diff --git a/modules/highgui/src/grfmt_tiff.cpp b/modules/highgui/src/grfmt_tiff.cpp
index 2d976c2d0..f40699f83 100644
--- a/modules/highgui/src/grfmt_tiff.cpp
+++ b/modules/highgui/src/grfmt_tiff.cpp
@@ -238,11 +238,15 @@ bool  TiffDecoder::readData( Mat& img )
                     {
                         case 8:
                         {
+                            uchar * bstart = buffer;
                             if( !is_tiled )
                                 ok = TIFFReadRGBAStrip( tif, y, (uint32*)buffer );
                             else
+                            {
                                 ok = TIFFReadRGBATile( tif, x, y, (uint32*)buffer );
-
+                                //Tiles fill the buffer from the bottom up
+                                bstart += (tile_height0 - tile_height) * tile_width0 * 4;
+                            }
                             if( !ok )
                             {
                                 close();
@@ -251,11 +255,11 @@ bool  TiffDecoder::readData( Mat& img )
 
                             for( i = 0; i < tile_height; i++ )
                                 if( color )
-                                    icvCvt_BGRA2BGR_8u_C4C3R( buffer + i*tile_width*4, 0,
+                                    icvCvt_BGRA2BGR_8u_C4C3R( bstart + i*tile_width0*4, 0,
                                                              data + x*3 + img.step*(tile_height - i - 1), 0,
                                                              cvSize(tile_width,1), 2 );
                                 else
-                                    icvCvt_BGRA2Gray_8u_C4C1R( buffer + i*tile_width*4, 0,
+                                    icvCvt_BGRA2Gray_8u_C4C1R( bstart + i*tile_width0*4, 0,
                                                               data + x + img.step*(tile_height - i - 1), 0,
                                                               cvSize(tile_width,1), 2 );
                             break;
@@ -280,19 +284,19 @@ bool  TiffDecoder::readData( Mat& img )
                                 {
                                     if( ncn == 1 )
                                     {
-                                        icvCvt_Gray2BGR_16u_C1C3R(buffer16 + i*tile_width*ncn, 0,
+                                        icvCvt_Gray2BGR_16u_C1C3R(buffer16 + i*tile_width0*ncn, 0,
                                                                   (ushort*)(data + img.step*i) + x*3, 0,
                                                                   cvSize(tile_width,1) );
                                     }
                                     else if( ncn == 3 )
                                     {
-                                        icvCvt_RGB2BGR_16u_C3R(buffer16 + i*tile_width*ncn, 0,
+                                        icvCvt_RGB2BGR_16u_C3R(buffer16 + i*tile_width0*ncn, 0,
                                                                (ushort*)(data + img.step*i) + x*3, 0,
                                                                cvSize(tile_width,1) );
                                     }
                                     else
                                     {
-                                        icvCvt_BGRA2BGR_16u_C4C3R(buffer16 + i*tile_width*ncn, 0,
+                                        icvCvt_BGRA2BGR_16u_C4C3R(buffer16 + i*tile_width0*ncn, 0,
                                                                (ushort*)(data + img.step*i) + x*3, 0,
                                                                cvSize(tile_width,1), 2 );
                                     }
@@ -302,12 +306,12 @@ bool  TiffDecoder::readData( Mat& img )
                                     if( ncn == 1 )
                                     {
                                         memcpy((ushort*)(data + img.step*i)+x,
-                                               buffer16 + i*tile_width*ncn,
+                                               buffer16 + i*tile_width0*ncn,
                                                tile_width*sizeof(buffer16[0]));
                                     }
                                     else
                                     {
-                                        icvCvt_BGRA2Gray_16u_CnC1R(buffer16 + i*tile_width*ncn, 0,
+                                        icvCvt_BGRA2Gray_16u_CnC1R(buffer16 + i*tile_width0*ncn, 0,
                                                                (ushort*)(data + img.step*i) + x, 0,
                                                                cvSize(tile_width,1), ncn, 2 );
                                     }
@@ -335,13 +339,13 @@ bool  TiffDecoder::readData( Mat& img )
                                 if(dst_bpp == 32)
                                 {
                                     memcpy((float*)(data + img.step*i)+x,
-                                           buffer32 + i*tile_width*ncn,
+                                           buffer32 + i*tile_width0*ncn,
                                            tile_width*sizeof(buffer32[0]));
                                 }
                                 else
                                 {
                                     memcpy((double*)(data + img.step*i)+x,
-                                         buffer64 + i*tile_width*ncn,
+                                         buffer64 + i*tile_width0*ncn,
                                          tile_width*sizeof(buffer64[0]));
                                 }
                             }
diff --git a/modules/highgui/test/test_grfmt.cpp b/modules/highgui/test/test_grfmt.cpp
index edccc0280..f451036ab 100644
--- a/modules/highgui/test/test_grfmt.cpp
+++ b/modules/highgui/test/test_grfmt.cpp
@@ -467,4 +467,45 @@ TEST(Highgui_Tiff, write_read_16bit_big_little_endian)
     }
 }
 
+class CV_GrfmtReadTifTiledWithNotFullTiles: public cvtest::BaseTest
+{
+public:
+    void run(int)
+    {
+        try
+        {
+            /* see issue #3472 - dealing with tiled images where the tile size is
+             * not a multiple of image size.
+             * The tiled images were created with 'convert' from ImageMagick,
+             * using the command 'convert <input> -define tiff:tile-geometry=128x128 -depth [8|16] <output>
+             * Note that the conversion to 16 bits expands the range from 0-255 to 0-255*255,
+             * so the test converts back but rounding errors cause small differences.
+             */
+            cv::Mat img = imread(string(ts->get_data_path()) + "readwrite/non_tiled.tif",-1);
+            if (img.empty()) ts->set_failed_test_info(cvtest::TS::FAIL_INVALID_TEST_DATA);
+            ASSERT_TRUE(img.channels() == 3);
+            cv::Mat tiled8 = imread(string(ts->get_data_path()) + "readwrite/tiled_8.tif", -1);
+            if (tiled8.empty()) ts->set_failed_test_info(cvtest::TS::FAIL_INVALID_TEST_DATA);
+            ASSERT_PRED_FORMAT2(cvtest::MatComparator(0, 0), img, tiled8);
+
+            cv::Mat tiled16 = imread(string(ts->get_data_path()) + "readwrite/tiled_16.tif", -1);
+            if (tiled16.empty()) ts->set_failed_test_info(cvtest::TS::FAIL_INVALID_TEST_DATA);
+            ASSERT_TRUE(tiled16.elemSize() == 6);
+            tiled16.convertTo(tiled8, CV_8UC3, 1./256.);
+            ASSERT_PRED_FORMAT2(cvtest::MatComparator(2, 0), img, tiled8);
+            // What about 32, 64 bit?
+        }
+        catch(...)
+        {
+            ts->set_failed_test_info(cvtest::TS::FAIL_EXCEPTION);
+        }
+        ts->set_failed_test_info(cvtest::TS::OK);
+    }
+};
+
+TEST(Highgui_Tiff, decode_tile_remainder)
+{
+    CV_GrfmtReadTifTiledWithNotFullTiles test; test.safe_run();
+}
+
 #endif