Bias field reduction by localized Lloyd–Max quantization

Bias field reduction is a common problem in medical imaging. A bias field usually manifests itself as a smooth intensity variation across the image. The resulting image inhomogeneity is a severe problem for posterior image processing and analysis techniques such as registration or segmentation. In this article, we present a novel debiasing technique based on localized Lloyd–Max quantization (LMQ). The local bias is modeled as a multiplicative field and is assumed to be slowly varying. The method is based on the assumption that the global, undegraded histogram is characterized by a limited number of gray values. The goal is then to find the discrete intensity values such that spreading those values according to the local bias field reproduces the global histogram as good as possible. We show that our method is capable of efficiently reducing (even strong) bias fields in 3D volumes.