diff --git a/TODO.txt b/TODO.txt
index bbf248be..ab5021a7 100644
--- a/TODO.txt
+++ b/TODO.txt
@@ -3,6 +3,11 @@ Version 0.11
 * Remove deprecated `reverse_map` parameter of `skimage.transform.warp`
 * Change depecrated `enforce_connectivity=False`on skimage.segmentation.slic
   and set it to True as default
+* Remove deprecated `skimage.measure.fit.BaseModel._params` attribute
+* Remove deprecated `skimage.measure.fit.BaseModel._params`,
+  `skimage.transform.ProjectiveTransform._matrix`,
+  `skimage.transform.PolynomialTransform._params`,
+  `skimage.transform.PiecewiseAffineTransform.affines_*` attributes
 
 Version 0.10
 ------------
diff --git a/doc/examples/applications/plot_geometric.py b/doc/examples/applications/plot_geometric.py
index 141ef51f..86dd5aaa 100644
--- a/doc/examples/applications/plot_geometric.py
+++ b/doc/examples/applications/plot_geometric.py
@@ -33,14 +33,14 @@ First we create a transformation using explicit parameters:
 
 tform = tf.SimilarityTransform(scale=1, rotation=math.pi / 2,
                                translation=(0, 1))
-print(tform._matrix)
+print(tform.params)
 
 """
 Alternatively you can define a transformation by the transformation matrix
 itself:
 """
 
-matrix = tform._matrix.copy()
+matrix = tform.params.copy()
 matrix[1, 2] = 2
 tform2 = tf.SimilarityTransform(matrix)
 
diff --git a/skimage/measure/fit.py b/skimage/measure/fit.py
index e16cd218..8f9ceb9c 100644
--- a/skimage/measure/fit.py
+++ b/skimage/measure/fit.py
@@ -1,4 +1,5 @@
 import math
+import warnings
 import numpy as np
 from scipy import optimize
 
@@ -11,7 +12,13 @@ def _check_data_dim(data, dim):
 class BaseModel(object):
 
     def __init__(self):
-        self._params = None
+        self.params = None
+
+    @property
+    def _params(self):
+        warnings.warn('`_params` attribute is deprecated, '
+                      'use `params` instead.')
+        return self.params
 
 
 class LineModel(BaseModel):
@@ -30,12 +37,13 @@ class LineModel(BaseModel):
 
         min{ sum((dist - x_i * cos(theta) + y_i * sin(theta))**2) }
 
-    The ``_params`` attribute contains the parameters in the following order::
-
-        dist, theta
-
     A minimum number of 2 points is required to solve for the parameters.
 
+    Attributes
+    ----------
+    params : tuple
+        Line model parameters in the following order `dist`, `theta`.
+
     """
 
     def estimate(self, data):
@@ -68,7 +76,7 @@ class LineModel(BaseModel):
         # line always passes through mean
         dist = X0[0] * math.cos(theta) + X0[1] * math.sin(theta)
 
-        self._params = (dist, theta)
+        self.params = (dist, theta)
 
     def residuals(self, data):
         """Determine residuals of data to model.
@@ -89,7 +97,7 @@ class LineModel(BaseModel):
 
         _check_data_dim(data, dim=2)
 
-        dist, theta = self._params
+        dist, theta = self.params
 
         x = data[:, 0]
         y = data[:, 1]
@@ -114,7 +122,7 @@ class LineModel(BaseModel):
         """
 
         if params is None:
-            params = self._params
+            params = self.params
         dist, theta = params
         return (dist - y * math.sin(theta)) / math.cos(theta)
 
@@ -136,7 +144,7 @@ class LineModel(BaseModel):
         """
 
         if params is None:
-            params = self._params
+            params = self.params
         dist, theta = params
         return (dist - x * math.cos(theta)) / math.sin(theta)
 
@@ -154,12 +162,13 @@ class CircleModel(BaseModel):
 
         min{ sum((r - sqrt((x_i - xc)**2 + (y_i - yc)**2))**2) }
 
-    The ``_params`` attribute contains the parameters in the following order::
-
-        xc, yc, r
-
     A minimum number of 3 points is required to solve for the parameters.
 
+    Attributes
+    ----------
+    params : tuple
+        Circle model parameters in the following order `xc`, `yc`, `r`.
+
     """
 
     def estimate(self, data):
@@ -203,7 +212,7 @@ class CircleModel(BaseModel):
         params0 = (xc0, yc0, r0)
         params, _ = optimize.leastsq(fun, params0, Dfun=Dfun, col_deriv=True)
 
-        self._params = params
+        self.params = params
 
     def residuals(self, data):
         """Determine residuals of data to model.
@@ -224,7 +233,7 @@ class CircleModel(BaseModel):
 
         _check_data_dim(data, dim=2)
 
-        xc, yc, r = self._params
+        xc, yc, r = self.params
 
         x = data[:, 0]
         y = data[:, 1]
@@ -249,7 +258,7 @@ class CircleModel(BaseModel):
 
         """
         if params is None:
-            params = self._params
+            params = self.params
         xc, yc, r = params
 
         x = xc + r * np.cos(t)
@@ -279,12 +288,18 @@ class EllipseModel(BaseModel):
     Thus you have ``2 * N`` equations (x_i, y_i) for ``N + 5`` unknowns (t_i,
     xc, yc, a, b, theta), which gives you an effective redundancy of ``N - 5``.
 
-    The ``_params`` attribute contains the parameters in the following order::
+    The ``params`` attribute contains the parameters in the following order::
 
         xc, yc, a, b, theta
 
     A minimum number of 5 points is required to solve for the parameters.
 
+    Attributes
+    ----------
+    params : tuple
+        Ellipse model parameters in the following order `xc`, `yc`, `a`,
+        `b`, `theta`.
+
     """
 
     def estimate(self, data):
@@ -353,7 +368,7 @@ class EllipseModel(BaseModel):
 
         params, _ = optimize.leastsq(fun, params0, Dfun=Dfun, col_deriv=True)
 
-        self._params = params[:5]
+        self.params = params[:5]
 
     def residuals(self, data):
         """Determine residuals of data to model.
@@ -374,7 +389,7 @@ class EllipseModel(BaseModel):
 
         _check_data_dim(data, dim=2)
 
-        xc, yc, a, b, theta = self._params
+        xc, yc, a, b, theta = self.params
 
         ctheta = math.cos(theta)
         stheta = math.sin(theta)
@@ -436,7 +451,7 @@ class EllipseModel(BaseModel):
         """
 
         if params is None:
-            params = self._params
+            params = self.params
         xc, yc, a, b, theta = params
 
         ct = np.cos(t)
@@ -550,7 +565,7 @@ def ransac(data, model_class, min_samples, residual_threshold,
 
     >>> model = EllipseModel()
     >>> model.estimate(data)
-    >>> model._params # doctest: +SKIP
+    >>> model.params # doctest: +SKIP
     array([ -3.30354146e+03,  -2.87791160e+03,   5.59062118e+03,
              7.84365066e+00,   7.19203152e-01])
 
@@ -558,7 +573,7 @@ def ransac(data, model_class, min_samples, residual_threshold,
     Estimate ellipse model using RANSAC:
 
     >>> ransac_model, inliers = ransac(data, EllipseModel, 5, 3, max_trials=50)
-    >>> ransac_model._params
+    >>> ransac_model.params
     array([ 20.12762373,  29.73563063,   4.81499637,  10.4743584 ,   0.05217117])
     >>> inliers
     array([False, False, False, False,  True,  True,  True,  True,  True,
diff --git a/skimage/measure/tests/test_fit.py b/skimage/measure/tests/test_fit.py
index 253ac0ea..3ef7a0f0 100644
--- a/skimage/measure/tests/test_fit.py
+++ b/skimage/measure/tests/test_fit.py
@@ -10,7 +10,7 @@ def test_line_model_invalid_input():
 
 def test_line_model_predict():
     model = LineModel()
-    model._params = (10, 1)
+    model.params = (10, 1)
     x = np.arange(-10, 10)
     y = model.predict_y(x)
     assert_almost_equal(x, model.predict_x(y))
@@ -19,7 +19,7 @@ def test_line_model_predict():
 def test_line_model_estimate():
     # generate original data without noise
     model0 = LineModel()
-    model0._params = (10, 1)
+    model0.params = (10, 1)
     x0 = np.arange(-100, 100)
     y0 = model0.predict_y(x0)
     data0 = np.column_stack([x0, y0])
@@ -33,16 +33,16 @@ def test_line_model_estimate():
     model_est.estimate(data)
 
     # test whether estimated parameters almost equal original parameters
-    assert_almost_equal(model0._params, model_est._params, 1)
+    assert_almost_equal(model0.params, model_est.params, 1)
 
 
 def test_line_model_residuals():
     model = LineModel()
-    model._params = (0, 0)
+    model.params = (0, 0)
     assert_equal(abs(model.residuals(np.array([[0, 0]]))), 0)
     assert_equal(abs(model.residuals(np.array([[0, 10]]))), 0)
     assert_equal(abs(model.residuals(np.array([[10, 0]]))), 10)
-    model._params = (5, np.pi / 4)
+    model.params = (5, np.pi / 4)
     assert_equal(abs(model.residuals(np.array([[0, 0]]))), 5)
     assert_almost_equal(abs(model.residuals(np.array([[np.sqrt(50), 0]]))), 0)
 
@@ -59,7 +59,7 @@ def test_circle_model_invalid_input():
 def test_circle_model_predict():
     model = CircleModel()
     r = 5
-    model._params = (0, 0, r)
+    model.params = (0, 0, r)
     t = np.arange(0, 2 * np.pi, np.pi / 2)
 
     xy = np.array(((5, 0), (0, 5), (-5, 0), (0, -5)))
@@ -69,7 +69,7 @@ def test_circle_model_predict():
 def test_circle_model_estimate():
     # generate original data without noise
     model0 = CircleModel()
-    model0._params = (10, 12, 3)
+    model0.params = (10, 12, 3)
     t = np.linspace(0, 2 * np.pi, 1000)
     data0 = model0.predict_xy(t)
 
@@ -82,12 +82,12 @@ def test_circle_model_estimate():
     model_est.estimate(data)
 
     # test whether estimated parameters almost equal original parameters
-    assert_almost_equal(model0._params, model_est._params, 1)
+    assert_almost_equal(model0.params, model_est.params, 1)
 
 
 def test_circle_model_residuals():
     model = CircleModel()
-    model._params = (0, 0, 5)
+    model.params = (0, 0, 5)
     assert_almost_equal(abs(model.residuals(np.array([[5, 0]]))), 0)
     assert_almost_equal(abs(model.residuals(np.array([[6, 6]]))),
                         np.sqrt(2 * 6**2) - 5)
@@ -101,7 +101,7 @@ def test_ellipse_model_invalid_input():
 def test_ellipse_model_predict():
     model = EllipseModel()
     r = 5
-    model._params = (0, 0, 5, 10, 0)
+    model.params = (0, 0, 5, 10, 0)
     t = np.arange(0, 2 * np.pi, np.pi / 2)
 
     xy = np.array(((5, 0), (0, 10), (-5, 0), (0, -10)))
@@ -111,7 +111,7 @@ def test_ellipse_model_predict():
 def test_ellipse_model_estimate():
     # generate original data without noise
     model0 = EllipseModel()
-    model0._params = (10, 20, 15, 25, 0)
+    model0.params = (10, 20, 15, 25, 0)
     t = np.linspace(0, 2 * np.pi, 100)
     data0 = model0.predict_xy(t)
 
@@ -124,13 +124,13 @@ def test_ellipse_model_estimate():
     model_est.estimate(data)
 
     # test whether estimated parameters almost equal original parameters
-    assert_almost_equal(model0._params, model_est._params, 0)
+    assert_almost_equal(model0.params, model_est.params, 0)
 
 
 def test_ellipse_model_residuals():
     model = EllipseModel()
     # vertical line through origin
-    model._params = (0, 0, 10, 5, 0)
+    model.params = (0, 0, 10, 5, 0)
     assert_almost_equal(abs(model.residuals(np.array([[10, 0]]))), 0)
     assert_almost_equal(abs(model.residuals(np.array([[0, 5]]))), 0)
     assert_almost_equal(abs(model.residuals(np.array([[0, 10]]))), 5)
@@ -141,7 +141,7 @@ def test_ransac_shape():
 
     # generate original data without noise
     model0 = CircleModel()
-    model0._params = (10, 12, 3)
+    model0.params = (10, 12, 3)
     t = np.linspace(0, 2 * np.pi, 1000)
     data0 = model0.predict_xy(t)
 
@@ -155,7 +155,7 @@ def test_ransac_shape():
     model_est, inliers = ransac(data0, CircleModel, 3, 5)
 
     # test whether estimated parameters equal original parameters
-    assert_equal(model0._params, model_est._params)
+    assert_equal(model0.params, model_est.params)
     for outlier in outliers:
         assert outlier not in inliers
 
@@ -204,5 +204,13 @@ def test_ransac_is_model_valid():
     assert_equal(inliers, None)
 
 
+def test_deprecated_params_attribute():
+    model = LineModel()
+    model.params = (10, 1)
+    x = np.arange(-10, 10)
+    y = model.predict_y(x)
+    assert_equal(model.params, model._params)
+
+
 if __name__ == "__main__":
     np.testing.run_module_suite()
diff --git a/skimage/transform/_geometric.py b/skimage/transform/_geometric.py
index a4587c10..092738bc 100644
--- a/skimage/transform/_geometric.py
+++ b/skimage/transform/_geometric.py
@@ -1,5 +1,6 @@
 import six
 import math
+import warnings
 import numpy as np
 from scipy import ndimage, spatial
 
@@ -103,6 +104,11 @@ class ProjectiveTransform(GeometricTransform):
     matrix : (3, 3) array, optional
         Homogeneous transformation matrix.
 
+    Attributes
+    ----------
+    params : (3, 3) array
+        Homogeneous transformation matrix.
+
     """
 
     _coeffs = range(8)
@@ -113,11 +119,17 @@ class ProjectiveTransform(GeometricTransform):
             matrix = np.eye(3)
         if matrix.shape != (3, 3):
             raise ValueError("invalid shape of transformation matrix")
-        self._matrix = matrix
+        self.params = matrix
+
+    @property
+    def _matrix(self):
+        warnings.warn('`_matrix` attribute is deprecated, '
+                      'use `params` instead.')
+        return self.params
 
     @property
     def _inv_matrix(self):
-        return np.linalg.inv(self._matrix)
+        return np.linalg.inv(self.params)
 
     def _apply_mat(self, coords, matrix):
         coords = np.array(coords, copy=False, ndmin=2)
@@ -133,7 +145,7 @@ class ProjectiveTransform(GeometricTransform):
         return dst[:, :2]
 
     def __call__(self, coords):
-        return self._apply_mat(coords, self._matrix)
+        return self._apply_mat(coords, self.params)
 
     def inverse(self, coords):
         """Apply inverse transformation.
@@ -235,7 +247,7 @@ class ProjectiveTransform(GeometricTransform):
         H.flat[list(self._coeffs) + [8]] = - V[-1, :-1] / V[-1, -1]
         H[2, 2] = 1
 
-        self._matrix = H
+        self.params = H
 
     def __add__(self, other):
         """Combine this transformation with another.
@@ -248,7 +260,7 @@ class ProjectiveTransform(GeometricTransform):
                 tform = self.__class__
             else:
                 tform = ProjectiveTransform
-            return tform(other._matrix.dot(self._matrix))
+            return tform(other.params.dot(self.params))
         else:
             raise TypeError("Cannot combine transformations of differing "
                             "types.")
@@ -284,6 +296,11 @@ class AffineTransform(ProjectiveTransform):
     translation : (tx, ty) as array, list or tuple, optional
         Translation parameters.
 
+    Attributes
+    ----------
+    params : (3, 3) array
+        Homogeneous transformation matrix.
+
     """
 
     _coeffs = range(6)
@@ -299,7 +316,7 @@ class AffineTransform(ProjectiveTransform):
         elif matrix is not None:
             if matrix.shape != (3, 3):
                 raise ValueError("Invalid shape of transformation matrix.")
-            self._matrix = matrix
+            self.params = matrix
         elif params:
             if scale is None:
                 scale = (1, 1)
@@ -311,34 +328,34 @@ class AffineTransform(ProjectiveTransform):
                 translation = (0, 0)
 
             sx, sy = scale
-            self._matrix = np.array([
+            self.params = np.array([
                 [sx * math.cos(rotation), -sy * math.sin(rotation + shear), 0],
                 [sx * math.sin(rotation),  sy * math.cos(rotation + shear), 0],
                 [                      0,                                0, 1]
             ])
-            self._matrix[0:2, 2] = translation
+            self.params[0:2, 2] = translation
         else:
             # default to an identity transform
-            self._matrix = np.eye(3)
+            self.params = np.eye(3)
 
     @property
     def scale(self):
-        sx = math.sqrt(self._matrix[0, 0] ** 2 + self._matrix[1, 0] ** 2)
-        sy = math.sqrt(self._matrix[0, 1] ** 2 + self._matrix[1, 1] ** 2)
+        sx = math.sqrt(self.params[0, 0] ** 2 + self.params[1, 0] ** 2)
+        sy = math.sqrt(self.params[0, 1] ** 2 + self.params[1, 1] ** 2)
         return sx, sy
 
     @property
     def rotation(self):
-        return math.atan2(self._matrix[1, 0], self._matrix[0, 0])
+        return math.atan2(self.params[1, 0], self.params[0, 0])
 
     @property
     def shear(self):
-        beta = math.atan2(- self._matrix[0, 1], self._matrix[1, 1])
+        beta = math.atan2(- self.params[0, 1], self.params[1, 1])
         return beta - self.rotation
 
     @property
     def translation(self):
-        return self._matrix[0:2, 2]
+        return self.params[0:2, 2]
 
 
 class PiecewiseAffineTransform(GeometricTransform):
@@ -349,13 +366,20 @@ class PiecewiseAffineTransform(GeometricTransform):
     a Delaunay triangulation of the points to form a mesh. Each triangle is
     used to find a local affine transform.
 
+    Attributes
+    ----------
+    affines : list of AffineTransform objects
+        Affine transformations for each triangle in the mesh.
+    inverse_affines : list of AffineTransform objects
+        Inverse affine transformations for each triangle in the mesh.
+
     """
 
     def __init__(self):
         self._tesselation = None
         self._inverse_tesselation = None
-        self.affines = []
-        self.inverse_affines = []
+        self.affines = None
+        self.inverse_affines = None
 
     def estimate(self, src, dst):
         """Set the control points with which to perform the piecewise mapping.
@@ -488,6 +512,11 @@ class SimilarityTransform(ProjectiveTransform):
     translation : (tx, ty) as array, list or tuple, optional
         x, y translation parameters.
 
+    Attributes
+    ----------
+    params : (3, 3) array
+        Homogeneous transformation matrix.
+
     """
 
     def __init__(self, matrix=None, scale=None, rotation=None,
@@ -501,7 +530,7 @@ class SimilarityTransform(ProjectiveTransform):
         elif matrix is not None:
             if matrix.shape != (3, 3):
                 raise ValueError("Invalid shape of transformation matrix.")
-            self._matrix = matrix
+            self.params = matrix
         elif params:
             if scale is None:
                 scale = 1
@@ -510,16 +539,16 @@ class SimilarityTransform(ProjectiveTransform):
             if translation is None:
                 translation = (0, 0)
 
-            self._matrix = np.array([
+            self.params = np.array([
                 [math.cos(rotation), - math.sin(rotation), 0],
                 [math.sin(rotation),   math.cos(rotation), 0],
                 [                 0,                    0, 1]
             ])
-            self._matrix[0:2, 0:2] *= scale
-            self._matrix[0:2, 2] = translation
+            self.params[0:2, 0:2] *= scale
+            self.params[0:2, 2] = translation
         else:
             # default to an identity transform
-            self._matrix = np.eye(3)
+            self.params = np.eye(3)
 
     def estimate(self, src, dst):
         """Set the transformation matrix with the explicit parameters.
@@ -585,7 +614,7 @@ class SimilarityTransform(ProjectiveTransform):
         # singular value
         a0, a1, b0, b1 = - V[-1, :-1] / V[-1, -1]
 
-        self._matrix = np.array([[a0, -b0, a1],
+        self.params = np.array([[a0, -b0, a1],
                                  [b0,  a0, b1],
                                  [ 0,   0,  1]])
 
@@ -593,18 +622,18 @@ class SimilarityTransform(ProjectiveTransform):
     def scale(self):
         if math.cos(self.rotation) == 0:
             # sin(self.rotation) == 1
-            scale = self._matrix[0, 1]
+            scale = self.params[0, 1]
         else:
-            scale = self._matrix[0, 0] / math.cos(self.rotation)
+            scale = self.params[0, 0] / math.cos(self.rotation)
         return scale
 
     @property
     def rotation(self):
-        return math.atan2(self._matrix[1, 0], self._matrix[1, 1])
+        return math.atan2(self.params[1, 0], self.params[1, 1])
 
     @property
     def translation(self):
-        return self._matrix[0:2, 2]
+        return self.params[0:2, 2]
 
 
 class PolynomialTransform(GeometricTransform):
@@ -619,6 +648,12 @@ class PolynomialTransform(GeometricTransform):
         Polynomial coefficients where `N * 2 = (order + 1) * (order + 2)`. So,
         a_ji is defined in `params[0, :]` and b_ji in `params[1, :]`.
 
+    Attributes
+    ----------
+    params : (2, N) array
+        Polynomial coefficients where `N * 2 = (order + 1) * (order + 2)`. So,
+        a_ji is defined in `params[0, :]` and b_ji in `params[1, :]`.
+
     """
 
     def __init__(self, params=None):
@@ -627,7 +662,13 @@ class PolynomialTransform(GeometricTransform):
             params = np.array([[0, 1, 0], [0, 0, 1]])
         if params.shape[0] != 2:
             raise ValueError("invalid shape of transformation parameters")
-        self._params = params
+        self.params = params
+
+    @property
+    def _params(self):
+        warnings.warn('`_params` attribute is deprecated, '
+                      'use `params` instead.')
+        return self.params
 
     def estimate(self, src, dst, order=2):
         """Set the transformation matrix with the explicit transformation
@@ -700,7 +741,7 @@ class PolynomialTransform(GeometricTransform):
         # singular value
         params = - V[-1, :-1] / V[-1, -1]
 
-        self._params = params.reshape((2, u / 2))
+        self.params = params.reshape((2, u / 2))
 
     def __call__(self, coords):
         """Apply forward transformation.
@@ -718,7 +759,7 @@ class PolynomialTransform(GeometricTransform):
         """
         x = coords[:, 0]
         y = coords[:, 1]
-        u = len(self._params.ravel())
+        u = len(self.params.ravel())
         # number of coefficients -> u = (order + 1) * (order + 2)
         order = int((- 3 + math.sqrt(9 - 4 * (2 - u))) / 2)
         dst = np.zeros(coords.shape)
@@ -726,8 +767,8 @@ class PolynomialTransform(GeometricTransform):
         pidx = 0
         for j in range(order + 1):
             for i in range(j + 1):
-                dst[:, 0] += self._params[0, pidx] * x ** (j - i) * y ** i
-                dst[:, 1] += self._params[1, pidx] * x ** (j - i) * y ** i
+                dst[:, 0] += self.params[0, pidx] * x ** (j - i) * y ** i
+                dst[:, 1] += self.params[1, pidx] * x ** (j - i) * y ** i
                 pidx += 1
 
         return dst
@@ -1046,14 +1087,14 @@ def warp(image, inverse_map=None, map_args={}, output_shape=None, order=1,
 
         # inverse_map is a homography
         elif isinstance(inverse_map, HOMOGRAPHY_TRANSFORMS):
-            matrix = inverse_map._matrix
+            matrix = inverse_map.params
 
         # inverse_map is the inverse of a homography
         elif (hasattr(inverse_map, '__name__')
               and inverse_map.__name__ == 'inverse'
               and get_bound_method_class(inverse_map) \
                   in HOMOGRAPHY_TRANSFORMS):
-            matrix = np.linalg.inv(six.get_method_self(inverse_map)._matrix)
+            matrix = np.linalg.inv(six.get_method_self(inverse_map).params)
 
         if matrix is not None:
             matrix = matrix.astype(np.double)
diff --git a/skimage/transform/tests/test_geometric.py b/skimage/transform/tests/test_geometric.py
index 06c4f652..2a6a5c7e 100644
--- a/skimage/transform/tests/test_geometric.py
+++ b/skimage/transform/tests/test_geometric.py
@@ -56,19 +56,19 @@ def test_similarity_estimation():
     # exact solution
     tform = estimate_transform('similarity', SRC[:2, :], DST[:2, :])
     assert_array_almost_equal(tform(SRC[:2, :]), DST[:2, :])
-    assert_equal(tform._matrix[0, 0], tform._matrix[1, 1])
-    assert_equal(tform._matrix[0, 1], - tform._matrix[1, 0])
+    assert_equal(tform.params[0, 0], tform.params[1, 1])
+    assert_equal(tform.params[0, 1], - tform.params[1, 0])
 
     # over-determined
     tform2 = estimate_transform('similarity', SRC, DST)
     assert_array_almost_equal(tform2.inverse(tform2(SRC)), SRC)
-    assert_equal(tform2._matrix[0, 0], tform2._matrix[1, 1])
-    assert_equal(tform2._matrix[0, 1], - tform2._matrix[1, 0])
+    assert_equal(tform2.params[0, 0], tform2.params[1, 1])
+    assert_equal(tform2.params[0, 1], - tform2.params[1, 0])
 
     # via estimate method
     tform3 = SimilarityTransform()
     tform3.estimate(SRC, DST)
-    assert_array_almost_equal(tform3._matrix, tform2._matrix)
+    assert_array_almost_equal(tform3.params, tform2.params)
 
 
 def test_similarity_init():
@@ -83,7 +83,7 @@ def test_similarity_init():
     assert_array_almost_equal(tform.translation, translation)
 
     # init with transformation matrix
-    tform2 = SimilarityTransform(tform._matrix)
+    tform2 = SimilarityTransform(tform.params)
     assert_array_almost_equal(tform2.scale, scale)
     assert_array_almost_equal(tform2.rotation, rotation)
     assert_array_almost_equal(tform2.translation, translation)
@@ -111,7 +111,7 @@ def test_affine_estimation():
     # via estimate method
     tform3 = AffineTransform()
     tform3.estimate(SRC, DST)
-    assert_array_almost_equal(tform3._matrix, tform2._matrix)
+    assert_array_almost_equal(tform3.params, tform2.params)
 
 
 def test_affine_init():
@@ -128,7 +128,7 @@ def test_affine_init():
     assert_array_almost_equal(tform.translation, translation)
 
     # init with transformation matrix
-    tform2 = AffineTransform(tform._matrix)
+    tform2 = AffineTransform(tform.params)
     assert_array_almost_equal(tform2.scale, scale)
     assert_array_almost_equal(tform2.rotation, rotation)
     assert_array_almost_equal(tform2.shear, shear)
@@ -155,14 +155,14 @@ def test_projective_estimation():
     # via estimate method
     tform3 = ProjectiveTransform()
     tform3.estimate(SRC, DST)
-    assert_array_almost_equal(tform3._matrix, tform2._matrix)
+    assert_array_almost_equal(tform3.params, tform2.params)
 
 
 def test_projective_init():
     tform = estimate_transform('projective', SRC, DST)
     # init with transformation matrix
-    tform2 = ProjectiveTransform(tform._matrix)
-    assert_array_almost_equal(tform2._matrix, tform._matrix)
+    tform2 = ProjectiveTransform(tform.params)
+    assert_array_almost_equal(tform2.params, tform.params)
 
 
 def test_polynomial_estimation():
@@ -173,20 +173,20 @@ def test_polynomial_estimation():
     # via estimate method
     tform2 = PolynomialTransform()
     tform2.estimate(SRC, DST, order=10)
-    assert_array_almost_equal(tform2._params, tform._params)
+    assert_array_almost_equal(tform2.params, tform.params)
 
 
 def test_polynomial_init():
     tform = estimate_transform('polynomial', SRC, DST, order=10)
     # init with transformation parameters
-    tform2 = PolynomialTransform(tform._params)
-    assert_array_almost_equal(tform2._params, tform._params)
+    tform2 = PolynomialTransform(tform.params)
+    assert_array_almost_equal(tform2.params, tform.params)
 
 
 def test_polynomial_default_order():
     tform = estimate_transform('polynomial', SRC, DST)
     tform2 = estimate_transform('polynomial', SRC, DST, order=2)
-    assert_array_almost_equal(tform2._params, tform._params)
+    assert_array_almost_equal(tform2.params, tform.params)
 
 
 def test_polynomial_inverse():
@@ -228,6 +228,15 @@ def test_invalid_input():
     assert_raises(ValueError, PolynomialTransform, np.zeros((3, 3)))
 
 
+def test_deprecated_params_attributes():
+    for t in ('projective', 'affine', 'similarity'):
+        tform = estimate_transform(t, SRC, DST)
+        assert_equal(tform._matrix, tform.params)
+
+    tform = estimate_transform('polynomial', SRC, DST, order=3)
+    assert_equal(tform._params, tform.params)
+
+
 if __name__ == "__main__":
     from numpy.testing import run_module_suite
     run_module_suite()
diff --git a/skimage/transform/tests/test_warps.py b/skimage/transform/tests/test_warps.py
index db936a3a..e49ab098 100644
--- a/skimage/transform/tests/test_warps.py
+++ b/skimage/transform/tests/test_warps.py
@@ -243,7 +243,7 @@ def test_invalid():
 
 def test_inverse():
     tform = SimilarityTransform(scale=0.5, rotation=0.1)
-    inverse_tform = SimilarityTransform(matrix=np.linalg.inv(tform._matrix))
+    inverse_tform = SimilarityTransform(matrix=np.linalg.inv(tform.params))
     image = np.arange(10 * 10).reshape(10, 10).astype(np.double)
     assert_array_equal(warp(image, inverse_tform), warp(image, tform.inverse))