This article proposes a novel framework for the locally-oriented evaluation of segmentation algorithms (LEFMIS). The presented approach is robust and takes into account local inter/intra-observer variability and the anisotropy of medical images. What is more, the framework makes it possible to distinguish types of error locally. These features are crucial in the context of cancer image data. The proposed framework is based on use of the signed anisotropic Euclidean distance transform and the distance projection. It can be used easily in many different applications with or without additional expert outlines (both inter- and intra-observer variability). The performance of the proposed framework is depicted using both artificial and kidney cancer CT data with experts' manual outlines. In the article, in the case of artificial data, it is presented that the manual outlines dispersion is symmetric in relation to the truth border. The effectiveness of the selected segmentation algorithm was analysed in the context of kidney cancer using computed tomography data. For the calculated local inter-observer variability, 80.11% of the surface points generated by the kidney segmentation algorithm are within one expert outline standard deviation and 97.96% are within five. An error distribution shift in the direction of type I error equivalent was also observed. Finally, the significance of the local estimation of error type differences is presented. The article shows the greater usefulness and flexibility of the proposed framework in comparison to the state-of-the-art methods. The exemplary usage of the LEFMIS with or without inter-/intra-observer variability is also presented.