Machine Vision and Applications (2010) 21:261–274 DOI 10.1007/s00138-008-0158-7 ORIGINAL PAPER Using bidimensional regression to assess face similarity Sarvani Kare · Ashok Samal · David Marx Received: 21 July 2006 / Revised: 15 August 2007 / Accepted: 17 June 2008 / Published online: 13 August 2008 © Springer-Verlag 2008 Abstract Face recognition is the identification of humans by the unique characteristics of their faces and forms the basis for many biometric systems. In this research the problem of feature-based face recognition is considered. Bidimensional regression (BDR) is an extension of standard regression to 2D variables. Bidimensional regression can be used to determine the degree of resemblance between two planar configura- tions of points and for assessing the nature of their geometry. A primary advantage of this approach is that no training is needed. The goal of this research is to explore the suitability of BDR for 2D matching. Specifically, we explore if bidi- mensional regression can be used as a basis for a similarity measure to compare faces. The approach is tested using stan- dard datasets. The results show that BDR can be effective in recognizing faces and hence can be used as an effective 2D matching technique. Keywords Face recognition · Landmarks · Bidimensional regression 1 Introduction Identification of humans by the unique characteristics of their faces has many applications and is the basis for many bio- metric systems. Recognition systems often involve measur- ing the similarity between faces and generating an ordering of faces based on the similarity of a face with known faces in a database. Human faces represent one of the most common visual patterns in the course of daily activities. It is widely known and recognized that features (e.g. eyes, ears, nose, lips S. Kare · A. Samal (B ) · D. Marx University of Nebraska-Lincoln, Lincoln, NE 68588-0115, USA e-mail: samal@cse.unl.edu and chin) are important in recognition of and discrimination between faces [1]. While face recognition has been of interest for over a hun- dred years [2], automated methods for face recognition have gained attention only within the last two decades [3, 4]. Many useful and important applications have been a strong driving force in this regard. Two different approaches for solving face recognition problem have been widely reported in literature: (a) feature-based and (b) holistic or direct methods. In fea- ture-based approaches, features such as eyes, nose, ears and chin are first recognized and then used to recognize faces. In holistic approaches (e.g. [4–6]), the whole face or a repre- sentation of the face is used for recognition. Face recognition technology has numerous applications in many different fields including government use (voter ver- ification, law enforcement), security (access control, resi- dential security, immigration checkpoints), people tracking (daycares, missing children, correctional institutions), and commercial applications (gaming, e-commerce, healthcare and banking). Face recognition systems are no longer lim- ited to identity verification and surveillance tasks. A growing number of applications are starting to use face recognition as the initial step towards interpreting human actions, inten- tion, and behavior, as a central part of next-generation smart environments [7]. In this paper, we present a hybrid approach in which important features in the whole face are used to recognize a face. Bidimensional regression has been proposed in geo- graphic information science as a mechanism to compare ancient and modern maps and in other applications [8]. It is an extension to ordinary regression analysis in which both the independent and dependent variables are two dimensional (2D). The goal of this research is to explore the suitability of this approach in face recognition applications. Bidimensional regression can be used to determine the degree of resem- 123