We address the problem of computing a local orientation map in a digital image. We show that standard image gray level quantization causes a strong bias in the repartition of orientations, hindering any accurate geometric analysis of the image. In continuation, a simple dequantization algorithm is proposed, which maintains all of the image information and transforms the quantization noise in a nearby Gaussian white noise (we actually prove that only Gaussian noise can maintain isotropy of orientations). Mathematical arguments are used to show that this results in the restoration of a high quality image isotropy. In contrast with other classical methods, it turns out that this property can be obtained without smoothing the image or increasing the signal-to-noise ratio (SNR). As an application, it is shown in the experimental section that, thanks to this dequantization of orientations, such geometric algorithms as the detection of nonlocal alignments can be performed efficiently. We also point out similar improvements of orientation quality when our dequantization method is applied to aliased images.