During　the　training　phase,　the　two-stage　longterm　and　short-term　sliding　window　scheme　is　introduced　for　data　augmentation　and　temporal　pooling.　Meanwhile,　a　joint　loss　integrating　both　the　cross-entropy　loss　and　the　triplet　loss　is　used　to　achieve　more　discriminative　expression　features.　In　the　testing　phase,　only　the　short-term　sliding　window　scheme　is　applied　to　the　whole　video　sequence　of　certain　geometric　images,　whose　outputs　further　go　through　the　deep　net　for　expression　similarity　measurement.　The　final　result　is　achieved　by　fusing　the　predicted　expression　scores　of　different　types　of　geometrical　images.　Experimental　results　reported　on　the　BU-　4DFE　database　demonstrate　the　effectiveness　of　the　proposed　approach.　©　2018　IEEE.