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more constistent way of determining ellipse parameters

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Johannes Schönberger
2012-05-12 10:05:14 +02:00
parent 04e444d90f
commit 87ddbbeabe
2 changed files with 44 additions and 23 deletions
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skimage/measure/_regionprops.py
+41 -18
View File
@@ -1,5 +1,5 @@
# coding: utf-8
import math
from math import sqrt, atan, pi as PI
import numpy as np
from scipy import ndimage
@@ -67,8 +67,15 @@ def regionprops(image, properties='all'):
* ConvexImage : HxJ ndarray
Convex hull image which has the same size as bounding box.
* Eccentricity : float
Linear eccentricity of the ellipse that has the same second-moments
as the region (0 <= eccentricity <= 1).
Eccentricity of the ellipse that has the same second-moments as the
region (1 <= Eccentricity < Inf), where Eccentricity = 1 corresponds
to a circular disk and elongated regions have Eccentricity > 1.
.. math::
a_1 = \mu _{2,0} + \mu _{0,2} + \sqrt{(\mu _{2,0} - \\
\mu _{0,2})^2 + 4 {\mu _{1,1}}^2}
a_2 = \mu _{2,0} + \mu _{0,2} - \sqrt{(\mu _{2,0} - \\
\mu _{0,2})^2 + 4 {\mu _{1,1}}^2}
Ecc = \frac{a_1}{a_2}
* EquivDiameter : float
The diameter of a circle with the same area as the region.
* EulerNumber : int
@@ -89,9 +96,17 @@ def regionprops(image, properties='all'):
* MajorAxisLength : float
The length of the major axis of the ellipse that has the same
normalized second central moments as the region.
.. math::
a_1 = \mu _{2,0} + \mu _{0,2} + \sqrt{(\mu _{2,0} - \\
\mu _{0,2})^2 + 4 {\mu _{1,1}}^2}
A = \sqrt{\frac{2 a_1}{\mu _{0,0}}}
* MinorAxisLength : float
The length of the minor axis of the ellipse that has the same
normalized second central moments as the region.
.. math::
a_2 = \mu _{2,0} + \mu _{0,2} - \sqrt{(\mu _{2,0} - \\
\mu _{0,2})^2 + 4 {\mu _{1,1}}^2}
A = \sqrt{\frac{2 a_2}{\mu _{0,0}}}
* Moments 3x3 ndarray
Spatial moments up to 3rd order.
.. math::
@@ -118,6 +133,8 @@ def regionprops(image, properties='all'):
References
----------
Wilhelm Burger, Mark Burge. Principles of Digital Image Processing: Core
Algorithms. Springer-Verlag, London, 2009.
B. Jähne. Digital Image Processing. Springer-Verlag,
Berlin-Heidelberg, 6. edition, 2005.
T. H. Reiss. Recognizing Planar Objects Using Invariant Image Features,
@@ -166,18 +183,17 @@ def regionprops(image, properties='all'):
cc = m[1,0] / m[0,0]
mu = _moments.central_moments(array, cr, cc, 3)
# elements of second order central moment covariance matrix
a = mu[2,0] / mu[0,0]
b = mu[1,1] / mu[0,0]
c = mu[0,2] / mu[0,0]
# eigenvalues of covariance matrix
l1 = abs(0.5 * (a + c - math.sqrt((a - c) ** 2 + 4 * b ** 2)))
l2 = abs(0.5 * (a + c + math.sqrt((a - c) ** 2 + 4 * b ** 2)))
# elements of the inertia tensor
a = mu[2,0]
b = mu[1,1]
c = mu[0,2]
# cached results which are used by several properties
_filled_image = None
_convex_image = None
_nu = None
_a1 = None
_a2 = None
if 'Area' in properties:
obj_props['Area'] = m[0,0]
@@ -202,11 +218,14 @@ def regionprops(image, properties='all'):
obj_props['ConvexImage'] = _convex_image
if 'Eccentricity' in properties:
obj_props['Eccentricity'] = \
math.sqrt(1 - (min(l1, l2) / max(l1, l2)) ** 2)
if _a2 is None:
_a2 = a + c - sqrt((a - c)**2 + 4 * b ** 2)
if _a1 is None:
_a1 = a + c + sqrt((a - c)**2 + 4 * b ** 2)
obj_props['Eccentricity'] = _a1 / _a2
if 'EquivDiameter' in properties:
obj_props['EquivDiameter'] = math.sqrt(4 * m[0,0] / math.pi)
obj_props['EquivDiameter'] = sqrt(4 * m[0,0] / PI)
if 'EulerNumber' in properties:
if _filled_image is None:
@@ -236,11 +255,15 @@ def regionprops(image, properties='all'):
_filled_image = ndimage.binary_fill_holes(array, STREL_8)
obj_props['FilledImage'] = _filled_image
if 'MinorAxisLength' in properties:
obj_props['MinorAxisLength'] = min(l1, l2)
if 'MajorAxisLength' in properties:
obj_props['MajorAxisLength'] = max(l1, l2)
if _a1 is None:
_a1 = a + c + sqrt((a - c)**2 + 4 * b ** 2)
obj_props['MajorAxisLength'] = sqrt(2 * _a1 / m[0,0])
if 'MinorAxisLength' in properties:
if _a2 is None:
_a2 = a1 = a + c - sqrt((a - c)**2 + 4 * b ** 2)
obj_props['MinorAxisLength'] = sqrt(2 * _a2 / m[0,0])
if 'Moments' in properties:
obj_props['Moments'] = m
@@ -251,7 +274,7 @@ def regionprops(image, properties='all'):
obj_props['NormalizedMoments'] = _nu
if 'Orientation' in properties:
obj_props['Orientation'] = - 0.5 * math.atan2(2 * b, a - c)
obj_props['Orientation'] = - 0.5 * atan(2 * b / (a - c))
if 'Solidity' in properties:
if _convex_image is None:
skimage/measure/tests/test_regionprops.py
+3 -5
View File
@@ -75,9 +75,7 @@ def test_convex_image():
def test_eccentricity():
eps = regionprops(SAMPLE, ['Eccentricity'])[0]['Eccentricity']
# MATLAB has different interpretation of ellipse than found in literature,
# here implemented as found in literature
assert_almost_equal(eps, 0.941726665966)
assert_almost_equal(eps, 2.9728364645382)
def test_equiv_diameter():
diameter = regionprops(SAMPLE, ['EquivDiameter'])[0]['EquivDiameter']
@@ -129,13 +127,13 @@ def test_minor_axis_length():
length = regionprops(SAMPLE, ['MinorAxisLength'])[0]['MinorAxisLength']
# MATLAB has different interpretation of ellipse than found in literature,
# here implemented as found in literature
assert_almost_equal(length, 5.92837619822)
assert_almost_equal(length, 4.869651403631)
def test_major_axis_length():
length = regionprops(SAMPLE, ['MajorAxisLength'])[0]['MajorAxisLength']
# MATLAB has different interpretation of ellipse than found in literature,
# here implemented as found in literature
assert_almost_equal(length, 17.6240929376)
assert_almost_equal(length, 8.396211749968)
def test_moments():
m = regionprops(SAMPLE, ['Moments'])[0]['Moments']