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parameters of ellipse match Matlab results

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This commit is contained in:
Johannes Schönberger
2012-05-22 23:28:13 +02:00
parent 8ec52869c7
commit b04138c39c
2 changed files with 15 additions and 34 deletions
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skimage/measure/_regionprops.py
+12 -31
View File
@@ -68,14 +68,8 @@ def regionprops(image, properties='all'):
Convex hull image which has the same size as bounding box.
* Eccentricity : float
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}
region. The eccentricity is the ratio of the distance between its
minor and major axis length. The value is between 0 and 1.
* EquivDiameter : float
The diameter of a circle with the same area as the region.
* EulerNumber : int
@@ -96,17 +90,9 @@ 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::
@@ -183,10 +169,13 @@ def regionprops(image, properties='all'):
cc = m[1,0] / m[0,0]
mu = _moments.central_moments(array, cr, cc, 3)
# elements of the inertia tensor
a = mu[2,0]
b = mu[1,1]
c = mu[0,2]
#: elements of the inertia tensor [a b; b c]
a = mu[2,0] / mu[0,0]
b = mu[1,1] / mu[0,0]
c = mu[0,2] / mu[0,0]
#: eigen values of inertia tensor
l1 = (a + c) / 2 + sqrt(4 * b ** 2 + (a - c) ** 2) / 2
l2 = (a + c) / 2 - sqrt(4 * b ** 2 + (a - c) ** 2) / 2
# cached results which are used by several properties
_filled_image = None
@@ -218,11 +207,7 @@ def regionprops(image, properties='all'):
obj_props['ConvexImage'] = _convex_image
if 'Eccentricity' in properties:
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
obj_props['Eccentricity'] = sqrt(1 - l2 / l1)
if 'EquivDiameter' in properties:
obj_props['EquivDiameter'] = sqrt(4 * m[0,0] / PI)
@@ -256,14 +241,10 @@ def regionprops(image, properties='all'):
obj_props['FilledImage'] = _filled_image
if 'MajorAxisLength' in properties:
if _a1 is None:
_a1 = a + c + sqrt((a - c)**2 + 4 * b ** 2)
obj_props['MajorAxisLength'] = sqrt(2 * _a1 / m[0,0])
obj_props['MajorAxisLength'] = 4 * sqrt(l1)
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])
obj_props['MinorAxisLength'] = 4 * sqrt(l2)
if 'Moments' in properties:
obj_props['Moments'] = m
skimage/measure/tests/test_regionprops.py
+3 -3
View File
@@ -75,7 +75,7 @@ def test_convex_image():
def test_eccentricity():
eps = regionprops(SAMPLE, ['Eccentricity'])[0]['Eccentricity']
assert_almost_equal(eps, 2.9728364645382)
assert_almost_equal(eps, 0.814629313427)
def test_equiv_diameter():
diameter = regionprops(SAMPLE, ['EquivDiameter'])[0]['EquivDiameter']
@@ -127,13 +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, 4.869651403631)
assert_almost_equal(length, 9.739302807263)
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, 8.396211749968)
assert_almost_equal(length, 16.7924234999)
def test_moments():
m = regionprops(SAMPLE, ['Moments'])[0]['Moments']