ipa: ipu3: Add a histogram class

This class will be used at least by AGC algorithm when quantiles are
needed for example. It stores a cumulative frequency histogram. Going from
cumulative frequency back to per-bin values is a single subtraction, while
going the other way is a loop.

Signed-off-by: Jean-Michel Hautbois <jeanmichel.hautbois@ideasonboard.com>
Reviewed-by: Kieran Bingham <kieran.bingham@ideasonboard.com>
Tested-by: Jacopo Mondi <jacopo@jmondi.org>
Signed-off-by: Kieran Bingham <kieran.bingham@ideasonboard.com>

src/ipa/libipa/histogram.cpp

@@ -0,0 +1,153 @@
+/* SPDX-License-Identifier: BSD-2-Clause */
+/*
+ * Copyright (C) 2019, Raspberry Pi (Trading) Limited
+ *
+ * histogram.cpp - histogram calculations
+ */
+#include "histogram.h"
+
+#include <cmath>
+
+#include "libcamera/internal/log.h"
+
+/**
+ * \file histogram.h
+ * \brief Class to represent Histograms and manipulate them
+ */
+
+namespace libcamera {
+
+namespace ipa {
+
+/**
+ * \class Histogram
+ * \brief The base class for creating histograms
+ *
+ * This class stores a cumulative frequency histogram, which is a mapping that
+ * counts the cumulative number of observations in all of the bins up to the
+ * specified bin. It can be used to find quantiles and averages between quantiles.
+ */
+
+/**
+ * \brief Create a cumulative histogram
+ * \param[in] data A pre-sorted histogram to be passed
+ */
+Histogram::Histogram(Span<uint32_t> data)
+{
+	cumulative_.reserve(data.size());
+	cumulative_.push_back(0);
+	for (const uint32_t &value : data)
+		cumulative_.push_back(cumulative_.back() + value);
+}
+
+/**
+ * \fn Histogram::bins()
+ * \brief Retrieve the number of bins currently used by the Histogram
+ * \return Number of bins
+ */
+
+/**
+ * \fn Histogram::total()
+ * \brief Retrieve the total number of values in the data set
+ * \return Number of values
+ */
+
+/**
+ * \brief Cumulative frequency up to a (fractional) point in a bin.
+ * \param[in] bin The bin up to which to cumulate
+ *
+ * With F(p) the cumulative frequency of the histogram, the value is 0 at
+ * the bottom of the histogram, and the maximum is the number of bins.
+ * The pixels are spread evenly throughout the “bin” in which they lie, so that
+ * F(p) is a continuous (monotonically increasing) function.
+ *
+ * \return The cumulative frequency from 0 up to the specified bin
+ */
+uint64_t Histogram::cumulativeFrequency(double bin) const
+{
+	if (bin <= 0)
+		return 0;
+	else if (bin >= bins())
+		return total();
+	int b = static_cast<int32_t>(bin);
+	return cumulative_[b] +
+	       (bin - b) * (cumulative_[b + 1] - cumulative_[b]);
+}
+
+/**
+ * \brief Return the (fractional) bin of the point through the histogram
+ * \param[in] q the desired point (0 <= q <= 1)
+ * \param[in] first low limit (default is 0)
+ * \param[in] last high limit (default is UINT_MAX)
+ *
+ * A quantile gives us the point p = Q(q) in the range such that a proportion
+ * q of the pixels lie below p. A familiar quantile is Q(0.5) which is the median
+ * of a distribution.
+ *
+ * \return The fractional bin of the point
+ */
+double Histogram::quantile(double q, uint32_t first, uint32_t last) const
+{
+	if (last == UINT_MAX)
+		last = cumulative_.size() - 2;
+	ASSERT(first <= last);
+
+	uint64_t item = q * total();
+	/* Binary search to find the right bin */
+	while (first < last) {
+		int middle = (first + last) / 2;
+		/* Is it between first and middle ? */
+		if (cumulative_[middle + 1] > item)
+			last = middle;
+		else
+			first = middle + 1;
+	}
+	ASSERT(item >= cumulative_[first] && item <= cumulative_[last + 1]);
+
+	double frac;
+	if (cumulative_[first + 1] == cumulative_[first])
+		frac = 0;
+	else
+		frac = (item - cumulative_[first]) / (cumulative_[first + 1] - cumulative_[first]);
+	return first + frac;
+}
+
+/**
+ * \brief Calculate the mean between two quantiles
+ * \param[in] lowQuantile low Quantile
+ * \param[in] highQuantile high Quantile
+ *
+ * Quantiles are not ideal for metering as they suffer several limitations.
+ * Instead, a concept is introduced here: inter-quantile mean.
+ * It returns the mean of all pixels between lowQuantile and highQuantile.
+ *
+ * \return The mean histogram bin value between the two quantiles
+ */
+double Histogram::interQuantileMean(double lowQuantile, double highQuantile) const
+{
+	ASSERT(highQuantile > lowQuantile);
+	/* Proportion of pixels which lies below lowQuantile */
+	double lowPoint = quantile(lowQuantile);
+	/* Proportion of pixels which lies below highQuantile */
+	double highPoint = quantile(highQuantile, static_cast<uint32_t>(lowPoint));
+	double sumBinFreq = 0, cumulFreq = 0;
+
+	for (double p_next = floor(lowPoint) + 1.0;
+	     p_next <= ceil(highPoint);
+	     lowPoint = p_next, p_next += 1.0) {
+		int bin = floor(lowPoint);
+		double freq = (cumulative_[bin + 1] - cumulative_[bin])
+			* (std::min(p_next, highPoint) - lowPoint);
+
+		/* Accumulate weigthed bin */
+		sumBinFreq += bin * freq;
+		/* Accumulate weights */
+		cumulFreq += freq;
+	}
+	/* add 0.5 to give an average for bin mid-points */
+	return sumBinFreq / cumulFreq + 0.5;
+}
+
+} /* namespace ipa */
+
+} /* namespace libcamera */