## 1 Introduction  
Flow velocity field measurement is important for analyzing the flow characteristics of oil-water two-phase immiscible flow, which directly affects the interpretation of logging data and design of logging instruments [1; 2]. Flow velocity field measurement methods include the capacitance method [3], conductance method [4], and electromagnetic method [5]. Current oilfield flow velocity field measurement is more inclined toward velocity distribution visualization measurement, which can obtain more detailed flow velocity field information and observe the flow characteristics more easily to guide oilfield development [6]. It is very difficult for the traditional measurement method to meet this requirement. Therefore, a new flow velocity field measurement method must be adopted. Particle image velocimetry (PIV) is an effective flow velocity field measurement technology in hydromechanics [7; 8]. Its characteristics of nondisturbance, noncontact, and full-field measurement [9] meet the requirements of oilfields. Therefore, it has promising potential applications. PIV was originally developed from laser speckle velocimetry [10]. Then, PIV was gradually digitized into digital particle image velocimetry (DPIV) with the advent of digital technology [11; 12; 13]and different illumination solutions, like LED or flash lamps were proposed for specific applications, where a laser source is inadequate due to the high tracers density (e.g., multiphase flows and liquid-granular flows). The intrinsic principle of DPIV is to capture the pattern movements by means of a cross-correlation optimization, as shown in Figure 1a[14]. During the process of measuring the flow velocity field, an appropriate amount of tracer is evenly sprinkled into the flow body. Then, a computer synchronously controls the pulsed laser light source and high-speed camera to illuminate the flow velocity field and record the instantaneous flow state [15; 16; 17]. Some scholars carry out hardware improvement at the foundation of the classical PIV system: [PERSON] [18] uses the LED lamp placed in front of the pipe to measure the velocity fields of granular flows and [PERSON] et al. [19], [PERSON] et al. [20], and [PERSON] et al. [21] use a light-emitting diode (LED) backlight source to replace the laser source, which has also achieved good measurement performance, as shown in Figure 1b. Finally, the recorded digital image is transmitted to the computer for further processing to obtain the instantaneous flow velocity field [22]. The traditional DPIV postprocessing algorithm is based on cross-correlation and the fast Fourier transform (FFT) algorithm [23; 24]. Although simple, it has many limitations. In Figure 2, the yellow points stand for the particles whose velocity is very high, the blue points stand for the particles those are still in the interrogation window, the brown points stand for the new particles, and the red points stand for the particles, which are out of the interrogation window for the displacement increases. As shown in Figure 2a, the consistent interrogation window size and position of the two images remains unchanged, so the red points run out the interrogation window. The matching particles in the interrogation window decrease as the displacement increases as a result of the consistent interrogation window size and position of the two images [25]. The accuracy of DPIV is affected by the numbers of matching particles, so this make the decrease in accuracy of DPIV. By offsetting the interrogation window using the predetermined pixel displacement to maximize the particle matching rate, [PERSON] et al. [26] and [PERSON] et al. [27] proposed discrete and continuous window offset technologies, respectively. However, this still has limitations in a flow field with a velocity gradient. As shown in Figure 2b, the yellow points still run out the interrogation. As shown in Figure 2c, [PERSON] et al.