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data/KITTI/test/calib/0000.txt

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+P0: 7.215377000000e+02 0.000000000000e+00 6.095593000000e+02 0.000000000000e+00 0.000000000000e+00 7.215377000000e+02 1.728540000000e+02 0.000000000000e+00 0.000000000000e+00 0.000000000000e+00 1.000000000000e+00 0.000000000000e+00  
+P1: 7.215377000000e+02 0.000000000000e+00 6.095593000000e+02 -3.875744000000e+02 0.000000000000e+00 7.215377000000e+02 1.728540000000e+02 0.000000000000e+00 0.000000000000e+00 0.000000000000e+00 1.000000000000e+00 0.000000000000e+00  
+P2: 7.215377000000e+02 0.000000000000e+00 6.095593000000e+02 4.485728000000e+01 0.000000000000e+00 7.215377000000e+02 1.728540000000e+02 2.163791000000e-01 0.000000000000e+00 0.000000000000e+00 1.000000000000e+00 2.745884000000e-03  
+P3: 7.215377000000e+02 0.000000000000e+00 6.095593000000e+02 -3.395242000000e+02 0.000000000000e+00 7.215377000000e+02 1.728540000000e+02 2.199936000000e+00 0.000000000000e+00 0.000000000000e+00 1.000000000000e+00 2.729905000000e-03  
+R0_rect: 9.999239000000e-01 9.837760000000e-03 -7.445048000000e-03 -9.869795000000e-03 9.999421000000e-01 -4.278459000000e-03 7.402527000000e-03 4.351614000000e-03 9.999631000000e-01  
+Tr_velo_to_cam: 7.533745000000e-03 -9.999714000000e-01 -6.166020000000e-04 -4.069766000000e-03 1.480249000000e-02 7.280733000000e-04 -9.998902000000e-01 -7.631618000000e-02 9.998621000000e-01 7.523790000000e-03 1.480755000000e-02 -2.717806000000e-01  
+Tr_imu_to_velo: 9.999976000000e-01 7.553071000000e-04 -2.035826000000e-03 -8.086759000000e-01 -7.854027000000e-04 9.998898000000e-01 -1.482298000000e-02 3.195559000000e-01 2.024406000000e-03 1.482454000000e-02 9.998881000000e-01 -7.997231000000e-01  

data/KITTI/test/calib/0003.txt

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+P0: 7.215377000000e+02 0.000000000000e+00 6.095593000000e+02 0.000000000000e+00 0.000000000000e+00 7.215377000000e+02 1.728540000000e+02 0.000000000000e+00 0.000000000000e+00 0.000000000000e+00 1.000000000000e+00 0.000000000000e+00  
+P1: 7.215377000000e+02 0.000000000000e+00 6.095593000000e+02 -3.875744000000e+02 0.000000000000e+00 7.215377000000e+02 1.728540000000e+02 0.000000000000e+00 0.000000000000e+00 0.000000000000e+00 1.000000000000e+00 0.000000000000e+00  
+P2: 7.215377000000e+02 0.000000000000e+00 6.095593000000e+02 4.485728000000e+01 0.000000000000e+00 7.215377000000e+02 1.728540000000e+02 2.163791000000e-01 0.000000000000e+00 0.000000000000e+00 1.000000000000e+00 2.745884000000e-03  
+P3: 7.215377000000e+02 0.000000000000e+00 6.095593000000e+02 -3.395242000000e+02 0.000000000000e+00 7.215377000000e+02 1.728540000000e+02 2.199936000000e+00 0.000000000000e+00 0.000000000000e+00 1.000000000000e+00 2.729905000000e-03  
+R0_rect: 9.999239000000e-01 9.837760000000e-03 -7.445048000000e-03 -9.869795000000e-03 9.999421000000e-01 -4.278459000000e-03 7.402527000000e-03 4.351614000000e-03 9.999631000000e-01  
+Tr_velo_to_cam: 7.533745000000e-03 -9.999714000000e-01 -6.166020000000e-04 -4.069766000000e-03 1.480249000000e-02 7.280733000000e-04 -9.998902000000e-01 -7.631618000000e-02 9.998621000000e-01 7.523790000000e-03 1.480755000000e-02 -2.717806000000e-01  
+Tr_imu_to_velo: 9.999976000000e-01 7.553071000000e-04 -2.035826000000e-03 -8.086759000000e-01 -7.854027000000e-04 9.998898000000e-01 -1.482298000000e-02 3.195559000000e-01 2.024406000000e-03 1.482454000000e-02 9.998881000000e-01 -7.997231000000e-01  

evaluation/box_util.py

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+from scipy.spatial import ConvexHull
+import numpy as np
+
+def boxoverlap(a,b,criterion="union"):
+    """
+        boxoverlap computes intersection over union for bbox a and b in KITTI format.
+        If the criterion is 'union', overlap = (a inter b) / a union b).
+        If the criterion is 'a', overlap = (a inter b) / a, where b should be a dontcare area.
+    """
+
+    x1 = max(a.x1, b.x1)
+    y1 = max(a.y1, b.y1)
+    x2 = min(a.x2, b.x2)
+    y2 = min(a.y2, b.y2)
+
+    w = x2-x1
+    h = y2-y1
+
+    if w<=0. or h<=0.:
+        return 0.
+    inter = w*h
+    aarea = (a.x2-a.x1) * (a.y2-a.y1)
+    barea = (b.x2-b.x1) * (b.y2-b.y1)
+    # intersection over union overlap
+    if criterion.lower()=="union":
+        o = inter / float(aarea+barea-inter)
+    elif criterion.lower()=="a":
+        o = float(inter) / float(aarea)
+    else:
+        raise TypeError("Unkown type for criterion")
+    return o
+
+
+def polygon_clip(subjectPolygon, clipPolygon):
+   """ Clip a polygon with another polygon.
+
+   Ref: https://rosettacode.org/wiki/Sutherland-Hodgman_polygon_clipping#Python
+
+   Args:
+     subjectPolygon: a list of (x,y) 2d points, any polygon.
+     clipPolygon: a list of (x,y) 2d points, has to be *convex*
+   Note:
+     **points have to be counter-clockwise ordered**
+
+   Return:
+     a list of (x,y) vertex point for the intersection polygon.
+   """
+   def inside(p):
+      return(cp2[0]-cp1[0])*(p[1]-cp1[1]) > (cp2[1]-cp1[1])*(p[0]-cp1[0])
+
+   def computeIntersection():
+      dc = [ cp1[0] - cp2[0], cp1[1] - cp2[1] ]
+      dp = [ s[0] - e[0], s[1] - e[1] ]
+      n1 = cp1[0] * cp2[1] - cp1[1] * cp2[0]
+      n2 = s[0] * e[1] - s[1] * e[0] 
+      n3 = 1.0 / (dc[0] * dp[1] - dc[1] * dp[0])
+      return [(n1*dp[0] - n2*dc[0]) * n3, (n1*dp[1] - n2*dc[1]) * n3]
+
+   outputList = subjectPolygon
+   cp1 = clipPolygon[-1]
+
+   for clipVertex in clipPolygon:
+      cp2 = clipVertex
+      inputList = outputList
+      outputList = []
+      s = inputList[-1]
+
+      for subjectVertex in inputList:
+         e = subjectVertex
+         if inside(e):
+            if not inside(s):
+               outputList.append(computeIntersection())
+            outputList.append(e)
+         elif inside(s):
+            outputList.append(computeIntersection())
+         s = e
+      cp1 = cp2
+      if len(outputList) == 0:
+          return None
+   return(outputList)
+
+
+def poly_area(x,y):
+    """ Ref: http://stackoverflow.com/questions/24467972/calculate-area-of-polygon-given-x-y-coordinates """
+    return 0.5*np.abs(np.dot(x,np.roll(y,1))-np.dot(y,np.roll(x,1)))
+
+def convex_hull_intersection(p1, p2):
+    """ Compute area of two convex hull's intersection area.
+        p1,p2 are a list of (x,y) tuples of hull vertices.
+        return a list of (x,y) for the intersection and its volume
+    """
+    inter_p = polygon_clip(p1,p2)
+    if inter_p is not None:
+        hull_inter = ConvexHull(inter_p)
+        return inter_p, hull_inter.volume
+    else:
+        return None, 0.0  
+
+def box3d_vol(corners):
+    ''' corners: (8,3) no assumption on axis direction '''
+    a = np.sqrt(np.sum((corners[0,:] - corners[1,:])**2))
+    b = np.sqrt(np.sum((corners[1,:] - corners[2,:])**2))
+    c = np.sqrt(np.sum((corners[0,:] - corners[4,:])**2))
+    return a*b*c
+
+def box3d_iou(corners1, corners2, criterion='union'):
+    ''' Compute 3D bounding box IoU.
+
+    Input:
+        corners1: numpy array (8,3), assume up direction is negative Y
+        corners2: numpy array (8,3), assume up direction is negative Y
+    Output:
+        iou: 3D bounding box IoU
+        iou_2d: bird's eye view 2D bounding box IoU
+
+    todo (rqi): add more description on corner points' orders.
+    '''
+    # corner points are in counter clockwise order
+    rect1 = [(corners1[i,0], corners1[i,2]) for i in range(3,-1,-1)]
+    rect2 = [(corners2[i,0], corners2[i,2]) for i in range(3,-1,-1)] 
+    area1 = poly_area(np.array(rect1)[:,0], np.array(rect1)[:,1])
+    area2 = poly_area(np.array(rect2)[:,0], np.array(rect2)[:,1])
+    inter, inter_area = convex_hull_intersection(rect1, rect2)
+
+    ymax = min(corners1[0,1], corners2[0,1])
+    ymin = max(corners1[4,1], corners2[4,1])
+    inter_vol = inter_area * max(0.0, ymax-ymin)
+    vol1 = box3d_vol(corners1)
+    vol2 = box3d_vol(corners2)
+    if criterion.lower() == 'union':
+	    iou = inter_vol / (vol1 + vol2 - inter_vol)
+	    iou_2d = inter_area/(area1+area2-inter_area)
+    elif criterion.lower() == 'a':
+        iou = inter_vol / vol1
+        iou_2d = inter_area / area1
+    else:
+        raise TypeError("Unkown type for criterion")
+    return iou, iou_2d
+
+def roty(t):
+    ''' Rotation about the y-axis. '''
+    c = np.cos(t)
+    s = np.sin(t)
+    return np.array([[c,  0,  s],
+                     [0,  1,  0],
+                     [-s, 0,  c]])
+
+def compute_box_3d(obj):
+    ''' Takes an object and a projection matrix (P) and projects the 3d
+        bounding box into the image plane.
+        Returns:
+            corners_2d: (8,2) array in left image coord.
+            corners_3d: (8,3) array in in rect camera coord.
+    '''
+    # compute rotational matrix around yaw axis
+    R = roty(obj.yaw)    
+
+    # 3d bounding box dimensions
+    l = obj.l
+    w = obj.w
+    h = obj.h
+
+    # 3d bounding box corners
+    x_corners = [l/2,l/2,-l/2,-l/2,l/2,l/2,-l/2,-l/2];
+    y_corners = [0,0,0,0,-h,-h,-h,-h];
+    z_corners = [w/2,-w/2,-w/2,w/2,w/2,-w/2,-w/2,w/2];
+
+    # rotate and translate 3d bounding box
+    corners_3d = np.dot(R, np.vstack([x_corners,y_corners,z_corners]))
+    #print corners_3d.shape
+    corners_3d[0,:] = corners_3d[0,:] + obj.X
+    corners_3d[1,:] = corners_3d[1,:] + obj.Y
+    corners_3d[2,:] = corners_3d[2,:] + obj.Z
+    # print('cornsers_3d: ', corners_3d)
+
+    return np.transpose(corners_3d)
+
+def box3doverlap(aa, bb, criterion='union'):
+	aa_3d = compute_box_3d(aa)
+	bb_3d = compute_box_3d(bb)
+
+	iou3d, iou2d = box3d_iou(aa_3d, bb_3d, criterion=criterion)
+	# print(iou3d)
+	# print(iou2d)
+	return iou3d