# Veins Depth Estimation Using Diffused Reflectance Parameter
## 2 State of the Art Algorithms  
[PERSON] et al. in [11] presented a method to estimate the average depth of blood vessels using optical densities (ODs). An OD is the logarithm of diffused reflectance at certain wavelength and is defined as:  
\[\text{OD}(\lambda)=-\text{log Rd}\,(\lambda), \tag{1}\]  
The value of OD depends on the depth and width of absorbing area in turbid medium. The ODs on two different isosbestic wavelengths (420 nm and 585 nm) are calculated and the average depth of blood vessels beneath the skin is calculated using their ratio (OD 420 nm/OD 585 nm). The major problem in this technique is the usage of wavelengths from visible light spectrum. The light in visible spectrum have limitation in deeper penetration to the skin. Therefore, the proposed technique fails in cases of deep blood vessels. Furthermore, the disparity in the melanin content in different subjects can also affect the results of this method. [PERSON] and [PERSON] have proposed a method for the imaging of an absorbing object embedded in a highly scattering medium [12]. This method is based on the image reconstruction with the probability distribution function of path-length and the diffused reflected light due to backscattering from the medium. Light is focused on the scattering medium and the intensity of the back-scattered light is measured in two different cases; medium with absorbing object and medium without absorbing object. In this analogy, the skin is a highly scattering medium which contains blood vessels as absorbing objects embedded within its third layer (hypodermis). The maximum path length 'L' is proportional to the spatial integration probability distribution function of backscattered light from the scattering medium. The principle is given in Equation (2):  
\[P(L)\ =\ \frac{\int_{0}^{L}p(s)ds}{\int_{0}^{\infty}p(s)ds}\approx\frac{ \int_{L}I_{a}ds}{\int_{L}I_{0}ds}, \tag{2}\]  
where, \(p(s)\) is the probability density function of the path-length for turbid medium. The parameters \(I_{a}\) and \(I_{0}\) are the intensity distributions of backscattered diffused light from the medium with and without an absorbing object embedded in it, \(s\) is the path length for the semi-infinite medium. The maximum path length \(L\) is defined to be proportional to the depth '\(d\)' of the absorbing object, i.e., \(L=\alpha\times d\). The proportionality constant was optimized through Monte Carlo simulations and \(\alpha\) is found to be 3 thus L = 3 \(\times\) d. The estimation of depth of absorbing material in turbid medium depends on the maximum path-length and the absorption of diffused light in the medium. This can be varied in case of veins depth estimation since the oxygenation state of hemoglobin affects the absorption of light. Therefore, this method is likely to produce large error in veins depth estimation from the skin surface. [PERSON] et al. presented a technique for the estimation of depth and thickness of blood region in scattering medium in [13]. This method is based on the ratios of ODs using three isosbestic wavelengths 420, 585 and 800 nm. The reflectance from the skin tissues adjacent to blood region are used to estimate the concentration of melanin, that is later used to compensate the ODs variation in different subjects. Monte Carlo simulations of light propagation in turbid medium for the experiments performed on tissue like phantom. The reported results in this method showed that the depth estimation can be performed maximum up to 2 mm. However, the subcutaneous veins in normal human beings can be 2 to 4 mm deep from the surface of skin. Furthermore, due to the high error of around 30% the use of the said technique can be questioned for the cases where depth of the vessels should be known precisely. Hence this method seems impractical for the depth estimation of subcutaneous veins in majority of the cases. Veins position estimation method from three-dimensional space using stereo vision is presented in [14].