Merge branch 'image'

README.md

@@ -109,6 +109,8 @@ M. K. Ahn, J. D. Tucker, W. Wu, and A. Srivastava. “Regression Models Using Sh
 
 J. D. Tucker, L. Shand, and K. Chowdhary. “Multimodal Bayesian Registration of Noisy Functions using Hamiltonian Monte Carlo”, Computational Statistics and Data Analysis, accepted, 2021.
 
+Q. Xie, S. Kurtek, E. Klassen, G. E. Christensen and A. Srivastava. Metric-based pairwise and multiple image registration. IEEE European Conference on Computer Vision (ECCV), September, 2014
+
 X. Zhang, S. Kurtek, O. Chkrebtii, and J. D. Tucker, “Elastic k-means clustering of functional data 
    for posterior exploration, with an application to inference on acute respiratory infection dynamics”, 
    arXiv:2011.12397 [stat.ME], 2020.

bin/ex_image_align.py

@@ -0,0 +1,53 @@
+#%%
+import fdasrsf as fs
+import numpy as np
+from scipy.io import loadmat
+import matplotlib.pyplot as plt
+
+dat = loadmat('image.mat')
+I1 = dat['I1']
+I2 = dat['I2']
+
+(m,n) = I1.shape
+
+I1 -= I1.min()
+I1 /= I1.max()
+
+I2 -= I2.min()
+I2 /= I2.max()
+
+F1 = np.zeros((m,n,2))
+F1[:,:,1],F1[:,:,0] = np.gradient(I1, 1/699,1/699)
+F2 = np.zeros((m,n,2))
+F2[:,:,1],F2[:,:,0] = np.gradient(I2, 1/699,1/699)
+
+F1 -= F1.min()
+F1 /= F1.max()
+
+F2 -= F2.min()
+F2 /= F2.max()
+
+# %%
+M = 10
+b = fs.formbasisTid(M, m, n, 't')
+
+gamnew,Inew,H,stepsize = fs.reparam_image(F1,F2,None,b,stepsize=1e-2, itermax=1000)
+
+I2_new = fs.apply_gam_imag(I2,gamnew)
+
+plt.figure()
+ax1 = plt.subplot(131)
+plt.imshow(I1)
+plt.title('I1');
+ax1 = plt.subplot(132)
+plt.imshow(I2)
+plt.title('I2');
+ax1 = plt.subplot(133)
+plt.imshow(I2_new)
+plt.title('I2 Warped');
+
+plt.figure()
+gamid = fs.makediffeoid(m,n)
+plt.quiver(gamid[:,:,0],gamid[:,:,1],gamid[:,:,0]-gamnew[:,:,0],gamid[:,:,1]-gamnew[:,:,1])
+
+# %%

doc/build/html/_modules/boxplots.html

@@ -54,7 +54,11 @@
 <li class="toctree-l1"><a class="reference internal" href="../pcr_regression.html">Elastic Principal Component Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../elastic_glm_regression.html">Elastic GLM Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../tolerance.html">Elastic Functional Tolerance Bounds</a></li>
+<<<<<<< HEAD
 <li class="toctree-l1"><a class="reference internal" href="../kmeans.html">Elastic Functional Clustering</a></li>
+=======
+<li class="toctree-l1"><a class="reference internal" href="../image.html">Elastic Image Warping</a></li>
+>>>>>>> image
 <li class="toctree-l1"><a class="reference internal" href="../curve_statistics.html">Curve Registration</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../geodesic.html">SRVF Geodesic Computation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../utility_functions.html">Utility Functions</a></li>

doc/build/html/_modules/geodesic.html

@@ -54,7 +54,11 @@
 <li class="toctree-l1"><a class="reference internal" href="../pcr_regression.html">Elastic Principal Component Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../elastic_glm_regression.html">Elastic GLM Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../tolerance.html">Elastic Functional Tolerance Bounds</a></li>
+<<<<<<< HEAD
 <li class="toctree-l1"><a class="reference internal" href="../kmeans.html">Elastic Functional Clustering</a></li>
+=======
+<li class="toctree-l1"><a class="reference internal" href="../image.html">Elastic Image Warping</a></li>
+>>>>>>> image
 <li class="toctree-l1"><a class="reference internal" href="../curve_statistics.html">Curve Registration</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../geodesic.html">SRVF Geodesic Computation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../utility_functions.html">Utility Functions</a></li>
@@ -104,7 +108,11 @@ <h1>Source code for geodesic</h1><div class="highlight"><pre>
 
 
 <div class="viewcode-block" id="plot_geod"><a class="viewcode-back" href="../geodesic.html#geodesic.plot_geod">[docs]</a><span class="k">def</span> <span class="nf">plot_geod</span><span class="p">(</span><span class="n">path</span><span class="p">):</span>
+<<<<<<< HEAD
 <span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+=======
+    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+>>>>>>> image
 <span class="sd">    Plots the geodesic path as a sequence of curves</span>
 
 <span class="sd">    :param path: numpy ndarray of shape (2,M,K) of M sample points of K samples along path</span>
@@ -210,7 +218,11 @@ <h1>Source code for geodesic</h1><div class="highlight"><pre>
 
 
 <div class="viewcode-block" id="path_straightening"><a class="viewcode-back" href="../geodesic.html#geodesic.path_straightening">[docs]</a><span class="k">def</span> <span class="nf">path_straightening</span><span class="p">(</span><span class="n">beta1</span><span class="p">,</span> <span class="n">beta2</span><span class="p">,</span> <span class="n">betamid</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">init</span><span class="o">=</span><span class="s2">&quot;rand&quot;</span><span class="p">,</span> <span class="n">T</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">5</span><span class="p">):</span>
+<<<<<<< HEAD
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+=======
+    <span class="sd">&quot;&quot;&quot;</span>
+>>>>>>> image
 <span class="sd">    Perform path straightening to find geodesic between two shapes in either</span>
 <span class="sd">    the space of closed curves or the space of affine standardized curves.</span>
 <span class="sd">    This algorithm follows the steps outlined in section 4.6 of the</span>

doc/build/html/_modules/index.html

@@ -54,7 +54,11 @@
 <li class="toctree-l1"><a class="reference internal" href="../pcr_regression.html">Elastic Principal Component Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../elastic_glm_regression.html">Elastic GLM Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../tolerance.html">Elastic Functional Tolerance Bounds</a></li>
+<<<<<<< HEAD
 <li class="toctree-l1"><a class="reference internal" href="../kmeans.html">Elastic Functional Clustering</a></li>
+=======
+<li class="toctree-l1"><a class="reference internal" href="../image.html">Elastic Image Warping</a></li>
+>>>>>>> image
 <li class="toctree-l1"><a class="reference internal" href="../curve_statistics.html">Curve Registration</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../geodesic.html">SRVF Geodesic Computation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../utility_functions.html">Utility Functions</a></li>
@@ -93,7 +97,11 @@ <h1>All modules for which code is available</h1>
 <li><a href="fPCA.html">fPCA</a></li>
 <li><a href="fPLS.html">fPLS</a></li>
 <li><a href="geodesic.html">geodesic</a></li>
+<<<<<<< HEAD
 <li><a href="kmeans.html">kmeans</a></li>
+=======
+<li><a href="image.html">image</a></li>
+>>>>>>> image
 <li><a href="pcr_regression.html">pcr_regression</a></li>
 <li><a href="regression.html">regression</a></li>
 <li><a href="time_warping.html">time_warping</a></li>

doc/build/html/_modules/time_warping.html

@@ -54,7 +54,11 @@
 <li class="toctree-l1"><a class="reference internal" href="../pcr_regression.html">Elastic Principal Component Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../elastic_glm_regression.html">Elastic GLM Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../tolerance.html">Elastic Functional Tolerance Bounds</a></li>
+<<<<<<< HEAD
 <li class="toctree-l1"><a class="reference internal" href="../kmeans.html">Elastic Functional Clustering</a></li>
+=======
+<li class="toctree-l1"><a class="reference internal" href="../image.html">Elastic Image Warping</a></li>
+>>>>>>> image
 <li class="toctree-l1"><a class="reference internal" href="../curve_statistics.html">Curve Registration</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../geodesic.html">SRVF Geodesic Computation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../utility_functions.html">Utility Functions</a></li>

doc/build/html/_modules/tolerance.html

@@ -54,7 +54,11 @@
 <li class="toctree-l1"><a class="reference internal" href="../pcr_regression.html">Elastic Principal Component Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../elastic_glm_regression.html">Elastic GLM Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../tolerance.html">Elastic Functional Tolerance Bounds</a></li>
+<<<<<<< HEAD
 <li class="toctree-l1"><a class="reference internal" href="../kmeans.html">Elastic Functional Clustering</a></li>
+=======
+<li class="toctree-l1"><a class="reference internal" href="../image.html">Elastic Image Warping</a></li>
+>>>>>>> image
 <li class="toctree-l1"><a class="reference internal" href="../curve_statistics.html">Curve Registration</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../geodesic.html">SRVF Geodesic Computation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../utility_functions.html">Utility Functions</a></li>
@@ -104,7 +108,11 @@ <h1>Source code for tolerance</h1><div class="highlight"><pre>
 
 
 <div class="viewcode-block" id="bootTB"><a class="viewcode-back" href="../tolerance.html#tolerance.bootTB">[docs]</a><span class="k">def</span> <span class="nf">bootTB</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">time</span><span class="p">,</span> <span class="n">a</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="mf">.99</span><span class="p">,</span> <span class="n">B</span><span class="o">=</span><span class="mi">500</span><span class="p">,</span> <span class="n">no</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">parallel</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<<<<<<< HEAD
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+=======
+    <span class="sd">&quot;&quot;&quot;</span>
+>>>>>>> image
 <span class="sd">    This function computes tolerance bounds for functional data containing</span>
 <span class="sd">    phase and amplitude variation using bootstrap sampling</span>
 

doc/build/html/_modules/utility_functions.html

@@ -54,7 +54,11 @@
 <li class="toctree-l1"><a class="reference internal" href="../pcr_regression.html">Elastic Principal Component Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../elastic_glm_regression.html">Elastic GLM Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../tolerance.html">Elastic Functional Tolerance Bounds</a></li>
+<<<<<<< HEAD
 <li class="toctree-l1"><a class="reference internal" href="../kmeans.html">Elastic Functional Clustering</a></li>
+=======
+<li class="toctree-l1"><a class="reference internal" href="../image.html">Elastic Image Warping</a></li>
+>>>>>>> image
 <li class="toctree-l1"><a class="reference internal" href="../curve_statistics.html">Curve Registration</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../geodesic.html">SRVF Geodesic Computation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../utility_functions.html">Utility Functions</a></li>

doc/build/html/_sources/index.rst.txt

@@ -28,7 +28,11 @@ using functional component analysis and regression.
    pcr_regression.rst
    elastic_glm_regression.rst
    tolerance.rst
+<<<<<<< HEAD
    kmeans.rst
+=======
+   image.rst
+>>>>>>> image
    curve_statistics.rst
    geodesic.rst
    utility_functions.rst
@@ -107,6 +111,8 @@ References
    for posterior exploration, with an application to inference on acute respiratory infection dynamics”, 
    arXiv:2011.12397 [stat.ME], 2020.
 
+   Q. Xie, S. Kurtek, E. Klassen, G. E. Christensen and A. Srivastava. Metric-based pairwise and multiple image registration. IEEE European Conference on Computer Vision (ECCV), September, 2014
+
 
 Indices and tables
 ==================

doc/build/html/boxplots.html

@@ -68,7 +68,11 @@
 <li class="toctree-l1"><a class="reference internal" href="pcr_regression.html">Elastic Principal Component Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="elastic_glm_regression.html">Elastic GLM Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="tolerance.html">Elastic Functional Tolerance Bounds</a></li>
+<<<<<<< HEAD
 <li class="toctree-l1"><a class="reference internal" href="kmeans.html">Elastic Functional Clustering</a></li>
+=======
+<li class="toctree-l1"><a class="reference internal" href="image.html">Elastic Image Warping</a></li>
+>>>>>>> image
 <li class="toctree-l1"><a class="reference internal" href="curve_statistics.html">Curve Registration</a></li>
 <li class="toctree-l1"><a class="reference internal" href="geodesic.html">SRVF Geodesic Computation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="utility_functions.html">Utility Functions</a></li>

doc/build/html/curve_functions.html

@@ -56,7 +56,11 @@
 <li class="toctree-l1"><a class="reference internal" href="pcr_regression.html">Elastic Principal Component Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="elastic_glm_regression.html">Elastic GLM Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="tolerance.html">Elastic Functional Tolerance Bounds</a></li>
+<<<<<<< HEAD
 <li class="toctree-l1"><a class="reference internal" href="kmeans.html">Elastic Functional Clustering</a></li>
+=======
+<li class="toctree-l1"><a class="reference internal" href="image.html">Elastic Image Warping</a></li>
+>>>>>>> image
 <li class="toctree-l1"><a class="reference internal" href="curve_statistics.html">Curve Registration</a></li>
 <li class="toctree-l1"><a class="reference internal" href="geodesic.html">SRVF Geodesic Computation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="utility_functions.html">Utility Functions</a></li>

doc/build/html/curve_statistics.html

@@ -23,7 +23,11 @@
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
     <link rel="next" title="SRVF Geodesic Computation" href="geodesic.html" />
+<<<<<<< HEAD
     <link rel="prev" title="Elastic Functional Clustering" href="kmeans.html" /> 
+=======
+    <link rel="prev" title="Elastic Image Warping" href="image.html" /> 
+>>>>>>> image
 </head>
 
 <body class="wy-body-for-nav"> 
@@ -58,6 +62,7 @@
 <li class="toctree-l1"><a class="reference internal" href="pcr_regression.html">Elastic Principal Component Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="elastic_glm_regression.html">Elastic GLM Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="tolerance.html">Elastic Functional Tolerance Bounds</a></li>
+<<<<<<< HEAD
 <li class="toctree-l1"><a class="reference internal" href="kmeans.html">Elastic Functional Clustering</a></li>
 <li class="toctree-l1 current"><a class="current reference internal" href="#">Curve Registration</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="#curve_stats.fdacurve"><code class="docutils literal notranslate"><span class="pre">fdacurve</span></code></a><ul>
@@ -72,6 +77,10 @@
 <li class="toctree-l2"><a class="reference internal" href="#curve_stats.randn"><code class="docutils literal notranslate"><span class="pre">randn()</span></code></a></li>
 </ul>
 </li>
+=======
+<li class="toctree-l1"><a class="reference internal" href="image.html">Elastic Image Warping</a></li>
+<li class="toctree-l1 current"><a class="current reference internal" href="#">Curve Registration</a></li>
+>>>>>>> image
 <li class="toctree-l1"><a class="reference internal" href="geodesic.html">SRVF Geodesic Computation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="utility_functions.html">Utility Functions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="curve_functions.html">Curve Functions</a></li>
@@ -296,9 +305,21 @@ <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this head
 
            </div>
           </div>
+<<<<<<< HEAD
           <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
         <a href="kmeans.html" class="btn btn-neutral float-left" title="Elastic Functional Clustering" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
         <a href="geodesic.html" class="btn btn-neutral float-right" title="SRVF Geodesic Computation" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a>
+=======
+          <footer>
+
+    <div class="rst-footer-buttons" role="navigation" aria-label="footer navigation">
+
+        <a href="geodesic.html" class="btn btn-neutral float-right" title="SRVF Geodesic Computation" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right"></span></a>
+
+
+        <a href="image.html" class="btn btn-neutral float-left" title="Elastic Image Warping" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left"></span> Previous</a>
+
+>>>>>>> image
     </div>
 
   <hr/>

doc/build/html/fPCA.html

@@ -73,7 +73,11 @@
 <li class="toctree-l1"><a class="reference internal" href="pcr_regression.html">Elastic Principal Component Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="elastic_glm_regression.html">Elastic GLM Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="tolerance.html">Elastic Functional Tolerance Bounds</a></li>
+<<<<<<< HEAD
 <li class="toctree-l1"><a class="reference internal" href="kmeans.html">Elastic Functional Clustering</a></li>
+=======
+<li class="toctree-l1"><a class="reference internal" href="image.html">Elastic Image Warping</a></li>
+>>>>>>> image
 <li class="toctree-l1"><a class="reference internal" href="curve_statistics.html">Curve Registration</a></li>
 <li class="toctree-l1"><a class="reference internal" href="geodesic.html">SRVF Geodesic Computation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="utility_functions.html">Utility Functions</a></li>

doc/build/html/fPLS.html

@@ -59,7 +59,11 @@
 <li class="toctree-l1"><a class="reference internal" href="pcr_regression.html">Elastic Principal Component Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="elastic_glm_regression.html">Elastic GLM Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="tolerance.html">Elastic Functional Tolerance Bounds</a></li>
+<<<<<<< HEAD
 <li class="toctree-l1"><a class="reference internal" href="kmeans.html">Elastic Functional Clustering</a></li>
+=======
+<li class="toctree-l1"><a class="reference internal" href="image.html">Elastic Image Warping</a></li>
+>>>>>>> image
 <li class="toctree-l1"><a class="reference internal" href="curve_statistics.html">Curve Registration</a></li>
 <li class="toctree-l1"><a class="reference internal" href="geodesic.html">SRVF Geodesic Computation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="utility_functions.html">Utility Functions</a></li>