There　are　several　methods　to　recognize　and　reconstruct　a　human　face　image.　The　principal　component　analysis　(PCA)　is　a　successful　approach　because　of　its　effective　extraction　of　the　global　feature　and　excellent　reconstruction　of　face　image.　However,　the　crucial　shortcomings　of　PCA　are　its　low　recognition　rate　and　overfitting　of　feature　extraction　which　leads　to　the　dependence　of　training　data　on　training　samples.　In　this　paper,　a　modified　two-dimension　principal　component　analysis　(2DPCA)　and　bidirectional　principal　component　analysis　(BDPCA)　methods　based　on　quaternion　matrix　are　proposed　to　recognize　and　reconstruct　a　color　face　image.　In　these　methods,　the　spatial　distribution　information　of　color　images　is　used　to　represent　a　color　face,　and　the　2DPCA　or　BDPCA　feature　of　color　face　image　is　extracted　by　reducing　the　dimensionality　in　both　column　and　row　directions.　A　method　obtaining　orthogonal　eigen-vector　set　of　quaternion　matrix　is　proposed.　Numerous　experiments　show　that　the　present　approach　based　on　quaternion　matrix　can　effectively　smooth　the　overfitting　issue　and　substantially　enhance　the　recognition　rate.　(C)　2010　Elsevier　B.V.　All　rights　reserved.