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+# Copyright 2014 The Chromium Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+
+"""This module provides implementations of common computer Vision operations."""
+
+from __future__ import division
+from telemetry.internal.util import external_modules
+
+np = external_modules.ImportRequiredModule('numpy')
+
+
+def AreLinesOrthogonal(line1, line2, tolerance):
+ """Returns true if lines are within tolerance radians of being orthogonal."""
+ # Map each line onto an angle between 0 and 180.
+ theta1 = np.arctan2(np.float(line1[1] - line1[3]),
+ np.float(line1[0] - line1[2]))
+ theta2 = np.arctan2(np.float(line2[1] - line2[3]),
+ np.float(line2[0] - line2[2]))
+ angle2 = abs(theta2 - theta1)
+ if angle2 >= np.pi:
+ angle2 -= np.pi
+ # If the difference between the angles is more than pi/2 - tolerance, the
+ # lines are not orthogonal.
+ return not abs(angle2 - (np.pi / 2.0)) > tolerance
+
+
+def FindLineIntersection(line1, line2):
+ """If the line segments intersect, returns True and their intersection.
+ Otherwise, returns False and the intersection of the line segments if they
+ were to be extended."""
+ # Compute g, and h, the factor by which each line must be extended to
+ # exactly touch the other line. If both are between 0 and 1, then the lines
+ # currently intersect. We use h to compute their intersection.
+ line1p1 = line1[:2]
+ line1p0 = line1[2:]
+ line2p1 = line2[:2]
+ line2p0 = line2[2:]
+ E = np.subtract(line1p1, line1p0)
+ F = np.subtract(line2p1, line2p0)
+ Pe = np.asfarray((-E[1], E[0]))
+ Pf = np.asfarray((-F[1], F[0]))
+ h = np.dot(np.subtract(line1p0, line2p0), Pe)
+ h = np.divide(h, np.dot(F, Pe))
+ g = np.dot(np.subtract(line2p0, line1p0), Pf)
+ g = np.divide(g, np.dot(E, Pf))
+ intersection = np.add(line2p0, np.dot(F, h))
+ intersect = (h >= -0.000001 and h <= 1.000001 and
+ g >= -0.000001 and g <= 1.000001)
+ return intersect, intersection
+
+
+def ExtendLines(lines, length):
+ """Extends lines in an array to a given length, maintaining the center
+ point. Does not necessarily maintain point order."""
+ half_length = length / 2.0
+ angles = np.arctan2(lines[:, 1] - lines[:, 3], lines[:, 0] - lines[:, 2])
+ xoffsets = half_length * np.cos(angles)
+ yoffsets = half_length * np.sin(angles)
+ centerx = (lines[:, 0] + lines[:, 2]) / 2.0
+ centery = (lines[:, 1] + lines[:, 3]) / 2.0
+ lines[:, 0] = centerx - xoffsets
+ lines[:, 2] = centerx + xoffsets
+ lines[:, 1] = centery - yoffsets
+ lines[:, 3] = centery + yoffsets
+ return lines
+
+
+def IsPointApproxOnLine(point, line, tolerance=1):
+ """Approximates distance between point and line for small distances using
+ the determinant and checks whether it's within the tolerance. Tolerance is
+ an approximate distance in pixels, precision decreases with distance."""
+ xd = line[0] - line[2]
+ yd = line[1] - line[3]
+ det = ((xd) * (point[1] - line[3])) - ((yd) * (point[0] - line[2]))
+ tolerance = float(tolerance) * (abs(xd) + abs(yd))
+ return abs(det) * 2.0 <= tolerance
+
+
+def SqDistances(points1, points2):
+ """Computes the square of the distance between two sets of points, or a
+ set of points and a point."""
+ d = np.square(points1 - points2)
+ return d[:, 0] + d[:, 1]
+
+
+def SqDistance(point1, point2):
+ """Computes the square of the distance between two points."""
+ d = np.square(point1 - point2)
+ return d[0] + d[1]