In [1]:

import numpy as np
import matplotlib.pyplot as plt

Visual Examples¶

In [78]:

np.random.seed(42)
m=1.2; b=0.3
x = np.random.random(10)
x.sort()
y = m*x+b +np.random.random(len(x))*0.1
plt.plot(x,y,'o')
m,b = np.polyfit(x,y,1)
plt.plot(x,x*m+b,'--')
plt.ylim(-1,5)
plt.show()

x2 = np.random.random(3)
y2 = (3*np.random.random(3)-1)*3
x = np.append(x,x2)
xsort = np.argsort(x)
y=np.append(y,y2)
y=y[xsort]
x=x[xsort]
plt.plot(x,y,'o')
plt.plot(x,x*m+b,'--',alpha=0.5)
m2,b2 = np.polyfit(x,y,1)
plt.plot(x,x*m2+b2,'--')
plt.ylim(-1,5)
plt.show()

In [ ]:

In [79]:

allPoints = np.arange(len(x))
xfit = np.linspace(min(x),max(x))
delta = 0.5
for i in range(10):
    np.random.shuffle(allPoints)
    points = allPoints[:2]
    xnew = x[points]
    ynew = y[points]
    mp,bp = np.polyfit(xnew,ynew,1)
    
    plt.plot(x,y,'o')
    plt.plot(xnew,ynew,f'oC{(1)%10}')
    plt.plot(xfit,xfit*mp+bp,f':C{(1)%10}')
    plt.fill_between(xfit, xfit*mp+bp-delta, xfit*mp+bp+delta,alpha=0.2,color='k')
    mask=((x*mp+bp+delta)>y)& (y>(x*mp+bp-delta))
    print("inliers=",np.sum((mask)))
    plt.ylim(-1,5)
    plt.show()

inliers= 8

inliers= 10

inliers= 10

inliers= 10

inliers= 3

inliers= 3

inliers= 2

inliers= 10

inliers= 3

inliers= 8

In [80]:

len(x)

Out[80]:

Linear Fits¶

In [117]:

np.random.seed(42)
m=1.2; b=0.3
x = np.random.random(10)
x.sort()
y = m*x+b +np.random.random(len(x))*0.1
plt.plot(x,y,'o')
m,b = np.polyfit(x,y,1)
plt.plot(x,x*m+b,'--')
plt.ylim(-1,5)
plt.show()

x2 = np.random.random(3)
y2 = (3*np.random.random(3)-1)*3
x = np.append(x,x2)
xsort = np.argsort(x)
y=np.append(y,y2)
y=y[xsort]
x=x[xsort]
plt.plot(x,y,'o')
plt.plot(x,x*m+b,'--',alpha=0.5)
m2,b2 = np.polyfit(x,y,1)
plt.plot(x,x*m2+b2,'--')
plt.ylim(-1,5)
plt.show()

Fixed Width¶

In [125]:

def RANSAC_linear(x,y,delta,nTrials):
    best_fit = -1
    mbest,bbest = -1,-1
    param_set = []
    allPoints = np.arange(len(x))
    for i in range(nTrials):
        # get new points
        np.random.shuffle(allPoints)
        points = allPoints[:2]
        xnew = x[points]
        ynew = y[points]
        # generate potential model
        mp,bp = np.polyfit(xnew,ynew,1)
        
        # calculate cost (inliers)
        mask=((x*mp+bp+delta)>y)& (y>(x*mp+bp-delta))
        inliers = np.sum(mask)
        if inliers > best_fit:
            best_fit,mbest,bbest = inliers,mp,bp
            param_set = []
        elif inliers == best_fit:
            param_set.append((mp,bp))
            
    return best_fit,mbest,bbest,param_set

In [126]:

delta = 0.5
best_fit,mbest,bbest,param_set = RANSAC_linear(x,y,delta,100)

In [127]:

print("Best # inliers:",best_fit)
print(f"True (m,b)={1.2,0.3} | guessed (m,b)={round(mbest,2),round(bbest,2)}")
print("other params found:",param_set)

Best # inliers: 11
True (m,b)=(1.2, 0.3) | guessed (m,b)=(1.03, 0.49)
other params found: [(1.0335475040063236, 0.4873716832986319)]

In [124]:

plt.plot(x,y,'o')
plt.plot(x,x*mbest+bbest,'--',label="RANSAC")
plt.plot(x,x*m+b,':',label='original')
# plt.plot(x,x*m2+b2,':',label='all points')
plt.fill_between(xfit, xfit*mbest+bbest-delta, xfit*mbest+bbest+delta,alpha=0.2,color='k')
plt.legend()
plt.ylim(-1,5)
plt.show()

In [128]:

np.random.seed(42)
m=1.2; b=0.3
x = np.random.random(70)*10
x.sort()
y = m*x+b +np.random.random(len(x))*1
plt.plot(x,y,'o')
m,b = np.polyfit(x,y,1)
plt.plot(x,x*m+b,'--')
# plt.ylim(-1,5)
plt.show()

x2 = np.random.random(30)*10;x2.sort()
y2 = (2*np.random.random(30)-1)
x = np.append(x,x2)
xsort = np.argsort(x)
y=np.append(y,y2)
y=y[xsort]
x=x[xsort]
plt.plot(x,y,'o')
plt.plot(x,x*m+b,'--',alpha=0.5)
m2,b2 = np.polyfit(x,y,1)
plt.plot(x,x*m2+b2,'--')
# plt.ylim(-1,5)
plt.show()