Interpolate/impute

The input parameter “interpolate” extens the data by this factor and is usefull to “smooth” the signal by a (linear) interpolation. It can also handle missing (nan) data! A smoothed signal can be more robust agains noise, and perform better in the detection of peaks and valleys. This step can be seen as pre-processing step before applying any method. The input is 1D numpy vector that can be interpolated by various methods for which the default is linear. Note that the initialization of findpeaks is fixed to linear. If another method is desired, it can be done by directly using the functionality: findpeaks.interpolate.interpolate_line1d().

Besides the 1d functionality, there is also a 2d functionlity in case you have x and y-cooridinates: findpeaks.interpolate.interpolate_line2d().

Interpolation methods:

  • String or integer

  • 0 : order degree

  • 1 : order degree

  • 2 : order degree

  • 3 : order degree

  • ‘linear’

  • ‘nearest’

  • ‘zero’

  • ‘slinear’

  • ‘quadratic’

  • ‘cubic’

  • ‘previous’

  • ‘next’

# Import library
import findpeaks
# Small dataset
X = [10,11,9,23,21,11,45,20,11,12]
# Interpolate the data using linear by factor 10
Xi = findpeaks.interpolate_line1d(X, method='linear', n=10, showfig=True)
# Print message
print('Input data lenth: %s, interpolated length: %s' %(len(X), len(Xi)))
# Input data lenth: 10, interpolated length: 100
Interpolation example

figP0

As mentioned before, the interpolate function findpeaks.interpolate.interpolate_line1d() can also handle missing data. Lets demonstrate this by example:

# Import library
import findpeaks
# Small dataset
X = [1,2,3,np.nan,np.nan,6,7,np.nan,9,10]
# Interpolate the data using linear method and n=1. This would not extend the data but simply impute missing values.
Xi = findpeaks.interpolate_line1d(X, method='linear', n=1)
print(Xi)
# array([ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])

The interpolate functionality is integrated in findpeaks by specifying the interpolate as the factor n. The advantage of the interpolation integration in findpeaks is the automatic mapping of the results back to the original data and imputing missing data. Otherwise, the detected peaks coordinates on the x-axis would always be different then for the input-data as the data is extended by interpolation.

# Import library
from findpeaks import findpeaks
# Init
fp = findpeaks(method='peakdetect', interpolate=10, lookahead=1)
# Small dataset
X = [10,11,9,23,21,11,45,20,11,12]
# Interpolate the data using linear by factor 10
results = fp.fit(X)
fp.plot()
Results without interpolation (left) and with (right)

figP1

figP2

Resize

The resize function findpeaks.stats.resize() is only applicable for 2D-arrays (images). The function resizes the images using functionality of python-opencv using default parameter settings.

Scale

The scale function findpeaks.stats.scale() is only applicable for 2D-arrays (images). Scaling data is an import pre-processing step to make sure all data is ranged between the minimum and maximum range.

The images are scaled between [0-255] by the following equation:

Ximg * (255 / max(Ximg))

Gray

The gray function findpeaks.stats.togray() is only applicable for 2D-arrays (images). The function sets the color to gray using functionality of python-opencv using the cv2.COLOR_BGR2GRAY settings.

Preprocessing

The preprocessing function is developed to pipeline the above mentioned functionalities findpeaks.findpeaks.findpeaks.preprocessing().

The pre-processing has 4 (optional) steps and are exectued in this order. After the last step, the peak detection method is applied.

    1. Resizing (to reduce computation time).

    1. Scaling color pixels between [0-255].

    1. Conversion to gray-scale.

    1. Denoising of the image.

Each of these steps can be controlled by setting the input parameters.

# Import library
from findpeaks import findpeaks
# Init
fp = findpeaks(method="topology", whitelist=['peak'], imsize=(50,100), scale=True, togray=True, denoise=None)
# Small dataset
X = fp.import_example("2dpeaks")

# Interpolate the data using linear by factor 10
results = fp.fit(X)
fp.plot(figure_order='horizontal')
# fp.plot_persistence()
Interpolation example 2d-array (image)

figP3