The paper presents a new model for single channel images low-level interpretation. The image is decomposed into a graph which captures a complete set of structural features. The description allows to accurately identify every edge location and its correct connectivity. The key features of the method are: vector description of the edges, subpixel precision, and parallelism of the underlying algorithm. The methodology outperforms classical and state of the art edge detectors at both conceptual and experimental levels. It also enables graph based algorithms for higher-level feature extraction. Any image processing pipeline can benefit from such results: e.g., controlled denoising, edge preserving filtering, upsampling, compression, vector and graph based pattern matching, neural network training.