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A novel and completely tracer free strategy to image composition and velocity fields during the mixing process of two liquids is introduced. The achieved temporal resolution, spatial resolution and sampling rate of 30 ns, 54 x 54 µm2 and 10 kHz, respectively, are sufficient to resolve Kolmogorov time and length scales as well as transient mixing phenomena of many technical mixing processes. During the injection of liquid water into liquid ethanol, mixing was quantitatively observed by means of high repetition rate Raman imaging using a laser cluster for the excitation of the Raman process with 8 successive light sheet pulses. One high speed camera was used to detect the CH-vibration Raman band signal of ethanol, while a second one was used to detect the OH-vibration Raman band signal of water and ethanol. From the ratio of both, the mixture composition field was computed. The dense flow field was determined by processing the mixture composition images with a variational optical flow method.
©2010 Optical Society of America
1. Introduction
Current trends in laser diagnostics for investigations into thermo-fluid dynamics focus on multi-parameter and high repetition rate imaging. This is especially true for the analysis of mixing processes.
The progress in multi-parameter imaging techniques is motivated by the requirement to observe the interaction of different parameters which influence the process under investigation. This may be the interaction of temperature and composition or the interaction of temperature (or composition) and the flow field. Both scalar fields (temperature and composition) characterize the mixing progress and may influence each other [1]. Additionally, the flow field characterizes the forced flow, which is driving the mixing progress from the macroscopic to the mesoscopic length scales [2]. Therefore, the simultaneous detection of two parameters, one indicating the mixing progress and the other one indicating the mixing-driving-force is beneficial to characterize the mixing mechanisms.
The progress in high repetition rate imaging techniques is motivated by the aim to temporally resolve transient mixing phenomena in turbulent flows and to track them in time. Consequently, the full characterization of turbulent mixing processes demands the application of multi-parameter imaging techniques at high repetition rates.
Several different techniques for multi-parameter imaging of scalar fields are known. They are usually based on the absorption and the subsequent emission of light, comprising planar laser-induced fluorescence (PLIF) [3] or planar laser-induced phosphorescence (PLIP) strategies [4]. Absorption/emission strategies feature a large interaction cross section, providing relatively large signal intensities. Therefore the pulse energies of commercially available high speed laser systems are sufficient to excite emissions from a light sheet, which can be reliably imaged at high frame rates onto an image intensified CMOS camera. Nevertheless, absorption/emission strategies at high repetition rates are usually realized to image one single parameter instead of multi-parameters simultaneously [5].
For quantitative PLIF measurements, fluorescence tracers with well characterized photophysical properties have to be used [6]. Here, fluorescence tracer molecules are used, if the components, which are naturally present in the flow, cannot be excited to fluorescence, or if the fluorescence behavior of the naturally present components is not known. In the latter case the components are substituted by non-fluorescing model substances and are traced with “quantitative” fluorescence molecules, whose fluorescence behavior is known. As the PLIF signals of fluorescence tracer molecules are affected by the mixture composition, the mixture temperature, and the mixture pressure, PLIF signals may be interpreted quantitatively only for those conditions which have been photophysically characterized [7, 8]. Additionally to this drawback of absorption/emission strategies, the excitation energy of each laser pulse and the spatial distribution of the excitation energy within the excitation laser light sheet have to be monitored and considered during the quantitative interpretation of PLIF or PLIP experiments.
The combination of a scalar field and a flow field imaging strategy, both at high repetition rates, offers the possibility to resolve simultaneously the mixing driving force and the mixing progress [9]. In this case, the flow field imaging strategy is usually based on the particle image velocimetry (PIV). PIV requests scatterers -either particles or droplets- which have to follow the flow ideally without any slip, which is not necessarily assured in high-turbulent flows. When the particle distribution in the excited light sheet is imaged at high repetition rates, the flow field can be extracted from the spatial shift of the patterns in the scattering images. If not naturally present in the flow, the scatterers have to be seeded to the flow. To overcome this drawback, Scholz et al. [10] used an optical flow algorithm to compute the flow field from the shift of the patterns, which have been present already in the PLIF images. Consequently the high repetition rate PLIF experiment was directly used to image the composition and the flow field simultaneously. In this case, no scatterers had to be seeded to the flow, but still a fluorescing component for the PLIF measurements had to be used.
In previous publications it was proven, that also Rayleigh [11] and Raman scattering based techniques [12–15] qualify for quantitative multi-parameter imaging. This is due to some Rayleigh and Raman inherent characteristics. First, these methods do not require tracer molecules, since they rely on probing molecular energy transitions of the naturally prevalent flow components. Second, Rayleigh and spontaneous Raman scattering own quantitative measurement strategies, as their signal intensity is directly proportional to the number density of probed molecules in a wide range of operation conditions. Third, spontaneous Raman scattering can be realized as a multi-parameter imaging technique, as -due to the species specific Raman shifts of particular transitions in molecules- the Raman signals of different components are frequency shifted individually and can be spectrally resolved well relative to the other spectral contributions. Nevertheless, due to the rather small Raman scattering cross sections, high energy pulsed laser sources in combination with high quantum efficiency detection devices are required for the two-dimensional detection of reliable Raman signal intensities. Compared to Raman scattering, the application of Rayleigh scattering, though featuring higher cross sections, may in many cases be nearly impossible due to interferences with background, stray light or other signal contributions at the same spectral position. Therefore, here we focused our work on Raman scattering.
The pulse energies of common high-speed laser systems are often not sufficient to excite detectable Raman signals in a light sheet. Therefore, a special laser cluster was used for high repetition rate Raman imaging. In 1999, when no high-speed lasers were available, a similar laser cluster was introduced by Kaminski et al. [16] to realize the first high repetition rate PLIF measurements in flames. Today this work is considered to be the pioneering work in high-speed PLIF [17], though –due to the limited number of subsequent images- the authors termed it high repetition rate instead of high-speed.
Here we introduce a high repetition rate Raman imaging technique, with a spatial resolution within the laser excitation light sheet of 54 x 54 µm2, a repetition rate of up to 10 kHz and a temporal resolution of a few tens of nanoseconds. Considering a water pipe flow with an inner diameter of 50 mm, a mean flow velocity of 1 m s−1 and a kinematic viscosity of water of 15.5·10−6 m2 s−1, the diameter related Reynolds number is approximately 3200. Assuming the turbulent fluctuation velocity to be highest as large as the mean flow velocity of 1 m s−1, the Kolmogorov length and time scales are approximately 120 µm and 890 µs, respectively, and hence significantly larger than the resolution limits of the Raman setup. Many mixing processes in chemical engineering, e.g, precipitation, crystallization or reaction in T-mixers, where two solvents are mixed, are characterized by similar Kolmogorov length and time scales, and can be studied comprehensively with the introduced Raman imaging strategy. Molecular tracers for conventional scalar field imaging, which are no more needed for Raman imaging, might influence the phase behavior and the solubility of different components in the system under investigation and affect the nucleation or reaction kinetics during crystallization and conversion, respectively. The same is true for particulate tracers, which have to be added for common PIV flow field investigations but are no more required here. In mixing systems for the crystallization of a solid phase, these particulate tracers will act as nucleation sites and open the path of heterogeneous nucleation, while the homogeneous nucleation path, which is required for the generation of especially small particles, will be blocked.
In this work, the limitations of the introduced Raman technology were tested in a free jet experiment, for which the Kolmogorov length and time scales are smaller than the resolution limit of the Raman setup. Nevertheless, the capability of the proposed measurement strategy for other applications –as mentioned above- can be demonstrated. Using neither a tracer for the composition analysis nor for the flow field analysis, the transient mixing phenomena during the injection of water in ethanol could be temporally resolved by the detection of composition and flow fields.
2. Experimental setup
The high repetition rate spontaneous Raman imaging experiment is sketched in Fig. 1 . The Raman process is excited with a pulsed frequency-doubled Q-switch Nd:YAG laser cluster from Thales operated at a wavelength of 532 nm. The laser cluster consists of four independent laser lines, each flash lamp pumped at 10 Hz. Two laser pulses with a temporal delay of 100 µs (double pulse option) are emitted from each laser line within one pump event. The temporal delay between each laser line is set 200 µs. Consequently, pulse bursts composed of 8 subsequent laser pulses are generated. The repetition rate of the 8 pulses within one burst is 10 kHz, while the repetition rate of the bursts is 10 Hz. The energy of each single-shot laser pulse is 200 mJ and the temporal pulse width (FWHM) is 8 ns.
Fig. 1 Schematic of the high repetition rate Raman imaging experiment; (M: Mirror, BS: Beam splitter, SL: Spherical lens, CL: Cylindrical lens, MC: Measuring Chamber, BPF: Band pass filter, LPF: Long pass filter, HS-C: High-Speed Camera)
Via one beam splitter (transmission 0.6, reflection 0.4) and several mirrors the single-shot laser pulse power was decreased in a single-loop pulse stretcher to avoid laser induced-ionization in the mixing chamber [18]. The original laser beam diameter was expanded by a factor of 3 in a telescope. Then a vertical light sheet was formed by a cylindrical lens (f = 350 mm) and launched through the center of the mixing chamber. The light sheet had a height of 20 mm and a thickness of approximately 200 µm.
The mixing chamber was filled with pure ethanol. For the injection of water, a capillary with an inner diameter of 1 mm was mounted at the bottom of the mixing chamber. The exit of the capillary was positioned exactly at the bottom edge of the vertical excitation light sheet. The injection was driven by a pressure difference between the mixing chamber (0.1 MPa) and the water reservoir (0.2 MPa). Under steady flow conditions, the mean outlet velocity at the nozzle was 10 m s−1.
Two high-speed cameras (LaVision HSS6) were used to image the laser light sheet by detecting the spontaneous Raman scattering signals. The camera detector was a CMOS chip with a pixel size of 20 x 20 µm2 and 1024 x 1024 pixels. Considering the pixel fill factor of 60%, the quantum efficiency of the CMOS chips in the wavelength range between 600 and 700 nm was 35-45%. Both cameras were arranged in a right angle detection path to exclude the detection of stimulated Raman signals. The cameras were equipped with identical long pass filters (Raman Razor Edge), to suppress the elastically scattered signals, and with identical camera lenses (f# = 1.2, f = 50 mm) and PK12 extension rings between the camera and the camera lens, to detect the Raman signals through a wide solid angle. The magnification of the detection system was 0.37. Additionally, each camera was equipped with one band pass filter. The center wavelength of one of the two band pass filters was at 630 nm with a width (FWHM) of 10 nm. Consequently, this one was used to collect the Raman signals of the CH-vibration of the ethanol molecules. The center wavelength of the other band pass filter was at 650 nm with a width (FWHM) of 7 nm. This one was used to collect the Raman signals of the OH-vibration of the water and ethanol molecules. Summarizing, one camera was used to image the distribution of the ethanol molecules alone and one camera was used to image the distribution of the water and ethanol molecules together. Therefore the ratio of the CH-vibration Raman image (ethanol) and the OH-vibration Raman image (ethanol and water) reflects the ethanol mole fraction xEtOH and provides as a consequence quantifiable information about the mixture composition. A further advantage of considering the ratio of two simultaneously acquired images is that pulse-to-pulse fluctuations within one laser burst or fluctuations of the laser pulse excitation profile cancel out. This advantage is especially beneficial for measurements in liquid mixing systems, where different refractive indices of the liquids perturb the excitation light sheet, but, as ratios are considered, do not negatively contribute to the accuracy of this measurement technique. Both cameras were temporally synchronized with the laser cluster.
3. Results
At first, the Raman experiment had to be calibrated. For this purpose, Raman imaging measurements were carried out in different mixtures of ethanol and water. The mixture composition is defined by the ethanol mole fraction, which is the number of ethanol molecules relative to the total number of water and ethanol molecules. To make the Raman imaging technique independent of the laser pulse excitation energy and the energy distribution in the excitation light sheet, the ratio images ICH/IOH of the CH-vibration Raman images and the OH-vibration Raman images were computed. From 50 ratio images ICH/IOH for one particular mixture composition, a mean image and a standard deviation image was processed. In the center of the mean image and the standard deviation image a region of interest (ROI) was defined by 350 x 350 pixels. From the pixel values inside the ROI of the mean image, a mean Raman intensity ratio value was calculated. From the pixel values within the ROI of the standard deviation image a mean Raman standard deviation value was calculated. In Fig. 2 the mean Raman intensity ratio ICH/IOH is displayed as a function of the ethanol mole fraction. The error bars represent the corresponding mean standard deviation.
Fig. 2 Calibrated Raman intensity ratio: ethanol mole fraction xEtOH as a function of the Raman intensity ratio ICH/IOH of the CH-vibration Raman band signal ICH and the OH-vibration Raman band signal IOH
Considering the procedure for deriving the standard deviation, it has to be pointed out, that its value reflects the mean standard deviation of the intensity ratio ICH/IOH for 50 measurements at a constant composition and for a fixed pixel. It does not reflect the inhomogeneity of one single intensity ratio image ICH/IOH, which had been taken from a homogeneous mixture. The inhomogeneity could be characterized by the standard deviation of all the pixel values within the ROI of one single intensity ratio image. This intensity ratio image inhomogeneity was found to be similar to the quantity of the error bars in Fig. 2.
When the ethanol mole fraction is increased from zero to one, the detected IOH signal intensities remain nearly constant. This is due to the fact that both, ethanol and water contribute to the Raman signal of the OH-vibration. Contrary, the detected Raman signal intensities ICH of the CH-vibration increase with the ethanol mole fraction. As a consequence the shot noise of ICH increases, too, which is reflected by the increasing error bars with increasing ethanol mole fraction in Fig. 2.
The calibration measurements were carried out exactly with the same laser and camera settings, which were used during the jet mixing experiments. The injection of water into ethanol was started by opening a ball valve very close to the capillary. Then, high repetition rate Raman imaging measurements were conducted. Identically to the calibration measurements, the intensity ratio images were computed from the CH-Raman and the OH-Raman signal images. From the calibration curve given in Fig. 2, the intensity ratio values of the pixels could be converted in ethanol mole fraction values. This procedure was done for each of the 8 excitation events. The corresponding 8 ethanol mole fraction images (not post-processed) are given in Fig. 3 .
Fig. 3 Ethanol mole fraction xEtOH distribution during the injection of water in ethanol detected by 8 subsequent laser pulses
It can clearly be seen, that the ethanol rich compositions outside the mixing regime of the jet are displayed with larger noise and larger image-to-image fluctuation with respect to the ethanol poor compositions in the mixing regime of the injected water jet. This must be assigned to the calibration data in Fig. 2, which also shows large error bars at ethanol rich compositions with respect to ethanol poor compositions.
Figure 3 also proofs that the transient mixing processes can be resolved, as one can follow the structures of the mixing field from one to the following image. For example, the separation of the structures, which are indicated by the numbers 1, 2 and 3, and their degradation can be followed. As the temporal shift between two subsequent image acquisitions is known, one can estimate the velocity of these structures by simply extracting the spatial shift of the respective structures from image to image. The knowledge of these rough velocities might be satisfying for many applications. But, if a comprehensive velocity field from all over the jet is required, this measure is not well suited. Therefore we will discuss the advantages and the disadvantages of an optical flow method below. Via the optical flow method a displacement field can be computed, which in particular regions of the jet has the potential to represent the “real” velocity field, while it provides “non-sense” velocity fields in other regions.
To compute the dense displacement field in the image sequence of Fig. 3 a variational optical flow method [19] was used with a brightness constancy assumption in the data term and an anisotropic flow-driven regulariser approach in the smoothness term [20]. The numerical minimization of the energy functional was done by a unidirectional multigrid method [21, 22]. It must be pointed out, that the availability of an image sequence, which is not interfered with any illumination pattern (inhomogeneous excitation light sheet) or irregular illumination strength (laser intensity pulse-to-pulse fluctuations) is prerequisite for this method. At least 8 subsequent images are required to calculate a reliable vector field using the optical flow algorithm. This reflects the fact that the algorithm is based on a sequence regularization strategy. Due to the estimated motion and the known time delay between the image acquisitions, the optical flow field can be calculated from the subsequent images shown in Fig. 3. Figure 4 shows the ethanol mole fraction distribution (back ground color) of the second image in Fig. 3, which is overlaid by the corresponding flow field (vector field), which illustrates the computed displacement per time between the first two acquisitions in Fig. 3 (rotated 90° clockwise).
Fig. 4 Composition and flow field distribution for the injection of water in ethanol. The ethanol mole fraction distribution (background color) corresponds to the second image in Fig. 3. The vector field corresponds to the displacement per time between the first two images in Fig. 3.
The length of the arrows represents the magnitude of the velocity, whereas the pointing direction of the arrows represents the direction of the velocity. Vectors representing velocities smaller than 2 m s−1 were deleted in Fig. 4. Regions where no vectors are given can be identified especially in the jet core and outside the mixing area of the jet, where rather large areas of homogeneous mole fraction values were determined. From large areas of homogeneous mole fractions, a reasonable displacement of subareas cannot be extracted computationally, though the subareas displacement should follow the mean displacement of the whole area of homogeneous mole fractions. Hence, the optical flow method evaluates non-sense displacements in the jet core, where large areas of homogeneous mole fraction values can be found. These areas are represented by computed velocities smaller than 2 m s−1 and consequently are not represented by vectors in Fig. 4. In the outer areas of the jet, where there are inhomogeneities in the mole fraction images, displacements can be extracted and can be represented as more reliable velocities. The evaluated velocities are in accord with what has been expected from the velocity of ethanol through the nozzle (see section: experimental setup). The combination of the composition and the corresponding flow field can be accomplished for the other images from Fig. 3, too (not given here), which consequently provides simultaneously acquired scalar and vector fields at high repetition rates to comprehensively analyze mixing phenomena.
For many technical applications, e.g. for the before mentioned T-mixer experiment to induce a reaction or to precipitate or to crystallize particles, the interplay of the velocity field and the mole fraction field is of interest especially in regions, where mixing takes place. These regions own inhomogeneities and as a consequence, the here introduced high repetition rate Raman imaging technique has the potential to characterize these mixing regions with respect to the mixing progress (mole fraction) and the mixing driving force (velocity). Regions of homogeneous mole fractions, which represent states before mixing or after complete mixing, are usually not in the focus of engineering mixing investigations. Additionally, the temporal and spatial resolution of the here introduced high repetition rate Raman imaging technique will resolve the Kolmogorov scales of the before mentioned T-mixer processes (could not be resolved for the jet experiment), which will improve the reliability of the optical flow velocity field evaluation.
4. Conclusions
High repetition rate Raman imaging for composition and flow field analysis was applied to resolve the transient mixing mechanisms during the injection of liquid water into liquid ethanol. Due to the small Raman scattering cross sections, the setup -as it was introduced- will remain restricted to systems with molecular densities similar to those in liquid systems. This also includes mixing at higher pressures e.g. for the generation of micro- and nanosized particles. Especially in the field of nanoparticle formation, mixing, nucleation and growth of the particles are taking place nearly in the same time frame. Due to the molecular number densities in high-pressure processes similar to liquids, Raman imaging at high repetition rate is giving rise to obtain information on the turbulent mixing process with a high temporal resolution.
The next field of a possible application is high repetition rate Raman imaging of gaseous flows with molecular number densities of about three orders of magnitude less. In order to achieve this, the excitation path and the detection path have to be improved significantly. The excitation path of the system cannot be improved to the required extent, as higher excitation intensities could damage the glass components in the experimental setup and would cause laser-induced break down in the mixing chamber. Unfortunately, a suitable laser for high speed Raman imaging which emits high energy pulses at rather long pulse widths in the order of several 100 ns at high repetition rates is not yet on the market. Considering the detection path, both high speed cameras can be equipped with high speed image intensifiers. This measure has the potential to compensate the low molecular number densities of gases. The disadvantage of image intensifiers is the decline in the signal-to-noise ratio and as a consequence, the computation of the displacement of inhomogeneities will be more challenging by the use of variational optical flow methods.
Aknowledgments
The authors gratefully acknowledge funding of the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German Research Foundation (DFG) in the framework of the German excellence initiative.
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