The quantification of blood vessels provides the means for assessing the severity of corneal neovascularization and the impact of any treatment process being followed. In this paper we propose a Contourlet Transform based approach to the detection, enhancement and quantification of blood vessels in corneal images. Initially a semi-automated approach is used to identify the boundary of the cornea and to segment the corneal region of interest (ROI). This is followed by the application of Contourlet Transforms to the difference of red and green colour planes of the ROI, an image that produces fewer artefacts due to reflections and highlights. The blood vessel regions are subsequently enhanced in the Countourlet domain before being inverse transformed to obtain a corneal ROI with enhanced contrast. The enhanced image is finally thresholded to form a binary image which undergoes thinning to produce the final binary image. The quantification of the blood vessels is carried out by calculating the ratio between pixels belonging to the blood vessels and background areas. Experimental results on four practical data sets obtained from patients suffering from different levels of corneal neovascularization are provided.