diff --git a/skimage/measure/fit.py b/skimage/measure/fit.py
index 7de90291..e800eb89 100644
--- a/skimage/measure/fit.py
+++ b/skimage/measure/fit.py
@@ -502,7 +502,7 @@ def _dynamic_max_trials(n_inliers, n_samples, min_samples, probability):
 def ransac(data, model_class, min_samples, residual_threshold,
            is_data_valid=None, is_model_valid=None,
            max_trials=100, stop_sample_num=np.inf, stop_residuals_sum=0,
-           stop_probability=1):
+           stop_probability=1, exceptions=Exception):
     """Fit a model to data with the RANSAC (random sample consensus) algorithm.
 
     RANSAC is an iterative algorithm for the robust estimation of parameters
@@ -573,6 +573,10 @@ def ransac(data, model_class, min_samples, residual_threshold,
         where the probability (confidence) is typically set to a high value
         such as 0.99, and e is the current fraction of inliers w.r.t. the
         total number of samples.
+    exceptions : exception class or tuple of exception classes
+        A list of exceptions that are ignored when estimating the model from a
+        random subset. By default all exceptions derived from the built-in
+        exception class `Exception` are ignored.
 
     Returns
     -------
@@ -688,7 +692,14 @@ def ransac(data, model_class, min_samples, residual_threshold,
 
         # estimate model for current random sample set
         sample_model = model_class()
-        sample_model.estimate(*samples)
+
+        if exceptions:
+            try:
+                sample_model.estimate(*samples)
+            except exceptions:
+                continue
+        else:
+            sample_model.estimate(*samples)
 
         # check if estimated model is valid
         if is_model_valid is not None and not is_model_valid(sample_model,
diff --git a/skimage/measure/tests/test_fit.py b/skimage/measure/tests/test_fit.py
index c2a71f71..c8e789fb 100644
--- a/skimage/measure/tests/test_fit.py
+++ b/skimage/measure/tests/test_fit.py
@@ -239,16 +239,32 @@ def test_ransac_dynamic_max_trials():
 
 
 def test_ransac_invalid_input():
-    assert_raises(ValueError, ransac, np.zeros((10, 2)), None, min_samples=-1,
-                                     residual_threshold=0)
     assert_raises(ValueError, ransac, np.zeros((10, 2)), None, min_samples=2,
-                                     residual_threshold=0, max_trials=-1)
+                  residual_threshold=0, max_trials=-1)
     assert_raises(ValueError, ransac, np.zeros((10, 2)), None, min_samples=2,
-                                     residual_threshold=0,
-                                     stop_probability=-1)
+                  residual_threshold=0, stop_probability=-1)
     assert_raises(ValueError, ransac, np.zeros((10, 2)), None, min_samples=2,
-                                     residual_threshold=0,
-                                     stop_probability=1.01)
+                  residual_threshold=0, stop_probability=1.01)
+
+
+def test_ransac_exceptions():
+    class Estimator(object):
+        def estimate(self, x):
+            raise AttributeError
+
+        def residuals(self, x):
+            return x
+
+    assert_raises(AttributeError, ransac, (np.zeros((10,)),), Estimator,
+                  min_samples=2, residual_threshold=0, exceptions=None)
+    assert_raises(AttributeError, ransac, (np.zeros((10,)),), Estimator,
+                  min_samples=2, residual_threshold=0, exceptions=tuple())
+
+    ransac((np.zeros((10,)),), Estimator, min_samples=2, residual_threshold=0)
+    ransac((np.zeros((10,)),), Estimator, min_samples=2,
+           residual_threshold=0, exceptions=AttributeError)
+    ransac((np.zeros((10,)),), Estimator, min_samples=2,
+           residual_threshold=0, exceptions=(AttributeError,))
 
 
 def test_deprecated_params_attribute():