Computerised analysis on skin lesion images has been reported to be helpful in achieving objective and reproducible diagnosis of melanoma. In particular, asymmetry in shape, colour and structure reflects the irregular growth of melanin under the skin and is of great importance for diagnosing the malignancy of skin lesions. This paper proposes a novel asymmetry analysis based on a newly developed pigmentation elevation model and the global point signatures (GPSs). Specifically, the pigmentation elevation model was first constructed by computer-based analysis of dermoscopy images, for the identification of melanin and haemoglobin. Asymmetry of skin lesions was then assessed through quantifying distributions of the pigmentation elevation model using the GPSs, derived from a Laplace-Beltrami operator. This new approach allows quantifying the shape and pigmentation distributions of cutaneous lesions simultaneously. Algorithm performance was tested on 351 dermoscopy images, including 88 malignant melanomas and 263 benign naevi, employing a support vector machine (SVM) with tenfold cross-validation strategy. Competitive diagnostic results were achieved using the proposed asymmetry descriptor only, presenting 86.36 % sensitivity, 82.13 % specificity and overall 83.43 % accuracy, respectively. In addition, the proposed GPS-based asymmetry analysis enables working on dermoscopy images from different databases and is approved to be inherently robust to the external imaging variations. These advantages suggested that the proposed method has good potential for follow-up treatment.