diff --git a/dlib/image_transforms/spatial_filtering.h b/dlib/image_transforms/spatial_filtering.h
index 5010bd531..c908c17f3 100644
--- a/dlib/image_transforms/spatial_filtering.h
+++ b/dlib/image_transforms/spatial_filtering.h
@@ -809,9 +809,7 @@ namespace dlib
         const typename image_type1::type& thresh
     )
     {
-        DLIB_ASSERT((width%2)==1 &&
-                     (height%2)==1 &&
-                     width > 0 &&
+        DLIB_ASSERT( width > 0 &&
                      height > 0 &&
                      out.nr() == img.nr() &&
                      out.nc() == img.nc() &&
@@ -832,21 +830,21 @@ namespace dlib
 
         dlib::impl::fast_deque<std::pair<long,pixel_type> > Q(std::max(width,height));
 
-        const long last_col = std::max(img.nc(), (width/2));
-        const long last_row = std::max(img.nr(), (height/2));
+        const long last_col = std::max(img.nc(), ((width-1)/2));
+        const long last_row = std::max(img.nr(), ((height-1)/2));
 
         // run max filter along rows of img
         for (long r = 0; r < img.nr(); ++r)
         {
             Q.clear();
-            for (long c = 0; c < width/2 && c < img.nc(); ++c)
+            for (long c = 0; c < (width-1)/2 && c < img.nc(); ++c)
             {
                 while (!Q.empty() && img[r][c] >= Q.back().second)
                     Q.pop_back();
                 Q.push_back(make_pair(c,img[r][c]));
             }
 
-            for (long c = width/2; c < img.nc(); ++c)
+            for (long c = (width-1)/2; c < img.nc(); ++c)
             {
                 while (!Q.empty() && img[r][c] >= Q.back().second)
                     Q.pop_back();
@@ -854,15 +852,15 @@ namespace dlib
                     Q.pop_front();
                 Q.push_back(make_pair(c,img[r][c]));
 
-                img[r][c-(width/2)] = Q.front().second;
+                img[r][c-((width-1)/2)] = Q.front().second;
             }
 
-            for (long c = last_col; c < img.nc() + (width/2); ++c)
+            for (long c = last_col; c < img.nc() + ((width-1)/2); ++c)
             {
                 while (!Q.empty() && Q.front().first <= c-width)
                     Q.pop_front();
 
-                img[r][c-(width/2)] = Q.front().second;
+                img[r][c-((width-1)/2)] = Q.front().second;
             }
         }
 
@@ -870,14 +868,14 @@ namespace dlib
         for (long cc = 0; cc < img.nc(); ++cc)
         {
             Q.clear();
-            for (long rr = 0; rr < height/2 && rr < img.nr(); ++rr)
+            for (long rr = 0; rr < (height-1)/2 && rr < img.nr(); ++rr)
             {
                 while (!Q.empty() && img[rr][cc] >= Q.back().second)
                     Q.pop_back();
                 Q.push_back(make_pair(rr,img[rr][cc]));
             }
 
-            for (long rr = height/2; rr < img.nr(); ++rr)
+            for (long rr = (height-1)/2; rr < img.nr(); ++rr)
             {
                 while (!Q.empty() && img[rr][cc] >= Q.back().second)
                     Q.pop_back();
@@ -885,15 +883,15 @@ namespace dlib
                     Q.pop_front();
                 Q.push_back(make_pair(rr,img[rr][cc]));
 
-                out[rr-(height/2)][cc] += std::max(Q.front().second, thresh);
+                out[rr-((height-1)/2)][cc] += std::max(Q.front().second, thresh);
             }
 
-            for (long rr = last_row; rr < img.nr() + (height/2); ++rr)
+            for (long rr = last_row; rr < img.nr() + ((height-1)/2); ++rr)
             {
                 while (!Q.empty() && Q.front().first <= rr-height)
                     Q.pop_front();
 
-                out[rr-(height/2)][cc] += std::max(Q.front().second, thresh);
+                out[rr-((height-1)/2)][cc] += std::max(Q.front().second, thresh);
             }
         }
     }
diff --git a/dlib/image_transforms/spatial_filtering_abstract.h b/dlib/image_transforms/spatial_filtering_abstract.h
index 6cbdab5c4..e305532c4 100644
--- a/dlib/image_transforms/spatial_filtering_abstract.h
+++ b/dlib/image_transforms/spatial_filtering_abstract.h
@@ -360,8 +360,6 @@ namespace dlib
             - image_type2 == an implementation of array2d/array2d_kernel_abstract.h
               and it must contain a scalar type
             - is_same_object(img,out) == false
-            - (width%2)==1 && (height%2)==1 
-              (i.e. width and height must be odd)
             - width > 0 && height > 0
         ensures
             - for all valid r and c:
diff --git a/dlib/test/scan_image.cpp b/dlib/test/scan_image.cpp
index 6ecb46c2e..0cbfee208 100644
--- a/dlib/test/scan_image.cpp
+++ b/dlib/test/scan_image.cpp
@@ -449,7 +449,8 @@ namespace
     void naive_max_filter (
         const image_type1& img,
         image_type2& out,
-        const rectangle& rect,
+        const long width,
+        const long height,
         typename image_type1::type thresh
         )
     {
@@ -460,11 +461,8 @@ namespace
         {
             for (long c = 0; c < img.nc(); ++c)
             {
-                const rectangle win = translate_rect(rect,point(c,r)).intersect(area);
-                if (!win.is_empty())
-                    out[r][c] += std::max(dlib::max(subm(array_to_matrix(img),win)), thresh);
-                else
-                    out[r][c] += thresh;
+                const rectangle win = centered_rect(point(c,r),width,height).intersect(area);
+                out[r][c] += std::max(dlib::max(subm(array_to_matrix(img),win)), thresh);
             }
         }
     }
@@ -491,7 +489,7 @@ namespace
 
         const int thresh = rnd.get_random_32bit_number();
 
-        naive_max_filter(img, out2, rect, thresh);
+        naive_max_filter(img, out2, rect.width(), rect.height(), thresh);
         max_filter(img, out, rect.width(), rect.height(), thresh);
 
         DLIB_TEST_MSG(array_to_matrix(out) == array_to_matrix(out2),
@@ -517,11 +515,19 @@ namespace
             test_max_filter(2,2,1,1,rnd);
             test_max_filter(3,3,1,1,rnd);
             test_max_filter(3,3,3,3,rnd);
+            test_max_filter(3,3,2,2,rnd);
             test_max_filter(3,3,3,5,rnd);
+            test_max_filter(3,3,6,8,rnd);
             test_max_filter(20,20,901,901,rnd);
             test_max_filter(5,5,1,5,rnd);
             test_max_filter(50,50,9,9,rnd);
             test_max_filter(50,50,9,9,rnd);
+            test_max_filter(50,50,10,10,rnd);
+            test_max_filter(50,50,11,10,rnd);
+            test_max_filter(50,50,10,11,rnd);
+            test_max_filter(50,50,10,21,rnd);
+            test_max_filter(50,50,20,10,rnd);
+            test_max_filter(50,50,20,10,rnd);
             test_max_filter(50,50,9,9,rnd);
             test_max_filter(20,20,1,901,rnd);
             test_max_filter(20,20,3,901,rnd);
@@ -533,8 +539,8 @@ namespace
             print_spinner();
             test_max_filter((int)rnd.get_random_8bit_number()%100+1,
                             (int)rnd.get_random_8bit_number()%100+1,
-                            (int)rnd.get_random_8bit_number()*2+1,
-                            (int)rnd.get_random_8bit_number()*2+1,
+                            (int)rnd.get_random_8bit_number()%150+1,
+                            (int)rnd.get_random_8bit_number()%150+1,
                             rnd);
         }
     }