diff --git a/skimage/measure/fit.py b/skimage/measure/fit.py
index ef81f8f9..8fde1ca2 100644
--- a/skimage/measure/fit.py
+++ b/skimage/measure/fit.py
@@ -502,6 +502,7 @@ class EllipseModel(BaseModel):
 
 
 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):
     """Fits a model to data with the RANSAC (random sample consensus) algorithm.
 
@@ -510,11 +511,13 @@ def ransac(data, model_class, min_samples, residual_threshold,
     the following tasks:
 
     1. Select `min_samples` random samples from the original data and check
-       whether the set of points is valid (`is_degenerate(*data)`).
-    2. Estimate a model to the random subset (`estimate(*data[random_subset]`).
+       whether the set of data is valid (see `is_data_valid`).
+    2. Estimate a model to the random subset
+       (`model_cls.estimate(*data[random_subset]`) and check whether the
+       estimated model is valid (see `is_model_valid`).
     3. Classify all data as inliers or outliers by calculating the residuals to
-       the estimated model (`residuals(*data)`) - all data samples with
-       residuals smaller than the `residual_threshold` are considered as
+       the estimated model (`model_cls.residuals(*data)`) - all data samples
+       with residuals smaller than the `residual_threshold` are considered as
        inliers.
     4. Save estimated model as best model if number of inlier samples is
        maximal. In case the current estimated model has the same number of
@@ -537,16 +540,21 @@ def ransac(data, model_class, min_samples, residual_threshold,
         `is_degenerate(*data)` must all take each data array as separate
         arguments.
     model_class : object
-        Object with the following methods implemented:
+        Object with the following object methods:
 
          * `estimate(*data)`
          * `residuals(*data)`
-         * `is_degenerate(*data)`
 
     min_samples : int
         The minimum number of data points to fit a model.
     residual_threshold : float
         Maximum distance for a data point to be classified as an inlier.
+    is_data_valid : function, optional
+        This function is called with the randomly selected data before the
+        model is fitted to it: `is_data_valid(*random_data)`.
+    is_model_valid : function, optional
+        This function is called with the estimated model and the randomly
+        selected data: `is_model_valid(model, *random_data)`, .
     max_trials : int, optional
         Maximum number of iterations for random sample selection.
     stop_sample_num : int, optional
@@ -640,19 +648,25 @@ def ransac(data, model_class, min_samples, residual_threshold,
 
     for _ in range(max_trials):
 
-        # choose random sample
+        # choose random sample set
         samples = []
         random_idxs = np.random.randint(0, N, min_samples)
         for d in data:
             samples.append(d[random_idxs])
 
-        # check if random sample is degenerate
-        if model_class.is_degenerate(*samples):
+        # check if random sample set is valid
+        if is_data_valid is not None and not is_data_valid(*samples):
             continue
 
-        # create new instance of model class for current sample
+        # estimate model for current random sample set
         sample_model = model_class()
         sample_model.estimate(*samples)
+
+        # check if estimated model is valid
+        if is_model_valid is not None and not is_model_valid(sample_model,
+                                                             *samples):
+            continue
+
         sample_model_residuals = np.abs(sample_model.residuals(*data))
         # consensus set / inliers
         sample_model_inliers = data_idxs[sample_model_residuals