Particle Image Velocimetry Fluid Dynamics

OpenPIV

Overview

OpenPIV (Open Particle Image Velocimetry) analyzes fluid flow from PIV image pairs. It covers preprocessing, cross-correlation, vector validation, outlier replacement, smoothing, and scaling to physical units.

Everything below is verified against openpiv 0.25.4. The API moves between releases — check inspect.signature() before trusting a snippet against a different version.

When to use

Use this skill when working with experimental PIV or flow-visualization image pairs: measuring 2D velocity fields, tuning interrogation-window parameters, validating vectors, or deriving vorticity, strain rate, and turbulence statistics. For simulating flow rather than measuring it, use a CFD skill instead.

Quick Start

Install OpenPIV:

uv pip install openpiv

# Pin it when the analysis needs to be reproducible -- this is the version every
# snippet below was checked against.
uv pip install "openpiv==0.25.4"

Run PIV analysis on an image pair:

import numpy as np
from openpiv import tools, pyprocess, validation, filters, scaling

frame_a = tools.imread("image_a.bmp")
frame_b = tools.imread("image_b.bmp")

# Cross-correlate. Returns (u, v, s2n) whenever sig2noise_method is not None.
u, v, s2n = pyprocess.extended_search_area_piv(
    frame_a.astype(np.int32),
    frame_b.astype(np.int32),
    window_size=32,
    overlap=12,
    dt=0.02,
    search_area_size=38,
    correlation_method="linear",   # required for search_area_size > window_size
    sig2noise_method="peak2peak",
)

x, y = pyprocess.get_coordinates(
    image_size=frame_a.shape,
    search_area_size=38,
    overlap=12,
)

# flags is a boolean array: True marks a spurious vector.
flags = validation.sig2noise_val(s2n, threshold=1.05)
u, v = filters.replace_outliers(u, v, flags, method="localmean", max_iter=3, kernel_size=2)

# Scale to physical units, then flip to image coordinates for plotting.
x, y, u, v = scaling.uniform(x, y, u, v, scaling_factor=96.52)
x, y, u, v = tools.transform_coordinates(x, y, u, v)

tools.save("vectors.txt", x, y, u, v, flags)

Or use the bundled CLI, which wraps exactly that pipeline:

python skills/openpiv/scripts/runner.py \
    --image frame_a.bmp --image frame_b.bmp --output_dir results --verbose

Core Concepts

PIV Fundamentals

Particle Image Velocimetry is an optical method for measuring fluid velocity by tracking illuminated tracer particles between two images.

Process flow:

1. Capture an image pair (frame_a, frame_b) separated by a known time dt.
2. Divide the images into interrogation windows.
3. Cross-correlate matching windows to find peak displacement.
4. Validate vectors (signal-to-noise, global range, local median).
5. Replace spurious vectors with interpolated values.
6. Scale pixel displacements to physical units.

Interrogation Window Parameters

window_size — correlation window in pixels (typically 16–128). Larger windows give better correlation but coarser spatial resolution.

overlap — pixels shared between adjacent windows (typically 50–75% of window_size). Higher overlap raises vector density and cost, but adjacent vectors become correlated rather than independent.

search_area_size — the window searched in the second frame. Must be ≥ window_size; a few pixels larger accommodates larger displacements. Pair an extended search area with correlation_method="linear" — the default "circular" relies on FFT wrap-around and aliases large displacements into small ones. See references/advanced_algorithms.md.

Rules of thumb: keep the largest displacement under about a quarter of window_size, and aim for 5–10 particles per window.

Signal-to-Noise Ratio

s2n measures how distinct the correlation peak is. sig2noise_method controls how it is computed — "peak2mean" (the function default) or "peak2peak". The two are on different scales, so a threshold tuned for one is meaningless for the other. Typical peak2peak thresholds are 1.05–1.3.

flags = validation.sig2noise_val(s2n, threshold=1.05)
# flags is bool: True == spurious. `~flags` selects the good vectors.

Common Operations

Dynamic Masking

Masking lives in openpiv.preprocess, not in an openpiv.masking module. It returns an (image, mask) tuple and expects a float image.

from openpiv import preprocess

# method="edges" for dark, sharp-edged objects; "intensity" for high-contrast objects.
frame_a_masked, mask_a = preprocess.dynamic_masking(
    frame_a.astype(np.float64), method="intensity", filter_size=7, threshold=0.005
)
frame_b_masked, mask_b = preprocess.dynamic_masking(
    frame_b.astype(np.float64), method="intensity", filter_size=7, threshold=0.005
)

Feed the returned image into the correlation step — it already has the masked region zeroed. Do not multiply the original frame by mask: masking is already applied, and for method="edges" the mask comes back as uint8 0/255 rather than boolean, so multiplying rescales the image by 255.

Multi-Pass Processing

Multi-pass (window deformation) lives in openpiv.windef, driven by a PIVSettings dataclass. pyprocess has no multi-pass entry point.

import numpy as np
from openpiv import scaling, windef

settings = windef.PIVSettings()
settings.windowsizes = (64, 32, 16)   # one entry per pass, decreasing (this is also the default)
settings.overlap = (32, 16, 8)        # same length as windowsizes
settings.num_iterations = 3           # number of passes to actually run
settings.sig2noise_threshold = 1.05

x, y, u, v, flags = windef.simple_multipass(
    frame_a.astype(np.int32), frame_b.astype(np.int32), settings
)

# Output is in PIXELS PER FRAME -- convert yourself. scaling.uniform only divides
# by scaling_factor, so apply dt separately.
dt = 0.02
x, y, u, v = scaling.uniform(x, y, u, v, scaling_factor=96.52)
u, v = u / dt, v / dt

simple_multipass already validates, replaces outliers, fills remaining NaNs with zeros, and calls transform_coordinates — do not repeat those steps.

Units trap: PIVSettings has dt and scaling_factor fields, but windef never uses either — first_pass calls extended_search_area_piv without dt, so the whole multi-pass chain works in pixels per frame. Setting settings.dt = 0.02 changes nothing about the returned values. Convert after the fact, as above.

For control over individual passes, windef.first_pass and windef.multipass_img_deform are the lower-level building blocks.

Validation and Post-Processing

Validation Methods

Every validator returns a boolean array where True marks a spurious vector.

# Signal-to-noise
flags = validation.sig2noise_val(s2n, threshold=1.05)

# Global range -- takes (min, max) TUPLES, positionally or as u_thresholds/v_thresholds.
flags = validation.global_val(u, v, (-300, 300), (-300, 300))

# Local median -- u_threshold and v_threshold are REQUIRED; size is the neighbourhood half-width.
flags = validation.local_median_val(u, v, u_threshold=30.0, v_threshold=30.0, size=1)

# Combine with boolean OR (not np.maximum -- these are bool arrays).
flags = (
    validation.sig2noise_val(s2n, threshold=1.05)
    | validation.global_val(u, v, (-300, 300), (-300, 300))
    | validation.local_median_val(u, v, u_threshold=30.0, v_threshold=30.0)
)

Set these thresholds in the units of u and v, not in pixels per frame. extended_search_area_piv divides by dt, so with dt=0.02 a 3 px/frame displacement arrives as 150 px/s. The thresholds above suit that case; the (-30, 30) figure that PIV literature and PIVSettings.min_max_u_disp use is a px/frame limit, and applying it to px/s output rejects the entire field. Either validate before scaling, or scale the thresholds by 1/dt too.

Outlier Replacement

u, v = filters.replace_outliers(
    u, v, flags, method="localmean", max_iter=3, tol=1e-3, kernel_size=2
)

method accepts "localmean", "disk", or "distance" — and only those three. An unrecognized name is not rejected; it falls through to an all-zero kernel and silently returns a useless field. Note that replacement fills the flagged positions with interpolated values — if you then overwrite them with NaN, the replacement was wasted. Choose one or the other:

# Keep flagged vectors out of the analysis entirely, instead of interpolating them.
u = np.where(flags, np.nan, u)
v = np.where(flags, np.nan, v)

Smoothing

Smoothing is openpiv.smoothn.smoothn; there is no openpiv.smooth module. It returns a tuple whose first element is the smoothed field, and it does not accept NaN input.

from openpiv.smoothn import smoothn

u_smooth, *_ = smoothn(np.nan_to_num(u), s=0.5)  # s: larger == smoother
v_smooth, *_ = smoothn(np.nan_to_num(v), s=0.5)
u_smooth = np.asarray(u_smooth)

Visualization

Vector Field Plotting

display_vector_field reads a saved vectors file and calls plt.show() internally, so select a non-interactive backend for batch runs.

import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
from openpiv import tools

fig, ax = plt.subplots(figsize=(8, 8))
tools.display_vector_field(
    "vectors.txt",
    ax=ax,
    scaling_factor=96.52,   # same factor used in scaling.uniform, to map back onto the image
    scale=50,
    width=0.0035,
   
    image_name="frame_a.bmp",
)
fig.savefig("vector_field.png", dpi=150, bbox_inches="tight")
plt.close(fig)

Custom Visualization

import numpy as np
import matplotlib.pyplot as plt

fig, axes = plt.subplots(1, 3, figsize=(15, 5))

mag = np.sqrt(u**2 + v**2)
for ax, field, title, cmap in [
    (axes[0], mag, "Velocity Magnitude", "viridis"),
    (axes[1], u, "U Velocity", "RdBu_r"),
    (axes[2], v, "V Velocity", "RdBu_r"),
]:
    im = ax.imshow(field, cmap=cmap)
    ax.set_title(title)
    plt.colorbar(im, ax=ax)

fig.tight_layout()
fig.savefig("velocity_components.png")
plt.close(fig)

Analysis Functions

scripts/analyze.py bundles these against a params.npz written by runner.py. It infers the physical grid spacing from the saved coordinates, so the derivatives come out per unit length:

import sys
sys.path.insert(0, "skills/openpiv/scripts")
from analyze import PIVAnalyzer

piv = PIVAnalyzer("results/params.npz")
vorticity = piv.compute_vorticity()          # dv/dx - du/dy
exx, eyy, exy = piv.compute_strain()
stats = piv.compute_statistics()             # u_mean, v_mean, rms_u, rms_v, tke
piv.plot_vector_field(save_path="quiver.png")

The standalone forms, if you would rather compute them inline:

Vorticity

def compute_vorticity(u, v, dx=1.0, dy=None):
    """Out-of-plane vorticity dv/dx - du/dy. Pass the physical grid spacing, not 1.0."""
    dy = dx if dy is None else dy
    return np.gradient(v, dx, axis=1) - np.gradient(u, dy, axis=0)

The grid spacing is (window_size - overlap) / scaling_factor in physical units, so leaving dx=1.0 yields vorticity per grid cell, not per unit length.

Sign convention: runner.py ends with transform_coordinates, which relabels the grid into a right-handed y-up frame but leaves the rows in image order, so the saved y decreases as the row index grows. The standalone forms above assume the opposite, so on a params.npz field they return -du/dy and flip the sign of the vorticity and the shear strain — negate the axis=0 derivatives, or use PIVAnalyzer, which reads the orientation off the saved coordinates.

Strain Rate

def compute_strain(u, v, dx=1.0, dy=None):
    """Return (exx, eyy, exy) of the 2D strain-rate tensor."""
    dy = dx if dy is None else dy
    du_dx = np.gradient(u, dx, axis=1)
    du_dy = np.gradient(u, dy, axis=0)
    dv_dx = np.gradient(v, dx, axis=1)
    dv_dy = np.gradient(v, dy, axis=0)
    return du_dx, dv_dy, 0.5 * (du_dy + dv_dx)

Turbulence Statistics

def compute_statistics(u, v):
    """Single-frame spatial statistics. NOT Reynolds decomposition."""
    u_prime = u - np.nanmean(u)
    v_prime = v - np.nanmean(v)
    rms_u, rms_v = np.nanstd(u_prime), np.nanstd(v_prime)
    return {
        "u_mean": np.nanmean(u),
        "v_mean": np.nanmean(v),
        "rms_u": rms_u,
        "rms_v": rms_v,
        "tke": 0.5 * (rms_u**2 + rms_v**2),
    }

Caveat: subtracting the spatial mean of one frame measures spatial variance, which equals turbulent intensity only for a homogeneous field. Genuine Reynolds decomposition needs an ensemble of image pairs: average over the time axis, then subtract that mean field from each realization.

CLI Usage

# Basic run
python skills/openpiv/scripts/runner.py \
    --image img1.bmp --image img2.bmp --output_dir results --verbose

# Tuned parameters with dynamic masking
python skills/openpiv/scripts/runner.py \
    --image frame_a.bmp \
    --image frame_b.bmp \
    --output_dir results \
    --window_size 32 \
    --overlap 12 \
    --search_area 38 \
    --dt 0.02 \
    --scaling 96.52 \
    --threshold 1.05 \
    --mask dynamic \
    --mask_method intensity \
    --verbose

CLI Options

Verify an install end to end against OpenPIV's own bundled image pair:

python skills/openpiv/scripts/run_example.py --output_dir /tmp/openpiv-demo

Output Files

• vectors.txt — tab-delimited, %.4e formatted, with a # x y u v flags mask comment header
• params.npz — NumPy archive with x, y, u, v, flags arrays
• vector_field.png — vector field drawn over the first frame

# x	y	u	v	flags	mask
2.1757e-01	3.5226e+00	-6.2220e-02	-2.7081e+00	0.0000e+00	0.0000e+00
4.8695e-01	3.5226e+00	-3.1587e-01	-2.9800e+00	0.0000e+00	0.0000e+00

flags is written as a float, 0 for a valid vector and 1 for a flagged one.

Best Practices

Parameter Selection

1. Window size — 32×32 suits most cases. 64/128 for better correlation at coarser resolution; 16/24 for finer resolution at the cost of noise.
2. Overlap — 50–75% of window size.
3. Threshold — raise it to reject more vectors; always re-tune after switching sig2noise_method.
4. Scaling factor — calibrate against a known reference such as a calibration grid, and keep the units straight (96.52 in OpenPIV's test1 tutorial data is px/mm).

Image Quality

• Particles visible and evenly distributed, 5–10 per interrogation window
• No saturated or overexposed regions
• Minimal background noise; consider background subtraction across a run

Processing Tips

1. Start from the defaults, then tune against the vector field you get.
2. Inspect the s2n distribution — a low median means poor correlation, not a bad threshold.
3. Visualize early; obvious problems (uniform vectors, edge artifacts) show up immediately.
4. Use multi-pass (windef) for flows with large velocity gradients or displacements.
5. Mask reflections and solid boundaries rather than letting them generate vectors.

Resources

references/

• advanced_algorithms.md — correlation and subpixel methods, multi-pass window deformation, PIVSettings fields, 3D and phase-separation modules

Load the reference when detailed algorithm or settings information is needed.