Objective: Focal cortical dysplasias (FCDs) are a common cause of apparently non-lesional drug-resistant focal epilepsy. Visual detection of subtle FCDs on MRI is clinically important and often challenging. In this study, we implemented a set of 3D local image filters adapted from computer vision applications to describe the normal cortex surrounding the gray-white junction. We created a normative model that serves as the basis for a novel multivariate outlier detection method for detecting FCDs. Methods: Standardized MPRAGE, T2 and FLAIR MR images were obtained in 15 patients with radiologically or histologically diagnosed FCDs and 30 healthy volunteers. Multiscale 3D local image filters were computed for each MR contrast then sampled onto the gray-white junction surface. We created a latent representation of normal cortical variability in healthy volunteers, allowing for identification of outlier regions and estimates of similarity in normal cortex and FCD lesions. Following local normalization, we automatically detected FCD lesions based on projection onto the mean FCD feature vector. Results: In our normative model, atypical cortical regions such as primary sensorimotor and paralimbic regions are outliers with similar features to FCDs. Our constrained outlier detection method for automated FCD detection based on this model demonstrated 80% sensitivity, 70% specificity, and AUC 0.91. Significance: Our normative modeling approach allows for identification of known atypical regions of normal cortex as well as FCD lesions. FCDs appear similar to some normal paralimbic and sensorimotor cortices, becoming more easily distinguished following local normalization. Our method for estimating similarity is generic and can be extended to identification of other types of lesions or normal cortical areas.