This paper presents a Fluency Image Coding System of beef rib-eye images for Beef Marbling Evaluation. This is the second in a series of cooperative researches with the Japan Livestock Technology Association under an initiative to construct an Automated Online Beef Marbling Grading Support System by image analysis techniques. Our first cooperative research was on a Beef Marbling Grading Method, and was published in this journal in Pattern Recognition Lett. 21 (12) (2000) 1037–1050. This second cooperative research focuses on a binary image coding system that supports remote observation of beef marbling structure from a database of coded beef rib-eye images by users including meat graders, livestock producers, and researchers. Image encoding is by a novel automatic contour compression method based on function approximation via interpolation using the Fluency Compactly Supported Sampling Functions of degree 2. Image decoding, based on interpolation of the encoded data by the similar functions, enables the web-browser based decoder to reconstruct the original fat contours smoothly even on Affine-transformed enlargement. Experimental results showing, respectively, size and image quality comparisons with other formats that support binary images and several enlargement schemes are included for evaluation.