Initial commit.

5 files changed, 1924 insertions, 0 deletions

diff --git a/.gitignore b/.gitignore
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index 0000000..24e7d80
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,2 @@
+**/__pycache__
+datasets
diff --git a/CommonData/SOURCE b/CommonData/SOURCE
new file mode 100644
index 0000000..2ad9d7b
--- /dev/null
+++ b/CommonData/SOURCE
@@ -0,0 +1 @@
+The spectral dataset file was copied from code published alongside Otsu et al.'s "Reproducing Spectral Reflectances From Tristimulus Colours". The article with the code is available http://lightmetrica.org/h-otsu/project/rgb2spec/
\ No newline at end of file
diff --git a/CommonData/spectrum_m.csv b/CommonData/spectrum_m.csv
new file mode 100644
index 0000000..004557e
--- /dev/null
+++ b/CommonData/spectrum_m.csv
@@ -0,0 +1,1270 @@
+color,380,390,400,410,420,430,440,450,460,470,480,490,500,510,520,530,540,550,560,570,580,590,600,610,620,630,640,650,660,670,680,690,700,710,720,730

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+1263,0.08478,0.10174000000000001,0.10602,0.1045,0.09996000000000001,0.09802000000000001,0.09738000000000001,0.09568000000000002,0.09092,0.08718,0.07976,0.07214,0.06814,0.06384,0.060899999999999996,0.05952,0.059019999999999996,0.05789999999999999,0.058019999999999995,0.06582000000000002,0.09204000000000001,0.15458,0.22798,0.26984,0.28785999999999995,0.29374,0.29354,0.29262,0.29138000000000003,0.29206,0.29212000000000005,0.2914800000000001,0.29312,0.29231999999999997,0.29346,0.29356000000000004

+1264,0.10734000000000002,0.16358,0.22946,0.24459999999999998,0.23406000000000002,0.22476,0.21966000000000002,0.2109,0.20934,0.21126,0.19973999999999997,0.1799,0.17374,0.16936,0.14801999999999998,0.13318,0.13788,0.16134,0.17306000000000002,0.20220000000000002,0.28004,0.38698,0.4837000000000001,0.5526,0.59114,0.61496,0.6255200000000001,0.6347400000000001,0.6406799999999999,0.6420600000000001,0.64474,0.6478200000000001,0.6546200000000001,0.66184,0.6648000000000001,0.6679999999999999

+1265,0.10936000000000001,0.14206000000000002,0.163,0.16212,0.15566,0.1504,0.14666,0.1446,0.14043999999999998,0.13624,0.12738,0.11661999999999999,0.11112,0.10588,0.09962000000000001,0.09678,0.09606,0.09832,0.09636,0.10166,0.14036,0.23582,0.34975999999999996,0.43520000000000003,0.48339999999999994,0.5047200000000001,0.51302,0.5151,0.51576,0.51634,0.51588,0.5163800000000001,0.51514,0.5153000000000001,0.51538,0.51556

+1266,0.08528,0.10347999999999999,0.11486,0.11184000000000001,0.10546,0.10012000000000001,0.09542,0.08963999999999998,0.08553999999999999,0.08206,0.0754,0.07002,0.06786,0.06294,0.056799999999999996,0.054959999999999995,0.057679999999999995,0.060640000000000006,0.058640000000000005,0.06268,0.07478,0.10804,0.16858,0.256,0.34896000000000005,0.42724,0.47982,0.51542,0.53838,0.5463199999999999,0.5404199999999999,0.5457,0.5673600000000001,0.5895600000000001,0.6077600000000001,0.62708

+1267,0.11377999999999999,0.14764,0.16906,0.16696,0.16,0.15434,0.1538,0.14906,0.14411999999999997,0.1387,0.12832,0.11658000000000002,0.10863999999999999,0.1022,0.09416,0.09309999999999999,0.09288,0.09104,0.08742,0.09523999999999999,0.13868,0.24465999999999996,0.38348,0.50892,0.59772,0.6530199999999999,0.67976,0.69558,0.70428,0.7090799999999999,0.71288,0.7185,0.7243999999999999,0.7288399999999999,0.73112,0.7348600000000001

+1268,0.08005999999999999,0.09516,0.10428,0.10211999999999999,0.09944,0.09746,0.09528,0.09096,0.08386,0.07608000000000001,0.06798,0.06154,0.057179999999999995,0.053459999999999994,0.04923999999999999,0.04766,0.04688,0.046439999999999995,0.04596,0.05182,0.06974,0.11672,0.19688,0.29084000000000004,0.37748000000000004,0.44720000000000004,0.49278000000000005,0.5193800000000002,0.53874,0.5516000000000001,0.5623,0.5729599999999999,0.5879199999999999,0.60332,0.61878,0.63262

diff --git a/demo.py b/demo.py
new file mode 100644
index 0000000..a15fa72
--- /dev/null
+++ b/demo.py
@@ -0,0 +1,51 @@
+import os
+import matplotlib.pyplot as plt
+from colour import (
+    SpectralShape, COLOURCHECKER_SDS, ILLUMINANT_SDS, sd_to_XYZ)
+
+from otsu2018 import load_Otsu2018_spectra, Clustering
+
+
+if __name__ == '__main__':
+    print('Loading spectral data...')
+    sds = load_Otsu2018_spectra('CommonData/spectrum_m.csv', every_nth=10)
+    shape = SpectralShape(380, 730, 10)
+
+    print('Initializing the clustering...')
+    clustering = Clustering(sds, shape)
+
+    print('Clustering...')
+    before = clustering.root.total_reconstruction_error()
+    clustering.do_best_splits(8)
+    after = clustering.root.total_reconstruction_error()
+
+    print('Error before: %g' % before)
+    print('Error after:  %g' % after)
+
+    print('Saving the dataset...')
+    os.makedirs('datasets', exist_ok=True)
+    clustering.write_python_dataset('datasets/otsu2018.py')
+
+    print('Plotting...')
+    clustering.root.visualise()
+
+    plt.figure()
+
+    examples = COLOURCHECKER_SDS['ColorChecker N Ohta'].items()
+    for i, (name, sd) in enumerate(examples):
+        plt.subplot(2, 3, 1 + i)
+        plt.title(name)
+
+        plt.plot(sd.wavelengths, sd.values, label='Original')
+
+        XYZ = sd_to_XYZ(sd, illuminant=ILLUMINANT_SDS['D65']) / 100
+        recovered_sd = clustering.reconstruct(XYZ)
+        plt.plot(recovered_sd.wavelengths, recovered_sd.values,
+                 label='Recovered')
+
+        plt.legend()
+
+        if i + 1 == 6:
+            break
+
+    plt.show()
diff --git a/otsu2018.py b/otsu2018.py
new file mode 100644
index 0000000..4f84cd3
--- /dev/null
+++ b/otsu2018.py
@@ -0,0 +1,600 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sklearn.decomposition
+
+from colour import (SpectralDistribution, STANDARD_OBSERVER_CMFS,
+                    ILLUMINANT_SDS, sd_to_XYZ, XYZ_to_xy)
+from colour.plotting import plot_chromaticity_diagram_CIE1931
+
+
+def load_Otsu2018_spectra(path, every_nth=1):
+    """
+    Loads a set of measured reflectances from Otsu et al.'s csv file.
+
+    TODO: This function can't determine the spectral shape.
+
+    Parameters
+    ----------
+    path : str
+        File path.
+    every_nth : int
+        Load only every n-th spectrum. The original files are huge, so this can
+        be useful for testing.
+    """
+    data = np.genfromtxt(path, delimiter=',', skip_header=1)
+
+    # The first column is the id and is redundant
+    data = data[:, 1:]
+
+    spectra = []
+    for i in range(data.shape[0]):
+        if i % every_nth != 0:
+            continue
+
+        values = data[i, :]
+        spectra.append(values)
+
+    return np.array(spectra)
+
+
+class Colours:
+    """
+    Represents multiple colours: their reflectances, XYZ tristimulus values
+    and xy coordinates. The cmfs and the illuminant are taken from the parent
+    Clustering.
+
+    This class also supports partitioning, or creating two smaller instances
+    of Colours, split along a horizontal or a vertical axis on the xy plane.
+    """
+
+    def __init__(self, clustering, reflectances):
+        """
+        Parameters
+        ==========
+        clustering : Clustering
+            The parent clustering. This determines what cmfs and illuminant
+            are used in colourimetric calculations.
+        reflectances : ndarray (n,m)
+            Reflectances of the ``n`` colours to be stored in this class.
+            The shape must match ``Clustering.shape`` with ``m`` points for
+            each colour.
+        """
+
+        self.reflectances = reflectances
+        self.XYZ = np.empty((reflectances.shape[0], 3))
+        self.xy = np.empty((reflectances.shape[0], 2))
+
+        for i in range(len(self)):
+            sd = SpectralDistribution(reflectances[i, :], clustering.wl)
+            XYZ = sd_to_XYZ(sd, illuminant=clustering.illuminant) / 100
+            self.XYZ[i, :] = XYZ
+            self.xy[i, :] = XYZ_to_xy(XYZ)
+
+    def __len__(self):
+        """
+        Counts the number of colours in this object.
+        """
+        return self.reflectances.shape[0]
+
+    def partition(self, x_or_y, axis):
+        """
+        Parameters
+        ==========
+        x_or_y : int
+            Whether to split according to X or Y coordinates.
+        axis : float
+            The coordinate that defines where the split happens.
+
+        Returns
+        =======
+        lesser : Colours
+            The left or lower part.
+        greater : Colours
+            The right or upper part.
+        """
+        mask = self.xy[:, x_or_y] <= axis
+
+        lesser = object.__new__(Colours)
+        greater = object.__new__(Colours)
+
+        lesser.reflectances = self.reflectances[mask, :]
+        greater.reflectances = self.reflectances[np.logical_not(mask), :]
+
+        lesser.XYZ = self.XYZ[mask, :]
+        greater.XYZ = self.XYZ[np.logical_not(mask), :]
+
+        lesser.xy = self.xy[mask, :]
+        greater.xy = self.xy[np.logical_not(mask), :]
+
+        return lesser, greater
+
+
+class ClusteringError(Exception):
+    """
+    Exception used for various errors originating from code in this file.
+    """
+    pass
+
+
+class Node:
+    """
+    Represents a node in the clustering tree.
+    """
+
+    _counter = 1
+
+    def __init__(self, clustering, colours):
+        """
+        Parameters
+        ==========
+        clustering : Clustering
+            The parent clustering. This determines what cmfs and illuminant
+            are used in colourimetric calculations.
+        colours : Colours
+            The colours that belong in this node.
+        """
+
+        self.clustering = clustering
+        self.colours = colours
+        self.children = None
+
+        self._cached_reconstruction_error = None
+        self.PCA_done = False
+
+        # This is just for __str__ and plots
+        self.number = Node._counter
+        Node._counter += 1
+
+    def __str__(self):
+        return 'Node #%d' % (self.number)
+
+    @property
+    def leaf(self):
+        """
+        Is this node a leaf? Tree leaves don't have any children and store
+        instances of ``Colours``.
+        """
+
+        return self.children is None
+
+    def split(self, children, split_x_or_y, split_i):
+        """
+        Turns a leaf into a node with the given children.
+
+        Parameters
+        ==========
+        children : tuple
+            Two instances of ``Node`` in a tuple.
+        split_x_or_y : int
+            Split's ``x_or_y``.
+        split_axis : float
+            Split's ``axis``.
+        """
+
+        if not self.leaf:
+            raise RuntimeError(
+                'Node.split called for a node that is not a leaf')
+
+        self.children = children
+        self.split_x_or_y = split_x_or_y
+        self.split_axis = self.colours.xy[split_i, split_x_or_y]
+        self.colours = None
+        self._cached_reconstruction_error = None
+
+    def _leaves_generator(self):
+        if self.leaf:
+            yield self
+        else:
+            for child in self.children:
+                yield from child.leaves
+
+    @property
+    def leaves(self):
+        """
+        Returns a generator of all leaves connected to this node.
+        """
+        return self._leaves_generator()
+
+    #
+    # PCA and reconstruction
+    #
+
+    def PCA(self):
+        """
+        Performs the principal component analysis on colours in this node.
+        """
+
+        if not self.leaf:
+            raise RuntimeError('Node.PCA called for a node that is not a leaf')
+
+        pca = sklearn.decomposition.PCA(3)
+        pca.fit(self.colours.reflectances)
+        self.basis_functions = pca.components_
+        self.mean = pca.mean_
+
+        # TODO: better names
+        M = np.empty((3, 3))
+        for i in range(3):
+            R = self.basis_functions[i, :]
+            M[:, i] = self.clustering.fast_sd_to_XYZ(R)
+
+        self.M_inverse = np.linalg.inv(M)
+        self.XYZ_mu = self.clustering.fast_sd_to_XYZ(self.mean)
+
+        self.PCA_done = True
+
+    def reconstruct(self, XYZ):
+        """
+        Reconstructs a reflectance using data stored in this node.
+
+        Parameters
+        ==========
+        XYZ : ndarray, (3,)
+            *CIE XYZ* tristimulus values to recover the spectral distribution
+            from.
+
+        Returns
+        -------
+        SpectralDistribution
+            Recovered spectral distribution.
+        """
+
+        weights = np.dot(self.M_inverse, XYZ - self.XYZ_mu)
+        reflectance = np.dot(weights, self.basis_functions) + self.mean
+        return SpectralDistribution(reflectance, self.clustering.wl)
+
+    def reconstruction_error(self):
+        """
+        For every colour in this node, its spectrum is reconstructed (using
+        PCA data in this node) and compared with its true, measured spectrum.
+        The errors are then summed up and returned.
+
+        Returns
+        =======
+        error : float
+            The sum reconstruction errors for this node.
+        """
+
+        if self._cached_reconstruction_error:
+            return self._cached_reconstruction_error
+
+        if not self.PCA_done:  # FIXME
+            self.PCA()
+
+        error = 0
+        for i in range(len(self.colours)):
+            sd = self.colours.reflectances[i, :]
+            XYZ = self.colours.XYZ[i, :]
+            recovered_sd = self.reconstruct(XYZ)
+            error += np.sum((sd - recovered_sd.values) ** 2)
+
+        self._cached_reconstruction_error = error
+        return error
+
+    def total_reconstruction_error(self):
+        """
+        Computes the reconstruction error for an entire subtree, starting at
+        this node.
+
+        Returns
+        =======
+        error : float
+            The total reconstruction error of the subtree.
+        """
+
+        if self.leaf:
+            return self.reconstruction_error()
+        else:
+            return sum([child.total_reconstruction_error()
+                        for child in self.children])
+
+    def partition(self, x_or_y, i):
+        """
+        Splits this node into two and returns them. This operation does not
+        affect the node it's used on. ``Node.split`` has to be called (with
+        data returned from this method) to actually alter the tree.
+
+        Parameters
+        ==========
+        x_or_y : int
+            Whether to split according to X or Y coordinates.
+        i : int
+            The index of the colour whose coordinates determine where the
+            split happens. Cannot be ``len(Node.colours)`` or greater.
+
+        Returns
+        =======
+        lesser : Node
+            The left or lower part.
+        greater : Node
+            The right or upper part.
+        """
+
+        axis = self.colours.xy[i, x_or_y]
+        partition = self.colours.partition(x_or_y, axis)
+
+        if len(partition[0]) <= 5 or len(partition[1]) <= 5:
+            raise ClusteringError('partition created parts that are too small')
+
+        lesser = Node(self.clustering, partition[0])
+        greater = Node(self.clustering, partition[1])
+        return lesser, greater
+
+    def split_quality(self, x_or_y, i):
+        """
+
+        Parameters
+        ==========
+        x_or_y : int
+            Whether to split according to X or Y coordinates.
+        i : int
+            Index of the colour whose coordinates determine where the
+            split happens. Cannot be ``len(Node.colours)`` or greater.
+
+        Returns
+        =======
+        error : float
+            Sum of reconstruction errors of the two nodes created from
+            splitting.
+        lesser, greater : tuple
+            Subnodes created from splitting.
+        """
+        lesser, greater = self.partition(x_or_y, i)
+
+        lesser.PCA()
+        greater.PCA()
+
+        error = lesser.reconstruction_error() + greater.reconstruction_error()
+        return error, (lesser, greater)
+
+    #
+    # Plotting
+    #
+
+    def _plot_colours(self, number):
+        if not self.leaf:
+            for child in self.children:
+                child._plot_colours(number)
+            return
+
+        symbols = ['+', '^', '*', '>', 'o', 'v', 'x', '<']
+        plt.plot(*self.colours.xy.T,
+                 "k" + symbols[number[0] % len(symbols)],
+                 label=str(self))
+        number[0] += 1
+
+    def visualise(self):
+        """
+        Plots the subtree on a xy chromaticity diagram. Does not call
+        ``plt.show``.
+        """
+        plot_chromaticity_diagram_CIE1931(standalone=False)
+        self._plot_colours([0])
+        plt.legend()
+
+
+class Clustering:
+    """
+    Represents the process of clustering and optimisation. Instances store
+    shared data such as cmfs and the illuminant.
+
+    Operations involving the entire tree, such as optimisation and
+    reconstruction, are implemented here.
+    """
+
+    def __init__(
+            self,
+            sds,
+            shape,
+            cmfs=STANDARD_OBSERVER_CMFS['CIE 1931 2 Degree Standard Observer'],
+            illuminant=ILLUMINANT_SDS['D65']):
+        """
+        Parameters
+        ----------
+        sds : ndarray (n,m)
+            Reflectances of the ``n`` reference colours to be used for
+            optimisation.
+        shape : SpectralShape
+            Spectral shape of ``sds``.
+        cmfs : XYZ_ColourMatchingFunctions, optional
+            Standard observer colour matching functions.
+        illuminant : SpectralDistribution, optional
+            Illuminant spectral distribution.
+        """
+
+        self.sds = sds
+        self.shape = shape
+        self.wl = shape.range()
+        self.dw = self.wl[1] - self.wl[0]
+        self.cmfs = cmfs.copy().align(shape)
+        self.illuminant = illuminant.copy().align(shape)
+        self.xy_w = XYZ_to_xy(sd_to_XYZ(illuminant, cmfs=cmfs))
+
+        # The normalising constant used in sd_to_XYZ.
+        self.k = 1 / (np.sum(self.cmfs.values[:, 1]
+                      * self.illuminant.values) * self.dw)
+
+        colours = Colours(self, sds)
+        self.root = Node(self, colours)
+
+    def fast_sd_to_XYZ(self, R):
+        """
+        Compute the XYZ tristimulus values of a given reflectance. Faster for
+        humans, by using cmfs and the illuminant stored in the ''Clustering'',
+        thus avoiding unnecessary repetition. Faster for computers, by using
+        a very simple and direct method.
+
+        Parameters
+        ----------
+        R : ndarray
+            Reflectance with shape matching the one used to construct this
+            ``Clustering``.
+
+        Returns
+        -------
+        ndarray (3,)
+            XYZ tristimulus values, normalised to 1.
+        """
+
+        E = self.illuminant.values * R
+        return self.k * np.dot(E, self.cmfs.values) * self.dw
+
+    def reconstruct(self, XYZ):
+        """
+        Finds the appropriate node and reconstructs the reflectance for the
+        given XYZ tristimulus values.
+
+        Parameters
+        ==========
+        XYZ : ndarray, (3,)
+            *CIE XYZ* tristimulus values to recover the spectral distribution
+            from.
+
+        Returns
+        -------
+        SpectralDistribution
+            Recovered spectral distribution.
+        """
+
+        xy = XYZ_to_xy(XYZ)
+
+        def search(node):
+            if node.leaf:
+                return node
+
+            if xy[node.split_x_or_y] >= node.split_axis:
+                return search(node.children[0])
+            else:
+                return search(node.children[1])
+
+        node = search(self.root)
+        return node.reconstruct(XYZ)
+
+    def find_best_split(self):
+        """
+        Check every possible split in the entire tree to find the one that will
+        reduce the error the most.
+
+        Returns
+        -------
+        best_split : (Node, int, int)
+            Tuple representing the best split found. It contains the ``Node``
+            that should be split, the split direction (``x_or_y``) and
+            the colour index (``i``).
+        best_partition : (Node, Node)
+            Subnodes to be used as children for the leaf.
+
+        Raises
+        ------
+        ClusteringError
+            If the tree has already been split too finely, further splits will
+            not be possible and this exception will be raised.
+        """
+
+        best_new_error = None
+        total_error = self.root.total_reconstruction_error()
+
+        for leaf in self.root.leaves:
+            total_error_minus_leaf = total_error - leaf.reconstruction_error()
+
+            for x_or_y in [0, 1]:
+                for i in range(len(leaf.colours)):
+                    try:
+                        split_error, partition = leaf.split_quality(x_or_y, i)
+                    except ClusteringError:
+                        continue
+
+                    new_error = total_error_minus_leaf + split_error
+
+                    if best_new_error is None or new_error < best_new_error:
+                        best_new_error = new_error
+                        best_split = (leaf, x_or_y, i)
+                        best_partition = partition
+
+                    print('%10s  %s %4d  %g'
+                          % (leaf, ['x', 'y'][x_or_y], i, new_error))
+
+        if best_new_error is None:
+            raise ClusteringError('no more splits were possible')
+
+        return best_split, best_partition
+
+    def do_best_splits(self, repeats):
+        """
+        Find the best split and perform it, and repeat the operation the
+        specified amount of times.
+
+        Parameters
+        ----------
+        repeats : int
+            Number of splits.
+        """
+        for repeat in range(repeats):
+            try:
+                (leaf, x_or_y, i), partition = self.find_best_split()
+            except ClusteringError:
+                print('WARNING: only %d splits were possible' % repeat)
+                break
+
+            print('==== Splitting %s, x_or_y=%d, i=%d ===='
+                  % (leaf, x_or_y, i))
+            leaf.split(partition, x_or_y, i)
+
+    def write_python_dataset(self, path):
+        """
+        Write the clustering into a Python dataset compatible with Colour's
+        ``colour.recovery.otsu2018`` code.
+
+        Parameters
+        ----------
+        path : string
+            File path.
+        """
+
+        with open(path, 'w') as fd:
+            fd.write('# Autogenerated, do not modify\n\n')
+
+            fd.write('from numpy import array\n')
+            fd.write('from colour import SpectralShape\n\n\n')
+
+            fd.write('OTSU_2018_SPECTRAL_SHAPE = SpectralShape%s\n\n\n'
+                     % self.shape)
+
+            # Basis functions
+
+            fd.write('OTSU_2018_BASIS_FUNCTIONS = [\n')
+            for i, leaf in enumerate(self.root.leaves):
+                leaf._i = i  # For use when writing the selection function
+                for line in (repr(leaf.basis_functions) + ',').splitlines():
+                    fd.write('    %s\n' % line)
+            fd.write(']\n\n\n')
+
+            # Means
+
+            fd.write('OTSU_2018_MEANS = [\n')
+            for leaf in self.root.leaves:
+                for line in (repr(leaf.mean) + ',').splitlines():
+                    fd.write('    %s\n' % line)
+            fd.write(']\n\n\n')
+
+            # Cluster selection function
+
+            fd.write('def select_cluster_Otsu2018(xy):\n')
+            fd.write('    x, y = xy\n\n')
+
+            def write_if(node, indent):
+                if node.leaf:
+                    fd.write('    ' * indent)
+                    fd.write('return %d  # %s\n' % (node._i, node))
+                    return
+
+                fd.write('    ' * indent)
+                fd.write('if %s <= %s:\n' % (['x', 'y'][node.split_x_or_y],
+                                             repr(node.split_axis)))
+                write_if(node.children[0], indent + 1)
+
+                fd.write('    ' * indent)
+                fd.write('else:\n')
+                write_if(node.children[1], indent + 1)
+
+            write_if(self.root, 1)