879 lines
26 KiB
C++
879 lines
26 KiB
C++
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#include "tcenterlinevectP.h"
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//==========================================================================
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//************************
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//* Polygonization *
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//************************
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//--------------------------------------------------------------------------
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//===============================
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// Raw Borders Extraction
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//===============================
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//Raw contour class definition
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class RawBorderPoint
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{
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TPoint m_position;
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int m_ambiguousTurn; //used to remember cases of multiple turning directions
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//in a RawBorder extraction.
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public:
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RawBorderPoint() : m_ambiguousTurn(0) {}
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RawBorderPoint(int i, int j) : m_position(i, j), m_ambiguousTurn(0) {}
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inline TPoint pos() const { return m_position; }
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inline int x() const { return m_position.x; }
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inline int y() const { return m_position.y; }
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enum { left = 1,
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right = 2 }; //Direction taken at ambiguous turning point
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inline int getAmbiguous() const { return m_ambiguousTurn; }
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inline void setAmbiguous(int direction) { m_ambiguousTurn = direction; }
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};
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//--------------------------------------------------------------------------
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class RawBorder : public std::vector<RawBorderPoint>
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{
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int m_xExternal; //x coordinate of a specific vertex in the outer
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//RawBorder which contains this inner one.
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TPointD *m_coordinateSums;
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TPointD *m_coordinateSquareSums;
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double *m_coordinateMixedSums;
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public:
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RawBorder() {}
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~RawBorder() {}
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void setXExternalPixel(int a) { m_xExternal = a; }
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int xExternalPixel() { return m_xExternal; }
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TPointD *&sums() { return m_coordinateSums; }
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TPointD *&sums2() { return m_coordinateSquareSums; }
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double *&sumsMix() { return m_coordinateMixedSums; }
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};
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//--------------------------------------------------------------------------
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//Of course we don't want RawBorders to be entirely copied whenever STL
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//requires to resize a BorderFamily...
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typedef std::vector<RawBorder *> BorderFamily;
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typedef std::vector<BorderFamily> BorderList;
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//--------------------------------------------------------------------------
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//==========================================================================
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//============================
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// Polygonizer Locals
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//============================
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namespace
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{
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//Const names
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enum { white = 0,
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black = 1 };
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enum { inner = 0,
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outer = 1,
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none = 2,
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invalid = 3 };
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}
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//=======================================================================================
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//-------------------------------
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// Raster Data Functions
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//-------------------------------
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//NOTA: Il tono di un TPixelCM32 rappresenta la transizione tra colore ink e colore paint.
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// di solito, se il tono e' basso abbiamo un colore ink - che puo' anche essere bianco,
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// in teoria...
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// Sarebbe opportuno che il vettorizzatore riconoscesse - per colormap - il colore
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// delle strokes.
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// Approcci: a) la Signaturemap diventa *piu'* di una bitmap e si seguono le outline
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// dei singoli colori.
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// => Sconnessioni tra i colori adiacenti. Bisogna introdurre la distanza tra
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// colori per seguire l'outline (ossia, i pixel tenuti a dx della outline
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// devono essere simili).
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//
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// b) Una volta vettorizzato tutto, si sceglie il colore della stroke.
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// E' possibile controllare il colore sui vertici delle sequenze semplificate
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// e fare una media.
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//NOTE: Transparency makes colors fade to white. Full transparent black pixels are considered white.
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//--------------------------------------------------------------------------
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template <typename T>
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class PixelEvaluator
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{
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TRasterPT<T> m_ras;
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int m_threshold;
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public:
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PixelEvaluator(const TRasterPT<T> &ras, int threshold)
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: m_ras(ras), m_threshold(threshold) {}
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inline unsigned char getBlackOrWhite(int x, int y);
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};
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//--------------------------------------------------------------------------
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template <>
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inline unsigned char PixelEvaluator<TPixel32>::getBlackOrWhite(int x, int y)
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{
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//return ras->pixels(y)[x].r + 2 * ras->pixels(y)[x].g + ras->pixels(y)[x].b <
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// threshold * (ras->pixels(y)[x].m / 255.0);
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//NOTE: Green is considered twice brighter than red or blue channel.
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//Using Value of HSV color model
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return tmax(m_ras->pixels(y)[x].r, tmax(m_ras->pixels(y)[x].g, m_ras->pixels(y)[x].b)) <
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m_threshold * (m_ras->pixels(y)[x].m / 255.0);
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//Using Lightness of HSV color model
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//return (max(ras->pixels(y)[x].r, max(ras->pixels(y)[x].g, ras->pixels(y)[x].b)) +
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// min(ras->pixels(y)[x].r, min(ras->pixels(y)[x].g, ras->pixels(y)[x].b))) / 2.0 <
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// threshold * (ras->pixels(y)[x].m / 255.0);
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//Using (relative) Luminance
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//return 0.2126 * ras->pixels(y)[x].r + 0.7152 * ras->pixels(y)[x].g + 0.0722 * ras->pixels(y)[x].b <
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// threshold * (ras->pixels(y)[x].m / 255.0);
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}
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template <>
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inline unsigned char PixelEvaluator<TPixelGR8>::getBlackOrWhite(int x, int y)
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{
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return m_ras->pixels(y)[x].value < m_threshold;
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}
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template <>
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inline unsigned char PixelEvaluator<TPixelCM32>::getBlackOrWhite(int x, int y)
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{
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return m_ras->pixels(y)[x].getTone() < m_threshold;
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}
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//--------------------------------------------------------------------------
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//Signaturemap format:
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// stores a map of bytes, whose first bit represents the color (black/white) of corresponding pixel, and
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// the rest its 'signature', used as an int to store information.
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//NOTE: given a TRaster32, the corresponding Signaturemap constructed is intended 0(white)-padded
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class Signaturemap
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{
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unsigned char *m_array;
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int m_rowSize;
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int m_colSize;
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public:
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Signaturemap(const TRasterP &ras, int threshold);
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~Signaturemap() { delete[] m_array; }
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template <typename T>
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void readRasterData(const TRasterPT<T> &ras, int threshold);
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inline int getRowSize() const { return m_rowSize; }
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inline int getColSize() const { return m_colSize; }
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unsigned char *pixelByte(int x, int y) { return &m_array[(y + 1) * m_rowSize + x + 1]; }
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bool getBitmapColor(int x, int y) const
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{
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return m_array[(y + 1) * m_rowSize + x + 1] & 1;
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}
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inline unsigned char getSignature(int x, int y) const
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{
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return m_array[(y + 1) * m_rowSize + x + 1] >> 1;
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}
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void setSignature(int x, int y, int val)
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{
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unsigned char *pixel = pixelByte(x, y);
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*pixel &= 1;
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*pixel |= (val << 1); //Si puo' fare meglio??
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}
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};
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//--------------------------------------------------------------------------
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Signaturemap::Signaturemap(const TRasterP &ras, int threshold)
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{
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//Extrapolate raster type
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TRaster32P rr = (TRaster32P)ras;
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TRasterGR8P rgr = (TRasterGR8P)ras;
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TRasterCM32P rt = (TRasterCM32P)ras;
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assert(rr || rgr || rt);
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//Read raster data
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if (rr) {
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rr->lock();
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readRasterData(rr, threshold);
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rr->unlock();
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} else if (rgr) {
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rgr->lock();
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readRasterData(rgr, threshold);
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rgr->unlock();
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} else {
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rt->lock();
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readRasterData(rt, threshold);
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rt->unlock();
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}
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}
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//--------------------------------------------------------------------------
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template <typename T>
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void Signaturemap::readRasterData(const TRasterPT<T> &ras, int threshold)
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{
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unsigned char *currByte;
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int x, y;
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PixelEvaluator<T> evaluator(ras, threshold);
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m_rowSize = ras->getLx() + 2;
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m_colSize = ras->getLy() + 2;
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m_array = new unsigned char[m_rowSize * m_colSize];
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memset(m_array, none << 1, m_rowSize);
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currByte = m_array + m_rowSize;
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for (y = 0; y < ras->getLy(); ++y) {
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*currByte = none << 1;
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currByte++;
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for (x = 0; x < ras->getLx(); ++x, ++currByte)
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*currByte = evaluator.getBlackOrWhite(x, y) | (none << 1);
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*currByte = none << 1;
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currByte++;
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}
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memset(currByte, none << 1, m_rowSize);
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}
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//--------------------------------------------------------------------------
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//Minority check for amiguous turning directions
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inline bool getMinorityCheck(const Signaturemap &ras, int x, int y)
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{
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//Assumes (x,y) is ambiguous case: 2 immediate surrounding pixels are white and 2 black
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return (ras.getBitmapColor(x + 1, y) +
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ras.getBitmapColor(x + 1, y - 1) +
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ras.getBitmapColor(x - 2, y) +
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ras.getBitmapColor(x - 2, y - 1) +
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ras.getBitmapColor(x - 1, y + 1) +
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ras.getBitmapColor(x - 1, y - 2) +
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ras.getBitmapColor(x, y + 1) +
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ras.getBitmapColor(x, y - 2)) > 4;
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}
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//--------------------------------------------------------------------------
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//Sets signature of a given border
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inline void setSignature(Signaturemap &ras, const RawBorder &border, int val)
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{
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unsigned int j;
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int yOld;
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//Set border's alpha channel
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yOld = border.back().y();
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for (j = 0; j < border.size(); ++j) {
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if (border[j].y() < yOld) {
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ras.setSignature(border[j].x(), border[j].y(), val);
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} else if (border[j].y() > yOld) {
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ras.setSignature(border[j].x(), yOld, val);
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}
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yOld = border[j].y();
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}
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}
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//==========================================================================
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//-------------------------------
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// Raw Borders Extraction
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//-------------------------------
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//RawBorderPoints correspond to lower-left pixel corners.
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//EXAMPLE: (0,0) is the lower-left *corner* of the image, whereas (0,0) also
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// represents coordinates of the lower-left *pixel*.
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//NOTE: 'Ambiguous turning' vertices are those of kind:
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//
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// B|W W|B
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// -x- -or- -x-
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// W|B B|W
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//
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//Keeping B on the right of our path-seeking direction, we may either turn
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//left or right at these points.
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RawBorder *extractPath(Signaturemap &ras, int x0, int y0,
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int pathType, int xOuterPixel, int despeckling)
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{
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RawBorder *path = new RawBorder;
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int x, y;
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short dirX, dirY;
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long int area = 0;
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bool nextLeftPixel, nextRightPixel;
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if (pathType == outer) {
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dirX = 0;
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dirY = 1;
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} else {
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dirX = 1;
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dirY = 0;
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area += y0;
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path->setXExternalPixel(xOuterPixel);
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}
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path->push_back(RawBorderPoint(x0, y0));
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//Check here if (x0, y0) is an ambiguous-direction point
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nextLeftPixel = ras.getBitmapColor(x0 + (dirY - dirX - 1) / 2, y0 + (-dirY - dirX - 1) / 2);
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nextRightPixel = ras.getBitmapColor(x0 + (-dirX - dirY - 1) / 2, y0 + (dirX - dirY - 1) / 2);
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if ((nextRightPixel == black) && (nextLeftPixel == white))
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path->back().setAmbiguous(dirX ? RawBorderPoint::left : RawBorderPoint::right);
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//Begin path extraction
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for (x = x0 + dirX, y = y0 + dirY; !(x == x0 && y == y0); x += dirX, y += dirY) {
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path->push_back(RawBorderPoint(x, y));
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//Calculate next direction
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nextLeftPixel = ras.getBitmapColor(x + (dirX - dirY - 1) / 2, y + (dirY + dirX - 1) / 2);
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nextRightPixel = ras.getBitmapColor(x + (dirX + dirY - 1) / 2, y + (dirY - dirX - 1) / 2);
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if ((nextRightPixel == black) && (nextLeftPixel == black)) {
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//Left Turn
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std::swap(dirY, dirX);
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dirX = -dirX;
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} else if ((nextRightPixel == white) && (nextLeftPixel == white)) {
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//Right Turn
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std::swap(dirY, dirX);
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dirY = -dirY;
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} else if ((nextRightPixel == white) && (nextLeftPixel == black)) {
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//path->back().setAmbiguous();
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//Do a surrounding check and connect minority color
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if (getMinorityCheck(ras, x, y) == black) {
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std::swap(dirY, dirX);
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dirY = -dirY;
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path->back().setAmbiguous(RawBorderPoint::right);
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} //right turn
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else {
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std::swap(dirY, dirX);
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dirX = -dirX;
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path->back().setAmbiguous(RawBorderPoint::left);
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} //left turn
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}
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//Also calculate border area
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area += y * dirX;
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//And sign treated pixel
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if (dirY != 0)
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ras.setSignature(x, y + (dirY - 1) / 2, pathType);
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}
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//If the inner region's overall area is under a given threshold,
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//then erase it (intended as image noise).
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if (abs(area) < despeckling) {
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setSignature(ras, *path, invalid);
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delete path;
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path = 0;
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}
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return path;
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}
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//--------------------------------------------------------------------------
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BorderList *extractBorders(const TRasterP &ras, int threshold, int despeckling)
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{
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Signaturemap byteImage(ras, threshold);
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BorderList *borderHierarchy = new BorderList;
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vector<RawBorder *> outerBorders;
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list<RawBorder *> innerBorders;
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RawBorder *foundPath;
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int x, y;
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bool Color, oldColor;
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int xOuterPixel = 0;
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bool enteredRegionType;
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unsigned char signature;
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//Traverse image to extract raw borders
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for (y = 0; y < ras->getLy(); ++y) {
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oldColor = white;
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enteredRegionType = outer;
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for (x = 0; x < ras->getLx(); ++x) {
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if (oldColor ^ (Color = byteImage.getBitmapColor(x, y))) {
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//Region type changes
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enteredRegionType = !enteredRegionType;
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if ((signature = byteImage.getSignature(x, y)) == none) {
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//We've found a border
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if (foundPath = extractPath(byteImage, x, y, !enteredRegionType, xOuterPixel, despeckling))
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if (enteredRegionType == outer)
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innerBorders.push_back(foundPath);
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else
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outerBorders.push_back(foundPath);
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}
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//If leaving a white region, remember it - in order to establish
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//border hierarchy in the future
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if (enteredRegionType == inner && signature != invalid)
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xOuterPixel = x;
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//Invalid pixels got signed by a cut-out path, due to insufficient area
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if (signature == invalid)
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byteImage.setSignature(x, y, none); //Restore them now
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oldColor = Color;
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}
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}
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}
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//Now, we have all borders found, but no hierarchy between them.
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unsigned int i;
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list<RawBorder *>::iterator l;
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//Build hierarchy
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innerBorders.push_front(0); //Just to keep a fixed list head
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for (i = 0; i < outerBorders.size(); ++i) {
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//Initialize a border family
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borderHierarchy->push_back(BorderFamily());
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borderHierarchy->back().push_back(outerBorders[i]);
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//Reset outerBorders[i]'s signature
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setSignature(byteImage, *outerBorders[i], none);
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//Now check inner borders for insideness - check if the outerPixel
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//remembered in path extraction has been cleared
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for (l = innerBorders.begin(), ++l; l != innerBorders.end(); ++l) {
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if (byteImage.getSignature((*l)->xExternalPixel(), (**l)[0].y()) == none) {
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borderHierarchy->back().push_back(*l);
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setSignature(byteImage, **l, none);
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l = innerBorders.erase(l);
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--l;
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}
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}
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}
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return borderHierarchy;
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}
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//--------------------------------------------------------------------------
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//==================================
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// Calculate optimal polygons
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//==================================
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//The optimal polygon for a given original border is found like:
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// 1) Find couples (i,k(i)), so that k(i) be the largest k:
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// d(j,ik) <= 1; for *all* i<j<k. (d is infinite-norm distance)
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// It can be shown that such a condition is equivalent to:
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// exists line l : d(l,j)<=1/2, for all i<=j<=k(i).
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// 2) Clean the above couples - find couples (i,l(i)):
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// l(i)=min{k(j)}, j=i..n.
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// 3) Calculate clipped couples (i',l'); where i'=i+1, l'=l(i)-1.
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// 4) Calculate sums for path penalties.
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// 5) Apply optimality algorithm.
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//NOTE: Weak simpleness reads like: a set of polygons is weak-simple if no edge
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// *crosses* another edge. Superposition and collision of edges with vertices
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// are still admitted.
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// => It can be shown that due to 1) and special conditions on ambiguous
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// turnings applied in both 1) and 3), weak simpleness is insured in
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// our polygonization.
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//--------------------------------------------------------------------------
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//Helper functions/classes: circular-indexed vectors
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//returns 1 whenever the triple (a,b,c) is 'circular' mod n.
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//NOTE: We'll find useful taking (i,i,j) as 1 and (i,j,j) as 0.
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inline bool isCircular(int a, int b, int c)
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{
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return a <= c ? a <= b && b < c : c > b || b >= a;
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}
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//--------------------------------------------------------------------------
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//Extracts a 'next corner' array - helps improving overall speed
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inline int *findNextCorners(RawBorder &path)
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{
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int i, currentCorner;
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int *corners = new int[path.size()];
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//NOTE: 0 is a corner, due to the path extraction procedure.
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|
currentCorner = 0;
|
|
for (i = path.size() - 1; i >= 0; --i) {
|
|
if (path[currentCorner].x() != path[i].x() &&
|
|
path[currentCorner].y() != path[i].y())
|
|
currentCorner = i + 1;
|
|
corners[i] = currentCorner;
|
|
}
|
|
|
|
return corners;
|
|
}
|
|
|
|
//--------------------------------------------------------------------------
|
|
|
|
//Calculate furthest k satisfying 1) for all fixed i.
|
|
inline int *furthestKs(RawBorder &path, int *&nextCorners)
|
|
{
|
|
|
|
int n = path.size();
|
|
int *kVector = new int[n];
|
|
|
|
enum { left,
|
|
up,
|
|
right,
|
|
down };
|
|
int directionsOccurred[4];
|
|
|
|
nextCorners = findNextCorners(path);
|
|
|
|
int i, j, k;
|
|
TPoint shift;
|
|
TPoint leftConstraint, rightConstraint, violatedConstraint;
|
|
TPoint newLeftConstraint, newRightConstraint;
|
|
TPoint jPoint, jNextPoint, iPoint, direction;
|
|
|
|
int directionSignature;
|
|
|
|
for (i = 0; i < n; ++i) {
|
|
//Initialize search
|
|
leftConstraint = rightConstraint = TPoint();
|
|
directionsOccurred[0] = directionsOccurred[1] = directionsOccurred[2] =
|
|
directionsOccurred[3] = 0;
|
|
j = i;
|
|
jNextPoint = iPoint = path[i].pos();
|
|
|
|
//Search for k(i)
|
|
while (1) {
|
|
|
|
//NOTE: Here using TPoint::operator= is less effective than setting
|
|
//its x and y components directly...
|
|
|
|
jPoint = jNextPoint;
|
|
jNextPoint = path[nextCorners[j]].pos();
|
|
|
|
//Update directions count
|
|
directionSignature = jNextPoint.x > jPoint.x ? right : jNextPoint.x < jPoint.x ? left
|
|
: jNextPoint.y > jPoint.y ? up : down;
|
|
directionsOccurred[directionSignature] = 1;
|
|
|
|
//If all 4 axis directions occurred, quit
|
|
if (directionsOccurred[left] && directionsOccurred[right] &&
|
|
directionsOccurred[up] && directionsOccurred[down]) {
|
|
k = j;
|
|
goto foundK;
|
|
}
|
|
|
|
//Update displacement from i
|
|
shift = jNextPoint - iPoint;
|
|
|
|
//Test j against constraints
|
|
//if(cross(shift, leftConstraint)<0 || cross(shift, rightConstraint)>0)
|
|
if (cross(shift, leftConstraint) < 0) {
|
|
violatedConstraint = leftConstraint;
|
|
break;
|
|
}
|
|
if (cross(shift, rightConstraint) > 0) {
|
|
violatedConstraint = rightConstraint;
|
|
break;
|
|
}
|
|
|
|
//Update constraints
|
|
if (abs(shift.x) > 1 || abs(shift.y) > 1) {
|
|
|
|
newLeftConstraint.x = shift.x +
|
|
(shift.y < 0 || (shift.y == 0 && shift.x < 0) ? 1 : -1);
|
|
newLeftConstraint.y = shift.y +
|
|
(shift.x > 0 || (shift.x == 0 && shift.y < 0) ? 1 : -1);
|
|
|
|
if (cross(newLeftConstraint, leftConstraint) >= 0)
|
|
leftConstraint = newLeftConstraint;
|
|
|
|
newRightConstraint.x = shift.x +
|
|
(shift.y > 0 || (shift.y == 0 && shift.x < 0) ? 1 : -1);
|
|
|
|
newRightConstraint.y = shift.y +
|
|
(shift.x < 0 || (shift.x == 0 && shift.y < 0) ? 1 : -1);
|
|
|
|
if (cross(newRightConstraint, rightConstraint) <= 0)
|
|
rightConstraint = newRightConstraint;
|
|
}
|
|
|
|
//Imposing strict constraint for ambiguous turnings, to ensure polygons' weak simpleness.
|
|
//Has to be defined *outside* abs checks.
|
|
if (path[nextCorners[j]].getAmbiguous()) {
|
|
if (path[nextCorners[j]].getAmbiguous() == RawBorderPoint::left)
|
|
rightConstraint = shift;
|
|
else
|
|
leftConstraint = shift;
|
|
}
|
|
|
|
j = nextCorners[j];
|
|
}
|
|
|
|
//At this point, constraints are violated by the next corner.
|
|
//Then, search for the last k between j and corners[j] not violating them.
|
|
|
|
direction = convert(normalize(convert(jNextPoint - jPoint)));
|
|
k = (j + cross(jPoint - iPoint, violatedConstraint) / cross(violatedConstraint, direction)) % n;
|
|
|
|
foundK:
|
|
|
|
kVector[i] = k;
|
|
}
|
|
|
|
return kVector;
|
|
}
|
|
|
|
//--------------------------------------------------------------------------
|
|
|
|
// Now find the effective intervals inside which we can define possible
|
|
// arcs approximating the given raw border:
|
|
// for every a in [i,res[i]], the arc connecting border[i] and
|
|
// border[a] will be a possible one.
|
|
inline int *calculateForwardArcs(RawBorder &border, bool ambiguitiesCheck)
|
|
{
|
|
int i, j, n = (int)border.size();
|
|
|
|
int *nextCorners;
|
|
int *k = furthestKs(border, nextCorners);
|
|
int *K = new int[n];
|
|
int *res = new int[n];
|
|
|
|
//find K[i]= min {k[j]}, j=i..n-1.
|
|
for (i = 0; i < n; ++i) {
|
|
for (j = i, K[i] = k[i]; isCircular(i, j, K[i]); j = (j + 1) % n)
|
|
if (isCircular(j, k[j], K[i]))
|
|
K[i] = k[j];
|
|
}
|
|
|
|
//Finally, we perform the following clean-up operations:
|
|
// first, extremities of [i,K[i]] are clipped away, to obtain a
|
|
// smoother optimal polygon (and deal with cases like the unitary
|
|
// square);
|
|
// second, arcs of the kind [i,j] with j<i, become [i,n].
|
|
|
|
for (i = n - 1, j = 0; j < n; i = j, ++j) {
|
|
res[j] = K[i] < j ? (K[i] == 0 ? n - 1 : n) : K[i] - 1;
|
|
}
|
|
|
|
//Amibiguities check for vertex and edge superpositions. Prevent problems in the forecoming
|
|
//straight-skeleton thinning process.
|
|
|
|
if (ambiguitiesCheck) {
|
|
for (i = 1; nextCorners[i] > 0; i = nextCorners[i]) {
|
|
if (border[i].getAmbiguous() == RawBorderPoint::right) {
|
|
//Check vertices from i (excluded) to res[res[i]]; if in it there exists vertex k so that pos(k)==pos(i)...
|
|
//This prevents the existence of 0 degree angles in the optimal polygon.
|
|
|
|
int rrPlus1 = (res[res[i] % n] + 1) % n;
|
|
|
|
for (j = nextCorners[i];
|
|
isCircular(i, j, rrPlus1) && j != i; //remember that isCircular(a,a,b) == 1 ...
|
|
j = nextCorners[j]) {
|
|
if (border[j].getAmbiguous() && (border[j].pos() == border[i].pos())) {
|
|
res[res[i] % n] = j - 1;
|
|
assert((res[i] % n) != j - 1);
|
|
|
|
//Further, ensure res is increasing
|
|
for (int k = res[i] % n; res[k] >= j - 1 && k >= 0; --k) {
|
|
res[k] = j - 1;
|
|
assert(k != j - 1);
|
|
}
|
|
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
delete[] k;
|
|
delete[] K;
|
|
delete[] nextCorners;
|
|
|
|
return res;
|
|
}
|
|
|
|
//--------------------------------------------------------------------------
|
|
|
|
//Let sum[i] and sum2[i] be respectively the sums of vertex coordinates
|
|
//from 0 to i, and the sums of their squares; sumsMix contain sums of
|
|
//xy terms.
|
|
inline void calculateSums(RawBorder &path)
|
|
{
|
|
unsigned int i, n = path.size();
|
|
TPointD currentRelativePos;
|
|
|
|
path.sums() = new TPointD[n + 1];
|
|
path.sums2() = new TPointD[n + 1];
|
|
path.sumsMix() = new double[n + 1];
|
|
|
|
path.sums()[0].x = path.sums()[0].y = path.sums2()[0].x = path.sums2()[0].y = 0;
|
|
for (i = 1; i < path.size(); ++i) {
|
|
currentRelativePos = convert(path[i].pos() - path[0].pos());
|
|
|
|
path.sums()[i] = path.sums()[i - 1] + currentRelativePos;
|
|
|
|
path.sums2()[i].x = path.sums2()[i - 1].x + currentRelativePos.x * currentRelativePos.x;
|
|
path.sums2()[i].y = path.sums2()[i - 1].y + currentRelativePos.y * currentRelativePos.y;
|
|
|
|
path.sumsMix()[i] = path.sumsMix()[i - 1] + currentRelativePos.x * currentRelativePos.y;
|
|
}
|
|
|
|
// path[n] is virtually intended as path[0], but we prefer to introduce
|
|
// it in the optimality algorithm's count
|
|
path.sums()[n].x = path.sums()[n].y = path.sums2()[n].x = path.sums2()[n].y = 0;
|
|
}
|
|
|
|
//--------------------------------------------------------------------------
|
|
|
|
//Let a,b the index-extremities of an arc of this path.
|
|
//Then return its penalty.
|
|
inline double penalty(RawBorder &path, int a, int b)
|
|
{
|
|
int n = b - a + 1;
|
|
|
|
TPointD v = convert(rotate90(path[b == path.size() ? 0 : b].pos() - path[a].pos()));
|
|
TPointD sum = path.sums()[b] - path.sums()[a];
|
|
TPointD sum2 = path.sums2()[b] - path.sums2()[a];
|
|
double sumMix = path.sumsMix()[b] - path.sumsMix()[a];
|
|
|
|
double F1 = sum2.x - 2 * sum.x * path[a].x() + n * path[a].x() * path[a].x();
|
|
double F2 = sum2.y - 2 * sum.y * path[a].y() + n * path[a].y() * path[a].y();
|
|
double F3 = sumMix - sum.x * path[a].y() - sum.y * path[a].x() + n * path[a].x() * path[a].y();
|
|
|
|
return sqrt((v.y * v.y * F1 + v.x * v.x * F2 - 2 * v.x * v.y * F3) / n);
|
|
}
|
|
|
|
//--------------------------------------------------------------------------
|
|
|
|
//NOTA: Il seguente algoritmo di riduzione assicura la semplicita' (debole) dei poligoni prodotti.
|
|
//
|
|
|
|
inline void reduceBorder(RawBorder &border, Contour &res, bool ambiguitiesCheck)
|
|
{
|
|
int i, j, k, a, *b, n = border.size(), m;
|
|
double newPenalty;
|
|
int minPenaltyNext;
|
|
int *minPenaltyNextArray = new int[n];
|
|
|
|
//Calculate preliminary infos
|
|
int *longestArcFrom = calculateForwardArcs(border, ambiguitiesCheck);
|
|
calculateSums(border);
|
|
|
|
double *penaltyToEnd = new double[n + 1];
|
|
|
|
//EXPLANATION:
|
|
//The fastest way to extract the optimal reduced border is based on the
|
|
//weakly monotonic property of longestArc[].
|
|
//The minimal number of its vertices 'm' is easily found by
|
|
//traversing the path with the longest step allowed. Let b[] be that
|
|
//succession; then, given res[i], it has to be reached by a vertex in
|
|
//the interval: {a[i-1], .. , b[i-1]}, where longestArc[a[i-1]]=a[i],
|
|
//longestArc[a[i-1]-1]<a[i], and a[m]=n.
|
|
|
|
//Calculate m
|
|
for (i = 0, m = 0; i < n; i = longestArcFrom[i])
|
|
++m;
|
|
|
|
//Calculate b[]
|
|
b = new int[m + 1];
|
|
b[m] = n;
|
|
for (i = 0, j = 0; j < m; i = longestArcFrom[i], ++j)
|
|
b[j] = i;
|
|
|
|
//NOTE: a[] need not be completely found - we just remember the
|
|
//a=a[j+1] currently needed.
|
|
|
|
//Now, build the optimal polygon
|
|
for (j = m - 1, a = n; j >= 0; --j) {
|
|
for (k = b[j]; k >= 0 && longestArcFrom[k] >= a; --k) {
|
|
penaltyToEnd[k] = infinity;
|
|
for (i = a; i <= longestArcFrom[k]; ++i) {
|
|
newPenalty = penaltyToEnd[i] + penalty(border, k, i);
|
|
if (newPenalty < penaltyToEnd[k])
|
|
penaltyToEnd[k] = newPenalty;
|
|
minPenaltyNext = i;
|
|
}
|
|
minPenaltyNextArray[k] = minPenaltyNext;
|
|
}
|
|
a = k + 1;
|
|
}
|
|
|
|
//Finally, read off the optimal polygon
|
|
|
|
res.resize(m);
|
|
for (i = j = 0; i < n; i = minPenaltyNextArray[i], ++j) {
|
|
res[j] = ContourNode(border[i].x(), border[i].y());
|
|
|
|
//Ambiguities are still remembered in the output polygon.
|
|
if (border[i].getAmbiguous() == RawBorderPoint::left)
|
|
res[j].setAttribute(ContourNode::AMBIGUOUS_LEFT);
|
|
if (border[i].getAmbiguous() == RawBorderPoint::right)
|
|
res[j].setAttribute(ContourNode::AMBIGUOUS_RIGHT);
|
|
}
|
|
|
|
delete[] longestArcFrom;
|
|
delete[] minPenaltyNextArray;
|
|
delete[] border.sums();
|
|
delete[] border.sums2();
|
|
delete[] border.sumsMix();
|
|
delete[] penaltyToEnd;
|
|
delete[] b;
|
|
}
|
|
|
|
//--------------------------------------------------------------------------
|
|
|
|
//Reduction caller and list copier.
|
|
inline void reduceBorders(BorderList &borders, Contours &result, bool ambiguitiesCheck)
|
|
{
|
|
unsigned int i, j;
|
|
|
|
//Initialize output container
|
|
result.resize(borders.size());
|
|
|
|
//Copy results
|
|
for (i = 0; i < borders.size(); ++i) {
|
|
result[i].resize(borders[i].size());
|
|
for (j = 0; j < borders[i].size(); ++j) {
|
|
reduceBorder(*borders[i][j], result[i][j], ambiguitiesCheck);
|
|
delete borders[i][j];
|
|
}
|
|
}
|
|
}
|
|
|
|
//--------------------------------------------------------------------------
|
|
|
|
//===========================
|
|
// Polygonization Main
|
|
//===========================
|
|
|
|
//Extracts a polygonal, minimal yet faithful representation of image contours
|
|
//Contours* polygonize(const TRasterP &ras){
|
|
void polygonize(const TRasterP &ras, Contours &polygons, VectorizerCoreGlobals &g)
|
|
{
|
|
BorderList *borders;
|
|
|
|
borders = extractBorders(ras, g.currConfig->m_threshold, g.currConfig->m_despeckling);
|
|
reduceBorders(*borders, polygons, g.currConfig->m_maxThickness > 0.0);
|
|
}
|