Evaluating poses

In this exercise you will compare distances between high-dimensional vectors of human poses (from a dataset of badminton poses). The dataset contains 18 sample poses, each defined by 25 points $(x_i, y_i)$. Your task is to calculate the Euclidean distance ($L_2$-norm) between all poses.

The dataset is loaded and stored in an $18\times 50$-dimensional Numpy array:

import numpy as np
import matplotlib.pyplot as plt

poses = np.load("data/poses.npy")

Each row in poses has the form $x_1, y_1, x_2, y_2, \dots, x_{25}, y_{25}$, i.e. it is a list of $50$ elements constituting $25$ points:

# Get the first pose and print it
print(poses[0])

[-27.99571178  -6.48683038  -0.11660905  -1.17064333   0.84333174
  -1.17055863   1.40324612  -0.75536782   1.64424262  -0.39685233
  -0.91658014  -1.19784466  -1.47706657  -0.75565014  -1.63809865
  -0.67290277  -0.0346016   -0.2573026    0.52441385  -0.28487094
   0.92472628   0.2406497    1.08637127   0.87586495  -0.35960773
  -0.2296778   -0.75350502   0.46266449  -0.75767282   1.26336037
 -27.99571178  -6.48683038 -27.99571178  -6.48683038   0.4412623
  -1.52924351  -0.43720223  -1.53048571  -1.23831741   1.26319098
  -1.39460965   1.34502082  -0.67480729   1.34740641   0.68458786
   1.12472817   1.08424651   1.09708925   1.16224962   0.93142511]

Note that the output above is still a 1D array, it is simply printed over multiple lines

The following cell contains a set of functions for plotting the poses. You do not need to study these - simply skip to the next section:

def limb_number_plot(s_pose_x,s_pose_y,n1,n2,c="red",label=None,axis = None):
  if label is not None:
    if (s_pose_x[n1]>-10.0) and (s_pose_x[n2]>-10.0) and (s_pose_y[n1]>-10.0) and (s_pose_y[n2]>-10.0): 
        axis.plot([s_pose_x[n1],s_pose_x[n2]], [s_pose_y[n1], s_pose_y[n2]],color = c, linestyle="-",label=label)
  else:
    if (s_pose_x[n1]>-10.0) and (s_pose_x[n2]>-10.0) and (s_pose_y[n1]>-10.0) and (s_pose_y[n2]>-10.0): 
        axis.plot([s_pose_x[n1],s_pose_x[n2]], [s_pose_y[n1], s_pose_y[n2]],color = c, linestyle="-")

def plot_single_pose(s_pose, a, c = "darkgreen", label=None, head = True):
    s_pose_x=s_pose[::2]
    s_pose_y=s_pose[1::2]
    limb_number_plot(s_pose_x,s_pose_y,2,5,c,axis=a)
    if label is not None:

        limb_number_plot(s_pose_x,s_pose_y,9,12,c,label,axis=a)
    else:
        limb_number_plot(s_pose_x,s_pose_y,9,12,c,axis=a)
    limb_number_plot(s_pose_x,s_pose_y,2,9,c,axis=a)
    limb_number_plot(s_pose_x,s_pose_y,5,12,c,axis=a)

    limb_number_plot(s_pose_x,s_pose_y,2,3,c,axis=a)
    limb_number_plot(s_pose_x,s_pose_y,3,4,c,axis=a)

    limb_number_plot(s_pose_x,s_pose_y,5,6,c,axis=a)
    limb_number_plot(s_pose_x,s_pose_y,6,7,c,axis=a)

    #left leg / foot
    limb_number_plot(s_pose_x,s_pose_y,9,10,c,axis=a)
    limb_number_plot(s_pose_x,s_pose_y,10,11,c,axis=a)
    limb_number_plot(s_pose_x,s_pose_y,11,22,c,axis=a)

    #right leg / foot
    limb_number_plot(s_pose_x,s_pose_y,12,13,c,axis=a)
    limb_number_plot(s_pose_x,s_pose_y,13,14,c,axis=a)
    limb_number_plot(s_pose_x,s_pose_y,14,19,c,axis=a)

    # head
    if head:
        limb_number_plot(s_pose_x,s_pose_y,0,15,c,axis=a)
        limb_number_plot(s_pose_x,s_pose_y,0,16,c,axis=a)

        limb_number_plot(s_pose_x,s_pose_y,15,17,c,axis=a)
        limb_number_plot(s_pose_x,s_pose_y,16,18,c,axis=a)
    return True

The cell below visualises each pose in the dataset:

# Create a 6x3 grid of subplots
fig, ax = plt.subplots(3, 6, figsize=(14, 8))

for i, p in enumerate(poses):
    axis = ax[i//6, i%6] # Select the appropriate subplot
    plot_single_pose(p, axis)

    axis.set_title(i)
    axis.set_xlim(-5, 5)
    axis.set_ylim(3,-3)


plt.tight_layout()

# Write your solution here

The following cell creates an 18x18 distance matrix:

import seaborn as sns
t = np.triu(np.ones_like(res))
sns.heatmap(res, annot=True, mask=t)

def plot_single(ax, i, p):
    ax.scatter(p[:, 0], p[:, 1]) # Plot the pose coordinates

    ax.set_title(i)
    ax.set_xlim(-5, 5)
    ax.set_ylim(3,-3)

def plot_pair(a, b):
    """Plot two poses side by side. a and b are indices.
    """
    fig, ax = plt.subplots(1, 2)

    ap = poses[a]
    bp = poses[b]

    plot_single_pose(ap, ax[0])
    plot_single_pose(bp, ax[1])
    #plot_single(ax[0], a, ap)
    #plot_single(ax[1], b, bp)

# Write your solution here

Plot of min difference pose pairs

Plot of max difference pose pairs

Plot of random pose pairs

# write your reflections here