A Hamming-Hausdorff distance-based interval-valued intuitionistic fuzzy knowledge measure (IVIFKM) is presented in this paper, upon with a methodology for image thresholding is based so as to achieve a better segmentation result. The latest achievement shows that there are two significant facets of knowledge measurement associated with an intuitionistic fuzzy set (IFS), i.e., the information content and the information clarity. With this understanding, a novel axiomatic system of IVIFKM is proposed. The normalized Hamming-Hausdorff distance is also improved and extended. Combined with the technique for order preference by similarity to ideal solution (TOPSIS), a novel IVIFKM is then established, complying fully with the requirement of the developed axiomatic system. The proposed measure is subsequently applied to image thresholding. Given the structural features of an interval-valued IFS (IVIFS) in itself, a more effective classification rule of pixels and a more efficient algorithm for interval-valued intuitionistic fuzzification of an image are suggested, respectively. The developed measure is finally used to calculate the amount of knowledge associated with the image to determine the best threshold for segmentation. Experimental results show that the developed knowledge-driven methodology, characterized by high stability and reliability, can produce much more satisfactory binary images with excellent performance metrics, routinely outperforming other thresholding ones. By this work, the latest IVIFKM theory is introduced into the field of image processing, thus providing a concrete instance for the potential applications of this theory in other related areas.