Dimensionality reduction by means of linear discriminant analysis (LDA) can generally lead to considerable improvements in classification accuracy and computation time. However, in supervised, pixel-based, image segmentation, the limiting factor of LDA that it cannot extract more than K - 1 features (K the number of classes) often prevents successfully employing it as K is typically small. Based on the observation that the kind of feature to extract should often depend on the kind of image structure that is in the vicinity, we propose to condition LDA on auxiliary variables extracted from the manual segmentations (which are only available in the training phase). The conditioned Fisher criteria obtained through this are subsequently combined to construct our final global Fisher-like dimensionality reduction criterion. This conditional LDA is capable of extracting more features than standard LDA, which can considerably improve the segmentation accuracy as our experiments show.