how to apply continuum removal in spectral graph

Question

I have to apply continuum removal on a graph and I have used scipy convexhull function to find convex hull, now i have to apply continuum removal.

here is the code-

import pandas as pd
import numpy as np
from scipy.spatial import ConvexHull
import matplotlib.pyplot as plt

data=open('15C80D4_00002.txt')
d=pd.read_table(data, sep=r'\t',header=None, names=['Wvl', 'Reflectance'],skiprows=1, 
engine='python')

x=d.iloc[:,:1]
a1=np.array(x)

y=d.iloc[:,1:]
b1=np.array(y)

points=np.concatenate((a1,b1), axis=1)


fig = plt.figure()
ax = fig.subplots()

hull = ConvexHull(points)
for simplex in hull.simplices:
    ax.plot(points[simplex,0], points[simplex,1], 'k-')

on plotting the graph i get convex hull graph

1. i dont want the bottom line, only upper part
2. i want the graph to be something like this picture, the graph should come in same axis after continuum removal

how can this be done?

Answer 1

If continuum removal simply equates to removing the (interpolated) convex hull, then the code below should do the trick. The basic idea is that we add two points, one at each end of the line, which have a lower y-value than any other point, and are thus guaranteed to form the "lower" part of the convex hull.
After the convex hull computation, we simply remove them again and are left with the "upper" part of the hull. From there you just have to interpolate the hull at the given x-coordinates to get a corresponding y' value, which you subtract from the original y-values.

import numpy as np
import matplotlib.pyplot as plt

from scipy.spatial import ConvexHull
from scipy.interpolate import interp1d

def continuum_removal(points, show=False):
    x, y = points.T
    augmented = np.concatenate([points, [(x[0], np.min(y)-1), (x[-1], np.min(y)-1)]], axis=0)
    hull = ConvexHull(augmented)
    continuum_points = points[np.sort([v for v in hull.vertices if v < len(points)])]
    continuum_function = interp1d(*continuum_points.T)
    yprime = y - continuum_function(x)

    if show:
        fig, axes = plt.subplots(2, 1, sharex=True)
        axes[0].plot(x, y, label='Data')
        axes[0].plot(*continuum_points.T, label='Continuum')
        axes[0].legend()
        axes[1].plot(x, yprime, label='Data - Continuum')
        axes[1].legend()

    return np.c_[x, yprime]

x = np.linspace(0, 1, 100)
y = np.random.randn(len(x))
points = np.c_[x, y]
new_points = continuum_removal(points, show=True)

plt.show()