From 4b099e8ade9805c8c8bc6bddf3f824eb905cb22f Mon Sep 17 00:00:00 2001
From: "PkLab.net" <github@pklab.net>
Date: Thu, 11 Aug 2016 19:32:29 +0200
Subject: [PATCH] Fix rho,phi exchange and amend linearPolar & logPolar docs
 with details and pics.

---
 modules/imgproc/doc/pics/polar_remap_doc.png |  Bin 0 -> 303653 bytes
 modules/imgproc/doc/pics/polar_remap_doc.svg | 3776 ++++++++++++++++++
 modules/imgproc/include/opencv2/imgproc.hpp  |   79 +-
 samples/cpp/polar_transforms.cpp             |   15 +-
 4 files changed, 3842 insertions(+), 28 deletions(-)
 create mode 100644 modules/imgproc/doc/pics/polar_remap_doc.png
 create mode 100644 modules/imgproc/doc/pics/polar_remap_doc.svg

diff --git a/modules/imgproc/doc/pics/polar_remap_doc.png b/modules/imgproc/doc/pics/polar_remap_doc.png
new file mode 100644
index 0000000000000000000000000000000000000000..e3e4105bb89d600376c7336f84bebe885799e9b1
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+           style="display:inline;fill:none;fill-rule:evenodd;stroke:#0000ff;stroke-width:0.99952435px;stroke-linecap:round;stroke-linejoin:miter;stroke-opacity:1"
+           d="m 1396.2964,459.29047 29.9858,0"
+           id="path12562-9"
+           inkscape:connector-curvature="0" />
+        <path
+           style="display:inline;fill:none;fill-rule:evenodd;stroke:#0000ff;stroke-width:0.99952435px;stroke-linecap:round;stroke-linejoin:miter;stroke-opacity:1"
+           d="m 1411.2896,444.2962 0,29.98566"
+           id="path12564-3"
+           inkscape:connector-curvature="0" />
+      </g>
+      <g
+         transform="matrix(0.5,0.8660254,-0.8660254,0.5,1153.4021,-905.96716)"
+         id="g5567-2"
+         style="display:inline;fill:none;stroke:#0000ff">
+        <path
+           style="display:inline;fill:none;fill-rule:evenodd;stroke:#0000ff;stroke-width:1px;stroke-linecap:round;stroke-linejoin:miter;stroke-opacity:1"
+           d="m 1396.2964,459.29047 29.9858,0"
+           id="path12562-8"
+           inkscape:connector-curvature="0" />
+        <path
+           style="display:inline;fill:none;fill-rule:evenodd;stroke:#0000ff;stroke-width:1px;stroke-linecap:round;stroke-linejoin:miter;stroke-opacity:1"
+           d="m 1411.2896,444.2962 0,29.98566"
+           id="path12564-5"
+           inkscape:connector-curvature="0" />
+      </g>
+    </g>
+    <path
+       style="display:inline;fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:1, 3.00000004;stroke-dashoffset:0;stroke-opacity:1"
+       d="m 2287.8127,322.85414 52.0123,0"
+       id="path9375-8-0"
+       inkscape:connector-curvature="0" />
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:17.5px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="1164.5468"
+       y="-392.44144"
+       id="text5769"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan5771"
+         x="1164.5468"
+         y="-392.44144"
+         style="text-align:start;text-anchor:start">Size: W:600 H:440 px</tspan><tspan
+         sodipodi:role="line"
+         x="1164.5468"
+         y="-370.56644"
+         style="text-align:start;text-anchor:start"
+         id="tspan5779">Center = x:240, y:220</tspan><tspan
+         sodipodi:role="line"
+         x="1164.5468"
+         y="-348.69144"
+         style="text-align:start;text-anchor:start"
+         id="tspan5777">magnitude=100px</tspan><tspan
+         sodipodi:role="line"
+         x="1164.5468"
+         y="-326.81644"
+         id="tspan5773"
+         style="text-align:start;text-anchor:start">angle = 60deg</tspan><tspan
+         sodipodi:role="line"
+         x="1164.5468"
+         y="-304.94144"
+         id="tspan5775"
+         style="text-align:start;text-anchor:start">maxRadius= 230px</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:17.5px;line-height:125%;font-family:sans-serif;text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="1403.5974"
+       y="-392.44144"
+       id="text5783"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan5785"
+         x="1403.5974"
+         y="-392.44144"
+         style="text-align:start;text-anchor:start">Kx = 600px / 230px = 2.609 =&gt; rho =  260.869px</tspan><tspan
+         sodipodi:role="line"
+         x="1403.5974"
+         y="-370.56644"
+         style="text-align:start;text-anchor:start"
+         id="tspan5787">Ky = 440px / 360deg = 1.222 pix/deg = phi = 73.333px</tspan><tspan
+         sodipodi:role="line"
+         x="1403.5974"
+         y="-348.69144"
+         style="text-align:start;text-anchor:start"
+         id="tspan5801">M = 600px / ln(230px) = 110.33 pn/ln(px) =&gt; rho = 508.103px</tspan></text>
+    <circle
+       style="display:inline;opacity:1;fill:none;fill-opacity:1;stroke:#ff0000;stroke-width:2;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+       id="path5214"
+       cx="-1804.0728"
+       cy="-305.4054"
+       transform="matrix(-0.9167673,0.39942172,-0.39942171,-0.91676731,278.38913,379.89069)"
+       r="230" />
+    <rect
+       style="display:inline;opacity:1;fill:#aaccff;fill-opacity:1;stroke:none;stroke-width:2;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+       id="rect5347-06"
+       width="600"
+       height="30"
+       x="1535.9006"
+       y="-220.60022"
+       transform="translate(278.38913,379.89069)" />
+    <text
+       transform="translate(278.38913,379.89069)"
+       xml:space="preserve"
+       style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:20px;line-height:125%;font-family:serif;-inkscape-font-specification:'serif Italic';text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;display:inline;fill:#0000ff;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;"
+       x="1836.0618"
+       y="-200.08264"
+       id="text10597-7-0-1"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan10599-7-1-1"
+         x="1836.0618"
+         y="-200.08264">b) Params References</tspan></text>
+  </g>
+  <metadata
+     id="metadata74">
+    <rdf:RDF>
+      <cc:Work>
+        <dc:format>image/svg+xml</dc:format>
+        <dc:type
+           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
+        <cc:license
+           rdf:resource="http://creativecommons.org/publicdomain/zero/1.0/" />
+        <dc:publisher>
+          <cc:Agent
+             rdf:about="http://openclipart.org/">
+            <dc:title>OpenCV</dc:title>
+          </cc:Agent>
+        </dc:publisher>
+        <dc:title></dc:title>
+        <dc:date>2016-08-08</dc:date>
+        <dc:description />
+        <dc:source />
+        <dc:creator>
+          <cc:Agent>
+            <dc:title>PkLab.net</dc:title>
+          </cc:Agent>
+        </dc:creator>
+        <dc:subject>
+          <rdf:Bag>
+            <rdf:li>linearPolar</rdf:li>
+            <rdf:li>logPolar</rdf:li>
+            <rdf:li>image processing</rdf:li>
+            <rdf:li>OpenCV</rdf:li>
+          </rdf:Bag>
+        </dc:subject>
+      </cc:Work>
+      <cc:License
+         rdf:about="http://creativecommons.org/publicdomain/zero/1.0/">
+        <cc:permits
+           rdf:resource="http://creativecommons.org/ns#Reproduction" />
+        <cc:permits
+           rdf:resource="http://creativecommons.org/ns#Distribution" />
+        <cc:permits
+           rdf:resource="http://creativecommons.org/ns#DerivativeWorks" />
+      </cc:License>
+    </rdf:RDF>
+  </metadata>
+</svg>
diff --git a/modules/imgproc/include/opencv2/imgproc.hpp b/modules/imgproc/include/opencv2/imgproc.hpp
index ee022476f0..b8d95e3fc1 100644
--- a/modules/imgproc/include/opencv2/imgproc.hpp
+++ b/modules/imgproc/include/opencv2/imgproc.hpp
@@ -284,9 +284,9 @@ enum InterpolationFlags{
     WARP_FILL_OUTLIERS   = 8,
     /** flag, inverse transformation
 
-    For example, polar transforms:
-    - flag is __not__ set: \f$dst( \phi , \rho ) = src(x,y)\f$
-    - flag is set: \f$dst(x,y) = src( \phi , \rho )\f$
+    For example, @ref cv::linearPolar or @ref cv::logPolar transforms:
+    - flag is __not__ set: \f$dst( \rho , \phi ) = src(x,y)\f$
+    - flag is set: \f$dst(x,y) = src( \rho , \phi )\f$
     */
     WARP_INVERSE_MAP     = 16
 };
@@ -2418,41 +2418,78 @@ CV_EXPORTS_W void getRectSubPix( InputArray image, Size patchSize,
 An example using the cv::linearPolar and cv::logPolar operations
 */
 
-/** @brief Remaps an image to log-polar space.
+/** @brief Remaps an image to semilog-polar coordinates space.
+
+Transform the source image using the following transformation (See @ref polar_remaps_reference_image "Polar remaps reference image"):
+\f[\begin{array}{l}
+  dst( \rho , \phi ) = src(x,y) \\
+  dst.size() \leftarrow src.size()
+\end{array}\f]
 
-transforms the source image using the following transformation:
-\f[dst( \phi , \rho ) = src(x,y)\f]
 where
-\f[\rho = M  \cdot \log{\sqrt{x^2 + y^2}} , \phi =atan(y/x)\f]
+\f[\begin{array}{l}
+  I = (dx,dy) = (x - center.x,y - center.y) \\
+  \rho = M \cdot log_e(\texttt{magnitude} (I)) ,\\
+  \phi = Ky \cdot \texttt{angle} (I)_{0..360 deg} \\
+\end{array}\f]
+
+and
+\f[\begin{array}{l}
+  M = src.cols / log_e(maxRadius) \\
+  Ky = src.rows / 360 \\
+\end{array}\f]
 
 The function emulates the human "foveal" vision and can be used for fast scale and
-rotation-invariant template matching, for object tracking and so forth. The function can not operate
-in-place.
-
+rotation-invariant template matching, for object tracking and so forth.
 @param src Source image
-@param dst Destination image
+@param dst Destination image. It will have same size and type as src.
 @param center The transformation center; where the output precision is maximal
-@param M Magnitude scale parameter.
+@param M Magnitude scale parameter. It determines the radius of the bounding circle to transform too.
 @param flags A combination of interpolation methods, see cv::InterpolationFlags
- */
+
+@note
+-   The function can not operate in-place.
+-   To calculate magnitude and angle in degrees @ref cv::cartToPolar is used internally thus angles are measured from 0 to 360 with accuracy about 0.3 degrees.
+*/
 CV_EXPORTS_W void logPolar( InputArray src, OutputArray dst,
                             Point2f center, double M, int flags );
 
-/** @brief Remaps an image to polar space.
+/** @brief Remaps an image to polar coordinates space.
+
+@anchor polar_remaps_reference_image
+![Polar remaps reference](pics/polar_remap_doc.png)
+
+Transform the source image using the following transformation:
+\f[\begin{array}{l}
+  dst( \rho , \phi ) = src(x,y) \\
+  dst.size() \leftarrow src.size()
+\end{array}\f]
 
-transforms the source image using the following transformation:
-\f[dst( \phi , \rho ) = src(x,y)\f]
 where
-\f[\rho = (src.width/maxRadius)  \cdot \sqrt{x^2 + y^2} , \phi =atan(y/x)\f]
+\f[\begin{array}{l}
+  I = (dx,dy) = (x - center.x,y - center.y) \\
+  \rho = Kx \cdot \texttt{magnitude} (I) ,\\
+  \phi = Ky \cdot \texttt{angle} (I)_{0..360 deg}
+\end{array}\f]
+
+and
+\f[\begin{array}{l}
+  Kx = src.cols / maxRadius \\
+  Ky = src.rows / 360
+\end{array}\f]
 
-The function can not operate in-place.
 
 @param src Source image
-@param dst Destination image
+@param dst Destination image. It will have same size and type as src.
 @param center The transformation center;
-@param maxRadius Inverse magnitude scale parameter
+@param maxRadius The radius of the bounding circle to transform. It determines the inverse magnitude scale parameter too.
 @param flags A combination of interpolation methods, see cv::InterpolationFlags
- */
+
+@note
+-   The function can not operate in-place.
+-   To calculate magnitude and angle in degrees @ref cv::cartToPolar is used internally thus angles are measured from 0 to 360 with accuracy about 0.3 degrees.
+
+*/
 CV_EXPORTS_W void linearPolar( InputArray src, OutputArray dst,
                                Point2f center, double maxRadius, int flags );
 
diff --git a/samples/cpp/polar_transforms.cpp b/samples/cpp/polar_transforms.cpp
index 3cbc431c3c..adbc955b17 100644
--- a/samples/cpp/polar_transforms.cpp
+++ b/samples/cpp/polar_transforms.cpp
@@ -34,10 +34,10 @@ int main( int argc, char** argv )
         return -1;
     }
 
-    namedWindow( "Linear-Polar", WINDOW_NORMAL );
-    namedWindow( "Log-Polar", WINDOW_NORMAL );
-    namedWindow( "Recovered Linear-Polar", WINDOW_NORMAL );
-    namedWindow( "Recovered Log-Polar", WINDOW_NORMAL );
+    namedWindow( "Linear-Polar", WINDOW_AUTOSIZE );
+    namedWindow( "Log-Polar", WINDOW_AUTOSIZE);
+    namedWindow( "Recovered Linear-Polar", WINDOW_AUTOSIZE);
+    namedWindow( "Recovered Log-Polar", WINDOW_AUTOSIZE);
 
     moveWindow( "Linear-Polar", 20,20 );
     moveWindow( "Log-Polar", 700,20 );
@@ -53,13 +53,14 @@ int main( int argc, char** argv )
             break;
 
         Point2f center( (float)frame.cols / 2, (float)frame.rows / 2 );
-        double M = (double)frame.cols / 8;
+        double radius = (double)frame.cols / 4;
+        double M = (double)frame.cols / log(radius);
 
         logPolar(frame,log_polar_img, center, M, INTER_LINEAR + WARP_FILL_OUTLIERS);
-        linearPolar(frame,lin_polar_img, center, M, INTER_LINEAR + WARP_FILL_OUTLIERS);
+        linearPolar(frame,lin_polar_img, center, radius, INTER_LINEAR + WARP_FILL_OUTLIERS);
 
         logPolar(log_polar_img, recovered_log_polar, center, M, WARP_INVERSE_MAP + INTER_LINEAR);
-        linearPolar(lin_polar_img, recovered_lin_polar_img, center, M, WARP_INVERSE_MAP + INTER_LINEAR + WARP_FILL_OUTLIERS);
+        linearPolar(lin_polar_img, recovered_lin_polar_img, center, radius, WARP_INVERSE_MAP + INTER_LINEAR + WARP_FILL_OUTLIERS);
 
         imshow("Log-Polar", log_polar_img );
         imshow("Linear-Polar", lin_polar_img );