## 1 Introduction  
Quality, including all attributes of manufactured products, is an essential objective of industrial production. Encompassing the measurable quantities and characteristics of the product, quality is regarded as a summary of the product determining its capability to meet needs, fulfill functions, and be effective [1]. In the development and production of industrial parts, both the macroscopic shape and the microstructure of the surface on an \(\upmu\)m-scale strongly influence the properties and performance of machined parts, including friction, wear, precision, fitting, anti-fatigue and anti-corrosion characteristics [2,3]. Controlling of surface roughness is mandatory to define the process and validate the quality of the machined part [4]. Due to the friction between the insert and the workpiece surface during material removing process, some inevitable phenomena, such as plastic deformation during chip separation and high-frequency vibrations of the processing system, emerge and are harmful to machining quality. It is well known that surface roughness is regarded as a microscale geometry error. Therefore, it can also serve as a useful vehicle that represents the operational state of the processing system. In the past few decades, with the advent of tactile profilometers, the stylus tracing (ST) method has become the most popular way of evaluating the surface quality of components. The principle of ST is based on measuring the surface texture and calculating the roughness parameter of _Ra_[5]. A schematic structure of a profilometer is shown in Figure 1. As illustrated, a kinematic mechanism drives the motion of a stylus, in which a diamond is fixed at the end. This kinematic unit records the vertical deflection of the stylus that moves over the straight paths on the investigated surface. In the process of measurement, the stylus is initially loaded on the measured surface and the surface height variation is obtained as it moves across the surface at a constant velocity [6]. However, there are some disadvantages to using this type of instrument. Owing to mechanical contact with the measured surface there is a potential risk of soft material damage. That is, the measuring process, as described above, inevitably results in scratches by the diamond stylus. On the other hand, the problem of inefficiency should be seriously considered as it cannot work online [7]. Besides the traditional contact stylus tracing technique, the availability of modern measuring technologies emerging from digital computer enhanced machine vision techniques have enabled us to evaluate surface quality through non-contact means [1; 6]. There are several promising methods to measure the roughness of machined surfaces. These methods include laser reflectivity, non-contact laser stylus metrology, scanning electron microscopy, compressed air measuring, focus variation, fringe projection technique, and a confocal laser scanning microscope [8; 9]. In particular, the development of a method of measuring surface roughness via machine vision-based techniques has attracted attention. [PERSON] proposed a method based on the difference of RGB color space to develop a correlation model between the sharpness and the surface roughness [3]. [PERSON] reported a novel device design for non-contact measuring of the cutting tool as well as the roughness of the machined surfaces using an optical sensor [1]. [PERSON] presented a new method that extracts the characteristic parameters of average texture cycle for surface texture with a straight shape to establish the relationship between the average texture cycle and the actual surface roughness [10]. [PERSON] investigated the relationship between surface roughness and image grey [11]. [PERSON] reported a workpiece profile acquisition method using image processing and fast Fourier transform [12; 13]. All the above mentioned methods require prior knowledge or equipment transformation for the roughness measurement. Correcting of the texture skew is also very important for the surface roughness estimation.