3 m at disparity data 1,069, and the distribution of data changed rapidly beyond a distance of approximately 5 m, as shown in Figure 2. For performing data fitting, the depth calibration model of Equation Axitinib cancer (1) has only two-degrees-of-freedom for the optimization variables; therefore, it has limitations in Inhibitors,Modulators,Libraries representing the curvature of our measurement data. Hence, we proposed an extended depth calibration model using a rational function, which contains higher degree-of-freedom in the optimization variable space [19]. Equation (2) shows the rational function model that is applied to the depth calibration of the Kinect? sensor:f(d)=P(d)Q(d)(P(d)=��i=1m��idi?1,Q(d)=��i=1n��m+idi?1)(2)where P(d) is the numerator polynomial and Q(d) is the denominator polynomial.
To perform depth calibration with the rational function model, a non-linear Inhibitors,Modulators,Libraries optimization method such as the Levenberg-Marquardt algorithm can be used. We obtained the depth calibration function with fourth-order polynomials of the numerator and denominator, which can transform disparity data into a real distance Inhibitors,Modulators,Libraries of up to approximately 15 m. The depth calibration parameters for the fourth-order rational function model are shown in Table 1. Figure 3 shows the fitting results and the fitting residual results for the depth calibration function in Equations (1) and (2), respectively. In Figure 3(a), both calibration functions seemed to fit the measurement data well. However, as seen in Figure 3(b), the residual error of the rational function model appeared to be nearer to the X-axis than the model represented by Equation (1).
This Inhibitors,Modulators,Libraries implies that the rational function model with a higher degree-of-freedom of the optimization variables can be fitted more precisely in the depth calibration problem. The norm of residual vector for Equation (1) and the rational AV-951 function were computed to be 1.045495 and 1.034060, respectively.Figure 3.Depth calibration results. (a) Fitting results (measurement data, Equation (1) model, fourth-order rational function model); (b) Residual (fitting error) results (Equation (1) model
Disposable lab-on-a-chip (LOC) devices are an attractive platform for the implementation of compact and robust analytical tests, which minimize sample volumes and simplify the handling of the measurements, both important factors in distributed analyses [1,2].
Among the diverse possibilities existing for LOC readout, optical methods [3] are those relevant to this work.Disposable LOC devices have been demonstrated for numerous sensing and selleck kinase inhibitor clinical applications [3], however, their dissemination is restricted by the instrumentation required for readout. LOC solutions for point of care (POC) or other distributed detections [2] are typically associated with dedicated and specific off-chip readers [4,5].