diff --git a/skimage/transform/geometric.py b/skimage/transform/geometric.py
index 7b59242e..71ec7752 100644
--- a/skimage/transform/geometric.py
+++ b/skimage/transform/geometric.py
@@ -5,9 +5,6 @@ from scipy import ndimage
 from skimage.util import img_as_float
 
 
-EPS = np.spacing(1)
-
-
 def _stackcopy(a, b):
     """Copy b into each color layer of a, such that::
 
@@ -182,8 +179,6 @@ def _transform(coords, matrix):
     # rescale to homogeneous coordinates
     dst[:, 0] /= dst[:, 2]
     dst[:, 1] /= dst[:, 2]
-    # values close to zero because of limited numerical precision
-    dst[np.abs(dst) < EPS] = 0
     return dst[:, :2]
 
 
diff --git a/skimage/transform/tests/test_geometric.py b/skimage/transform/tests/test_geometric.py
index a227f597..d0edace1 100644
--- a/skimage/transform/tests/test_geometric.py
+++ b/skimage/transform/tests/test_geometric.py
@@ -92,10 +92,12 @@ def test_polynomial():
     assert_array_almost_equal(tform.fwd(SRC), DST, 6)
 
 def test_homography():
-    x = img_as_float(np.arange(9, dtype=np.uint8).reshape((3, 3)) + 1)
+    x = np.zeros((5,5), dtype=np.uint8)
+    x[1, 1] = 255
+    x = img_as_float(x)
     theta = -np.pi/2
     M = np.array([[np.cos(theta),-np.sin(theta),0],
-                  [np.sin(theta), np.cos(theta),2],
+                  [np.sin(theta), np.cos(theta),4],
                   [0,             0,            1]])
     x90 = homography(x, M, order=1)
     assert_array_almost_equal(x90, np.rot90(x))