Depth estimation of face images using the nonlinear least-squares model

Zhan Li Sun, Kin Man Lam, Qing Wei Gao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

35 Citations (Scopus)


In this paper, we propose an efficient algorithm to reconstruct the 3D structure of a human face from one or more of its 2D images with different poses. In our algorithm, the nonlinear least-squares model is first employed to estimate the depth values of facial feature points and the pose of the 2D face image concerned by means of the similarity transform. Furthermore, different optimization schemes are presented with regard to the accuracy levels and the training time required. Our algorithm also embeds the symmetrical property of the human face into the optimization procedure, in order to alleviate the sensitivities arising from changes in pose. In addition, the regularization term, based on linear correlation, is added in the objective function to improve the estimation accuracy of the 3D structure. Further, a model-integration method is proposed to improve the depth-estimation accuracy when multiple nonfrontal-view face images are available. Experimental results on the 2D and 3D databases demonstrate the feasibility and efficiency of the proposed methods.
Original languageEnglish
Article number6216413
Pages (from-to)17-30
Number of pages14
JournalIEEE Transactions on Image Processing
Issue number1
Publication statusPublished - 2 Jan 2013


  • 3D face reconstruction
  • face recognition
  • nonlinear least-squares model

ASJC Scopus subject areas

  • Software
  • General Medicine
  • Computer Graphics and Computer-Aided Design


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