In mechanical manufacturing, the state of a machined part surface is very crucial, particularly in aeronautics, and as a result, great care must be exercised in its measurement. Over the past few years, many research studies have been carried out to mitigate the disadvantages (contact, off-line inspection, speed of limited measurement) inherent in the classic measurement of the roughness by contact with a stylus. The contribution of this paper is to demonstrate the feasibility of the contactless inspection of part surface roughness using an optical microscope. Unlike most works in the domain that use image average of grey level and the average cycle of the texture, a new image characteristic named the gradient factor of the image is defined and used to estimate the part roughness parameters. The effect of the vision system parameters on image quality is investigated then the statistical characteristics of the images best describing the machined surface are determined and used to estimate the roughness parameters. The study shows that several roughness parameters ($R_a$, $R_q$, $R_v$, $R_t$ and $R_z$) can be estimated using only image-extracted features and models, without the need to know the machining parameters used to generate the surface. The results obtained with the vision system are comparable to those obtained with a stylus contact surface roughness measurement system, and could help in the online monitoring of the surface roughness.