findpeaks

This library findpeaks aims to detect peaks in a 1-dimensional vector and 2-dimensional arrays (images) without making any assumption on the peak shape or baseline noise. To make sure that peaks can be detected across global and local heights, and in noisy data, multiple pre-processing and denoising methods are implemented.

Navigate to API documentations for more detailed and structured information.

Contents

• Installation
• Contribute
• Citation
• Maintainers
• License

Installation

• Install findpeaks from PyPI (recommended). findpeaks is compatible with Python 3.6+ and runs on Linux, MacOS X and Windows.
• A new environment can be created as following:

pip install findpeaks

Import findpeaks package

from findpeaks import findpeaks

Example 1: 1D-vector low resolution

# Load library
from findpeaks import findpeaks
# Data
X = [9,60,377,985,1153,672,501,1068,1110,574,135,23,3,47,252,812,1182,741,263,33]
# Initialize
fp = findpeaks(lookahead=1)
results = fp.fit(X)
# Plot
fp.plot()

# Initialize with interpolation parameter
fp = findpeaks(lookahead=1, interpolate=10)
results = fp.fit(X)
fp.plot()

Example 2: 1D vector low resolution

# Load library
from findpeaks import findpeaks
# Data
X = [10,11,9,23,21,11,45,20,11,12]
# Initialize
fp = findpeaks(method='peakdetect', lookahead=1)
results = fp.fit(X)
# Plot
fp.plot()

fp = findpeaks(method='topology', lookahead=1)
results = fp.fit(X)
fp.plot()
fp.plot_persistence()

# Initialize with interpolate parameter
fp = findpeaks(method='peakdetect', lookahead=1, interpolate=10)
results = fp.fit(X)
fp.plot()

fp = findpeaks(method='topology', lookahead=1, interpolate=10)
results = fp.fit(X)
fp.plot()

Example 3: 1D-vector high resolution

# Load library
import numpy as np
from findpeaks import findpeaks

# Data
i = 10000
xs = np.linspace(0,3.7*np.pi,i)
X = (0.3*np.sin(xs) + np.sin(1.3 * xs) + 0.9 * np.sin(4.2 * xs) + 0.06 * np.random.randn(i))

# Initialize
fp = findpeaks(method='peakdetect')
results = fp.fit(X)
# Plot
fp.plot1d()

fp = findpeaks(method='topology', limit=1)
results = fp.fit(X)
fp.plot1d()
fp.plot_persistence()

Example 4: 2D-array (image) using default settings

# Import library
from findpeaks import findpeaks

# Import example
X = fp.import_example()
print(X)
array([[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.4, 0.4],
       [0. , 0. , 0. , 0. , 0. , 0. , 0.7, 1.4, 2.2, 1.8],
       [0. , 0. , 0. , 0. , 0. , 1.1, 4. , 6.5, 4.3, 1.8],
       [0. , 0. , 0. , 0. , 0. , 1.4, 6.1, 7.2, 3.2, 0.7],
       [..., ..., ..., ..., ..., ..., ..., ..., ..., ...],
       [0. , 0.4, 2.9, 7.9, 5.4, 1.4, 0.7, 0.4, 1.1, 1.8],
       [0. , 0. , 1.8, 5.4, 3.2, 1.8, 4.3, 3.6, 2.9, 6.1],
       [0. , 0. , 0.4, 0.7, 0.7, 2.5, 9. , 7.9, 3.6, 7.9],
       [0. , 0. , 0. , 0. , 0. , 1.1, 4.7, 4. , 1.4, 2.9],
       [0. , 0. , 0. , 0. , 0. , 0.4, 0.7, 0.7, 0.4, 0.4]])

# Initialize
fp = findpeaks(method='mask')
# Fit
fp.fit(X)

# Plot the pre-processing steps
fp.plot_preprocessing()
# Plot all
fp.plot()

# Initialize
fp = findpeaks(method='topology')
# Fit
fp.fit(X)

The input figure

The masking approach detects the correct peaks.

fp.plot()

Conversion from 2d to 3d mesh plots looks very nice. But there is a rough surface because of the low-resolution input data.

fp.plot_mesh()

The persistence plot appears to detect the right peaks.

fp.plot_persistence()

Example 5: 2D-array (image) with pre-processing steps

# Import library
from findpeaks import findpeaks

# Import example
X = fp.import_example()

# Initialize
fp = findpeaks(method='topology', scale=True, denoise=10, togray=True, imsize=(50,100), verbose=3)

# Fit
results = fp.fit(X)

# Plot all
fp.plot()

Show the plots:

fp.plot_preprocessing()

The masking does not work so well because the pre-processing steps includes some weighted smoothing which is not ideal for the masking approach.

fp.plot()

The mesh plot has higher resolution because the pre-processing steps caused some smoothing.

fp.plot_mesh()

The Persistence plot does show the detection of correct peaks.

fp.plot_persistence()

Denoising example

from findpeaks import findpeaks
fp = findpeaks()
img = fp.import_example('2dpeaks_image')
import findpeaks

# filters parameters
# window size
winsize = 15
# damping factor for frost
k_value1 = 2.0
# damping factor for lee enhanced
k_value2 = 1.0
# coefficient of variation of noise
cu_value = 0.25
# coefficient of variation for lee enhanced of noise
cu_lee_enhanced = 0.523
# max coefficient of variation for lee enhanced
cmax_value = 1.73

# Some pre-processing
# Resize
img = findpeaks.stats.resize(img, size=(300,300))
# Make grey image
img = findpeaks.stats.togray(img)
# Scale between [0-255]
img = findpeaks.stats.scale(img)

# Denoising
# fastnl
img_fastnl = findpeaks.stats.denoise(img.copy(), method='fastnl', window=winsize)
# bilateral
img_bilateral = findpeaks.stats.denoise(img.copy(), method='bilateral', window=winsize)
# frost filter
image_frost = findpeaks.frost_filter(img.copy(), damping_factor=k_value1, win_size=winsize)
# kuan filter
image_kuan = findpeaks.kuan_filter(img.copy(), win_size=winsize, cu=cu_value)
# lee filter
image_lee = findpeaks.lee_filter(img.copy(), win_size=winsize, cu=cu_value)
# lee enhanced filter
image_lee_enhanced = findpeaks.lee_enhanced_filter(img.copy(), win_size=winsize, k=k_value2, cu=cu_lee_enhanced, cmax=cmax_value)
# mean filter
image_mean = findpeaks.mean_filter(img.copy(), win_size=winsize)
# median filter
image_median = findpeaks.median_filter(img.copy(), win_size=winsize)

Plotting

import matplotlib.pyplot as plt
plt.figure(); plt.imshow(img_fastnl, cmap='gray'); plt.title('Fastnl'); plt.grid(False)
plt.figure(); plt.imshow(img_bilateral, cmap='gray'); plt.title('Bilateral')
plt.figure(); plt.imshow(image_frost, cmap='gray'); plt.title('Frost')
plt.figure(); plt.imshow(image_kuan, cmap='gray'); plt.title('Kuan')
plt.figure(); plt.imshow(image_lee, cmap='gray'); plt.title('Lee')
plt.figure(); plt.imshow(image_lee_enhanced, cmap='gray'); plt.title('Lee Enhanced')
plt.figure(); plt.imshow(image_mean, cmap='gray'); plt.title('Mean')
plt.figure(); plt.imshow(image_median, cmap='gray'); plt.title('Median')

Find peaks on the denoised image

from findpeaks import findpeaks
fp = findpeaks(scale=False, denoise=None, togray=False, imsize=False, verbose=3)
fp.fit(image_lee_enhanced)
fp.plot_persistence()
fp.plot_mesh(wireframe=False, title='image_lee_enhanced')

Citation

Please cite findpeaks in your publications if this is useful for your research. Here is an example BibTeX entry:

@misc{erdogant2020findpeaks,
  title={findpeaks},
  author={Erdogan Taskesen},
  year={2020},
  howpublished={\url{https://github.com/erdogant/findpeaks}},
}

References

• https://github.com/erdogant/findpeaks
• https://github.com/Anaxilaus/peakdetect
• https://www.sthu.org/blog/13-perstopology-peakdetection/index.html

Maintainer

Erdogan Taskesen, github: [erdogant](https://github.com/erdogant)
Contributions are welcome.
See [LICENSE](LICENSE) for details.