Based on the digital communication companding transformation principle,a 16-polygonal line geometric partition method which maps 12-bit image data to 8-bit data was proposed to display 12-bit image information on a 8-bit gray scale monitor. The formulas for calculating the linear and nonlinear quantization Signal to Noise Ratio (SNRs) were derived. By comparing SNRs of three different quantization methods, it was indicated that the SNR of 8-bit nonlinear quantization is consistent with that of 12-bit linear quantization at less than 35 dB and that is in the stable increase at large than 35 dB. Experiments show that this method can effectively improve the weak signal of the image, and the details of a low luminance image can be observed clearly on a 8-bit monitor. Although the high luminance part of the image is compressed, it has little affect on the image details and SNRs. The proposed method is applicable to gray images and color images. Experimental results are fully consistent with theoretical expectations.