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TextDetection.cpp
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/*
*Copyright 2011 Miquel Angel Farre Guiu
*
*This file is part of my personal textDetector implementation based in the Microsoft Research Publication
*"Detecting Text in Natural Scenes with Stroke Width Transform".
*
*textDetector is free software: you can redistribute it and/or modify it under the terms of the GNU General
*Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option)
*any later *version.
*
*textDetector is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied
*warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
*
*You should have received a copy of the GNU General Public License along with Foobar. If not, see http://www.gnu.org/licenses/.
*
*To compile, run: gcc `pkg-config --cflags --libs opencv` -o textDetector src/TextDetection.cpp src/pseudocolor.c
*/
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/connected_components.hpp>
#include <boost/unordered_map.hpp>
#include <boost/graph/floyd_warshall_shortest.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <cassert>
#include <cmath>
#include <stdio.h>
#include <iostream>
#include <opencv/cv.h>
#include <opencv/highgui.h>
#include <opencv/cxcore.h>
#include <math.h>
#include <time.h>
#include <utility>
#include <algorithm>
#include <vector>
#include <limits.h>
#include "TextDetection.h"
#include "cv_util.h"
#define PI 3.14159265
#define DEBUG(x) x
//#define DEBUG(x)
using namespace std;
//GEOMETRIC FUNCTIONS
float orientation2D(const Point2d& p, const Point2d& q, const Point2d& r)
{
float area = (((float)q.x - (float)p.x) * ((float)r.y - (float)p.y)) - (((float)r.x - (float)p.x) * ((float)q.y - (float)p.y));
return area;
}
bool classifyIntersection(Point2d p0, Point2d p1, Point2d q0, Point2d q1)
{
float first = orientation2D(p0, p1, q0);
float second = orientation2D(p0, p1, q1);
//Segments are crossing
if(first*second<0){
//check again inverting points
float first2 = orientation2D(q0, q1, p0);
float second2 = orientation2D(q0, q1, p1);
//crossing
if (first2*second2<0){
return true;
}
//in contact by a point
else if(first2 ==0 || second2 ==0){
return false;
}
else {
return false;
}
}
}
//
std::vector < std::pair < CvPoint,
CvPoint > >findBoundingBoxes (std::vector < std::vector < Point2d >
>&components, std::vector < Chain > &chains,
std::vector < std::pair < Point2d,
Point2d > >&compBB, IplImage * output)
{
std::vector < std::pair < CvPoint, CvPoint > >bb;
bb.reserve (chains.size ());
for (std::vector < Chain >::iterator chainit = chains.begin ();
chainit != chains.end (); chainit++)
{
int
minx = output->width;
int
miny = output->height;
int
maxx = 0;
int
maxy = 0;
for (std::vector < int >::const_iterator cit =
chainit->components.begin (); cit != chainit->components.end ();
cit++)
{
miny = std::min (miny, compBB[*cit].first.y);
minx = std::min (minx, compBB[*cit].first.x);
maxy = std::max (maxy, compBB[*cit].second.y);
maxx = std::max (maxx, compBB[*cit].second.x);
}
CvPoint p0 = cvPoint (minx, miny);
CvPoint p1 = cvPoint (maxx, maxy);
// aspect ratio filtering of the text box
if (((float) (maxy - miny) / (float) (maxx - minx)) >= 0.7)
continue;
std::pair < CvPoint, CvPoint > pair (p0, p1);
bb.push_back (pair);
}
return bb;
}
void
normalizeImage (IplImage * input, IplImage * output)
{
assert (input->depth == IPL_DEPTH_32F);
assert (input->nChannels == 1);
assert (output->depth == IPL_DEPTH_32F);
assert (output->nChannels == 1);
float
maxVal = 0;
float
minVal = 1e100;
for (int row = 0; row < input->height; row++)
{
const float *
ptr = (const float *) (input->imageData + row * input->widthStep);
for (int col = 0; col < input->width; col++)
{
if (*ptr < 0)
{
}
else
{
maxVal = std::max (*ptr, maxVal);
minVal = std::min (*ptr, minVal);
}
ptr++;
}
}
float
difference = maxVal - minVal;
for (int row = 0; row < input->height; row++)
{
const float *
ptrin = (const float *) (input->imageData + row * input->widthStep);
float *
ptrout = (float *) (output->imageData + row * output->widthStep);
for (int col = 0; col < input->width; col++)
{
if (*ptrin < 0)
{
*ptrout = 1;
}
else
{
*ptrout = ((*ptrin) - minVal) / difference;
}
ptrout++;
ptrin++;
}
}
}
void
renderComponents (IplImage * SWTImage,
std::vector < std::vector < Point2d > >&components,
IplImage * output)
{
for (std::vector < std::vector < Point2d > >::iterator it =
components.begin (); it != components.end (); it++)
{
for (std::vector < Point2d >::iterator pit = it->begin ();
pit != it->end (); pit++)
{
CV_IMAGE_ELEM (output, float, pit->y, pit->x) =
CV_IMAGE_ELEM (SWTImage, float, pit->y, pit->x);
}
}
for (int row = 0; row < output->height; row++)
{
float *
ptr = (float *) (output->imageData + row * output->widthStep);
for (int col = 0; col < output->width; col++)
{
if (*ptr == 0)
{
*ptr = -1;
}
ptr++;
}
}
float
maxVal = 0;
float
minVal = 1e100;
for (int row = 0; row < output->height; row++)
{
const float *
ptr = (const float *) (output->imageData + row * output->widthStep);
for (int col = 0; col < output->width; col++)
{
if (*ptr == 0)
{
}
else
{
maxVal = std::max (*ptr, maxVal);
minVal = std::min (*ptr, minVal);
}
ptr++;
}
}
float
difference = maxVal - minVal;
for (int row = 0; row < output->height; row++)
{
float *
ptr = (float *) (output->imageData + row * output->widthStep);
for (int col = 0; col < output->width; col++)
{
if (*ptr < 1)
{
*ptr = 1;
}
else
{
*ptr = ((*ptr) - minVal) / difference;
}
ptr++;
}
}
}
void
renderComponentsWithBoxes (IplImage * SWTImage,
std::vector < std::vector < Point2d > >&components,
std::vector < std::pair < Point2d,
Point2d > >&compBB, IplImage * output)
{
IplImage *
outTemp = cvCreateImage (cvGetSize (output), IPL_DEPTH_32F, 1);
renderComponents (SWTImage, components, outTemp);
std::vector < std::pair < CvPoint, CvPoint > >bb;
bb.reserve (compBB.size ());
for (std::vector < std::pair < Point2d, Point2d > >::iterator it =
compBB.begin (); it != compBB.end (); it++)
{
CvPoint p0 = cvPoint (it->first.x, it->first.y);
CvPoint p1 = cvPoint (it->second.x, it->second.y);
std::pair < CvPoint, CvPoint > pair (p0, p1);
bb.push_back (pair);
}
IplImage *
out = cvCreateImage (cvGetSize (output), IPL_DEPTH_8U, 1);
cvConvertScale (outTemp, out, 255, 0);
cvCvtColor (out, output, CV_GRAY2RGB);
cvReleaseImage (&outTemp);
cvReleaseImage (&out);
//int count = 0;
//Changing colors and drawing rectangles
for (std::vector < std::pair < CvPoint, CvPoint > >::iterator it =
bb.begin (); it != bb.end (); it++)
{
CvScalar c;
/*if (count % 3 == 0) c=cvScalar(255,0,0);
else if (count % 3 == 1) c=cvScalar(0,255,0);
else c=cvScalar(0,0,255);
count++; */
c = cvScalar (0, 255, 0);
cvRectangle (output, it->first, it->second, c, 2);
}
}
std::vector < std::pair < CvPoint,
CvPoint > >mergeBoundingBoxes (std::vector < std::pair < CvPoint,
CvPoint > >boxes, CvSize size)
{
std::vector < std::pair < CvPoint, CvPoint > >mergedBB;
std::vector < std::vector < int > >
cells;
typedef
boost::adjacency_list <
boost::vecS,
boost::vecS,
boost::undirectedS >
Graph;
Graph
G;
//Initialize map
for (int j = 0; j < size.height; j++)
for (int i = 0; i < size.width; i++)
{
std::vector < int >
inicial;
inicial.push_back (-1);
cells.push_back (inicial);
}
//Filling the map
for (int box = 0; box < boxes.size (); box++)
{
for (int i = boxes[box].first.y; i <= boxes[box].second.y; i++)
{
for (int j = boxes[box].first.x; j <= boxes[box].second.x; j++)
{
cells[j + i * size.width].push_back (box);
}
}
}
//Creating the graph
for (int i = 0; i < cells.size (); i++)
{
if (cells[i].size () > 2)
{
for (int val = 1; val < cells[i].size () - 1; val++)
{
add_edge (cells[i][val], cells[i][val + 1], G);
}
}
else if(cells[i].size() == 2)
{
add_edge(cells[i][1],cells[i][1],G);
}
}
std::vector < int >
component (num_vertices (G));
int
num = connected_components (G, &component[0]);
std::vector < int >::size_type
i;
//merging BB
for (int i = 0; i < num; i++)
{
bool
compFound = false;
int
minx = INT_MAX;
int
miny = INT_MAX;
int
maxx = INT_MIN;
int
maxy = INT_MIN;
for (int j = 0; j < component.size (); j++)
{
if (component[j] == i)
{
miny = std::min (miny, boxes[j].first.y);
minx = std::min (minx, boxes[j].first.x);
maxy = std::max (maxy, boxes[j].second.y);
maxx = std::max (maxx, boxes[j].second.x);
compFound = true;
}
}
if (compFound)
{
CvPoint p0 = cvPoint (minx, miny);
CvPoint p1 = cvPoint (maxx, maxy);
std::pair < CvPoint, CvPoint > pair (p0, p1);
mergedBB.push_back (pair);
}
}
std::cout << "mergedBB size " << mergedBB.size () << std::endl;
return mergedBB;
}
std::vector < std::pair < CvPoint,
CvPoint > >renderChainsWithBoxes (IplImage * SWTImage,
std::vector < std::vector < Point2d >
>&components,
std::vector < Chain > &chains,
std::vector < std::pair < Point2d,
Point2d > >&compBB, IplImage * output)
{
// keep track of included components
std::vector < bool > included;
included.reserve (components.size ());
for (unsigned int i = 0; i != components.size (); i++)
{
included.push_back (false);
}
for (std::vector < Chain >::iterator it = chains.begin ();
it != chains.end (); it++)
{
for (std::vector < int >::iterator cit = it->components.begin ();
cit != it->components.end (); cit++)
{
included[*cit] = true;
}
}
std::vector < std::vector < Point2d > >componentsRed;
for (unsigned int i = 0; i != components.size (); i++)
{
if (included[i])
{
componentsRed.push_back (components[i]);
}
}
IplImage *
outTemp = cvCreateImage (cvGetSize (output), IPL_DEPTH_32F, 1);
std::cout << componentsRed.size () << " components after chaining" << std::
endl;
renderComponents (SWTImage, componentsRed, outTemp);
std::vector < std::pair < CvPoint, CvPoint > >bb;
bb = findBoundingBoxes (components, chains, compBB, outTemp);
cvReleaseImage (&outTemp);
int
count = 0;
for (std::vector < std::pair < CvPoint, CvPoint > >::iterator it =
bb.begin (); it != bb.end (); it++)
{
CvScalar c;
if (count % 3 == 0)
c = cvScalar (255, 0, 0);
else if (count % 3 == 1)
c = cvScalar (0, 255, 0);
else
c = cvScalar (0, 0, 255);
count++;
cvRectangle (output, it->first, it->second, c, 2);
}
return bb;
}
std::vector < std::pair < CvPoint, CvPoint > >textDetection (IplImage * in,
bool
dark_on_light,
IplImage *
edgeImage,
IplImage *
gradientX,
IplImage *
gradientY,
float
chain_strictness_pi,
float
denom_pi_swt_acceptation_angle,
float
max_color_dist)
{
assert (in->depth == IPL_DEPTH_8U);
assert (in->nChannels == 3);
std::vector < std::vector < Point2d > >validComponents;
std::vector < std::pair < Point2d, Point2d > >compBB;
std::vector < Point2dFloat > compCenters;
std::vector < float > compMedians;
std::vector < Point2d > compDimensions;
std::vector < Chain > chains;
std::vector < std::pair < CvPoint, CvPoint > >tempBB;
std::vector < std::vector < Point2d > >components;
std::vector < Ray > rays;
IplImage *
input = cvCreateImage (cvGetSize (in), IPL_DEPTH_8U, 3);
input = cvCloneImage (in);
std::cout << "Running textDetection with dark_on_light " << dark_on_light <<
std::endl;
// Calculate SWT and return ray vectors
IplImage *
SWTImage = cvCreateImage (cvGetSize (input), IPL_DEPTH_32F, 1);
for (int row = 0; row < input->height; row++)
{
float *
ptr = (float *) (SWTImage->imageData + row * SWTImage->widthStep);
for (int col = 0; col < input->width; col++)
{
*ptr++ = -1;
}
}
strokeWidthTransform (edgeImage, input, gradientX, gradientY,
dark_on_light, SWTImage, rays,
denom_pi_swt_acceptation_angle);
SWTMedianFilter (SWTImage, rays);
DEBUG (IplImage *
output2 = cvCreateImage (cvGetSize (input), IPL_DEPTH_32F, 1);
normalizeImage (SWTImage, output2);
IplImage *
saveSWT = cvCreateImage (cvGetSize (input), IPL_DEPTH_8U, 1);
cvConvertScale (output2, saveSWT, 255, 0);
if (dark_on_light)
{
cvSaveImage ("SWT_0.png", saveSWT);
writePseudoImage (saveSWT, std::string ("pseudo_SWT_0.png"));}
else
{
cvSaveImage ("SWT_1.png", saveSWT);
writePseudoImage (saveSWT, std::string ("pseudo_SWT_1.png"));}
cvReleaseImage (&output2); cvReleaseImage (&saveSWT);)
// Calculate legally connect components from SWT and gradient image.
// return type is a vector of vectors, where each outer vector is a component and
// the inner vector contains the (y,x) of each pixel in that component.
components =
findLegallyConnectedComponents (SWTImage, input, rays);
// Filter the components
filterComponents (SWTImage, components, validComponents, compCenters,
compMedians, compDimensions, compBB);
DEBUG (IplImage *
output3 = cvCreateImage (cvGetSize (input), 8U, 3);
renderComponentsWithBoxes (SWTImage, validComponents, compBB,
output3);
if (dark_on_light) cvSaveImage ("components_0.png", output3);
else
cvSaveImage ("components_1.png", output3);
cvReleaseImage (&output3);)
// Make chains of components
chains =
makeChains (input, validComponents, compCenters, compMedians,
compDimensions, compBB, chain_strictness_pi, max_color_dist);
tempBB =
renderChainsWithBoxes (SWTImage, validComponents, chains, compBB, input);
DEBUG (if (dark_on_light) cvSaveImage ("render_0.png", input);
else
cvSaveImage ("render_1.png", input);)
cvReleaseImage (&input);
cvReleaseImage (&SWTImage);
return tempBB;
}
bool
vector2dSort (const Ray& r1, const Ray& r2)
{
return r1.length < r2.length;
}
void
strokeWidthTransform (IplImage * edgeImage,
IplImage * colorImage,
IplImage * gradientX,
IplImage * gradientY,
bool dark_on_light,
IplImage * SWTImage,
std::vector < Ray > &rays,
float denom_pi_acceptation_angle)
{
// First pass
float
prec = .05;
float
max = 0;
for (int row = 0; row < edgeImage->height; row++)
{
const uchar *
ptr =
(const uchar *) (edgeImage->imageData + row * edgeImage->widthStep);
for (int col = 0; col < edgeImage->width; col++)
{
if (*ptr > 0)
{
Ray r;
Point2d p;
p.x = col;
p.y = row;
r.p = p;
std::vector < Point2d > points;
points.push_back (p);
float
curX = (float) col + 0.5;
float
curY = (float) row + 0.5;
int
curPixX = col;
int
curPixY = row;
float
G_x = CV_IMAGE_ELEM (gradientX, float, row, col);
float
G_y = CV_IMAGE_ELEM (gradientY, float, row, col);
// normalize gradient
float
mag = sqrt ((G_x * G_x) + (G_y * G_y));
if (dark_on_light)
{
G_x = -G_x / mag;
G_y = -G_y / mag;
}
else
{
G_x = G_x / mag;
G_y = G_y / mag;
}
while (true)
{
curX += G_x * prec;
curY += G_y * prec;
if ((int) (floor (curX)) != curPixX
|| (int) (floor (curY)) != curPixY)
{
curPixX = (int) (floor (curX));
curPixY = (int) (floor (curY));
// check if pixel is outside boundary of image
if (curPixX < 0 || (curPixX >= SWTImage->width)
|| curPixY < 0 || (curPixY >= SWTImage->height))
{
break;
}
Point2d pnew;
pnew.x = curPixX;
pnew.y = curPixY;
points.push_back (pnew);
if (CV_IMAGE_ELEM (edgeImage, uchar, curPixY, curPixX) > 0)
{
r.q = pnew;
// dot product
float
G_xt = CV_IMAGE_ELEM (gradientX, float, curPixY,
curPixX);
float
G_yt = CV_IMAGE_ELEM (gradientY, float, curPixY,
curPixX);
mag = sqrt ((G_xt * G_xt) + (G_yt * G_yt));
if (dark_on_light)
{
G_xt = -G_xt / mag;
G_yt = -G_yt / mag;
}
else
{
G_xt = G_xt / mag;
G_yt = G_yt / mag;
}
if (acos (G_x * -G_xt + G_y * -G_yt) <
PI / (float) denom_pi_acceptation_angle)
{
r.length = sqrt (((float) r.q.x -
(float) r.p.x) * ((float) r.q.x -
(float) r.p.x) + ((float) r.q.y -
(float) r.p.y) * ((float) r.q.y -
(float) r.p.y));
max = std::max ( max, r.length);
r.points = points;
rays.push_back (r);
}
break;
}
}
}
}
ptr++;
}
}
// First filtering of Rays, deleting possible outliers that cross more than INTERSECTION
#define INTERSECTIONS 2
std::vector<Ray> bigRays;
std::vector<Ray> newRays;
std::vector<int> intersected(rays.size(),0);
std::vector<int> bigRaysPositions;
std::vector< vector<int> > bigRaysIntersected;
int firstBigRayPosition=-1;
bool firstBigRayFound = false;
std::sort(rays.begin(),rays.end(),&vector2dSort);
for(int i=0; i< rays.size();i++)
{
if(rays[i].length > max/3.0)
{
if(!firstBigRayFound)
{
firstBigRayFound = true;
firstBigRayPosition = i;
}
bigRays.push_back(rays[i]);
}
}
//initialize
for(int i=0;i<bigRays.size();i++)
{
vector<int> v;
v.push_back(-1);
bigRaysIntersected.push_back(v);
}
// counting intersections
for (int i =0; i< rays.size();i++)
{
for(int k=0;k<bigRays.size();k++)
{
// if((rays[i].p.x == bigRays[k].p.x)&&(rays[i].p.y == bigRays[k].p.y)&&(rays[i].q.x == bigRays[k].q.x)&&
// (rays[i].q.y == bigRays[k].q.y))
if(i>= firstBigRayPosition)
{
// it is a big ray
continue;
}
if(classifyIntersection(rays[i].p,rays[i].q,bigRays[k].p,bigRays[k].q))
{
bigRaysIntersected[k].push_back(i);
intersected[i]++;
}
}
}
for (int i =0; i< rays.size();i++)
{
bool badRay = false;
int badRayNum = -1;
/*for(int k=0;k<bigRays.size();k++)
{
if((rays[i].p.x == bigRays[k].p.x)&&(rays[i].p.y == bigRays[k].p.y)&&(rays[i].q.x == bigRays[k].q.x)&&
(rays[i].q.y == bigRays[k].q.y))
{
badRay = true;
badRayNum = k;
break;
}
}*/
if(i>=firstBigRayPosition)
{
badRay = true;
badRayNum = i-firstBigRayPosition;
}
if((intersected[i]>=INTERSECTIONS)&&(!badRay))
{
continue;
}
if(badRay)
{
bool plot = false;
for (int m=1;m<bigRaysIntersected[badRayNum].size();m++)
{
if(intersected[bigRaysIntersected[badRayNum][m]] < INTERSECTIONS )
plot = true;
}
if(!plot)
continue;
}
newRays.push_back(rays[i]);
for (std::vector < Point2d >::iterator pit =
rays[i].points.begin (); pit != rays[i].points.end ();
pit++)
{
if (CV_IMAGE_ELEM
(SWTImage, float, pit->y, pit->x) < 0)
{
CV_IMAGE_ELEM (SWTImage, float, pit->y,
pit->x) = rays[i].length;
}
else
{
CV_IMAGE_ELEM (SWTImage, float, pit->y,
pit->x) =
std::min (rays[i].length,
CV_IMAGE_ELEM (SWTImage,
float,
pit->y,
pit->x));
}
}
}
rays = newRays;
}
void
SWTMedianFilter (IplImage * SWTImage, std::vector < Ray > &rays)
{
float median;
for (std::vector < Ray >::iterator rit = rays.begin (); rit != rays.end ();
rit++)
{
for (std::vector < Point2d >::iterator pit = rit->points.begin ();
pit != rit->points.end (); pit++)
{
pit->SWT = CV_IMAGE_ELEM (SWTImage, float, pit->y, pit->x);
}
std::sort (rit->points.begin (), rit->points.end (), &Point2dSort);
median = (rit->points[rit->points.size () / 2]).SWT;
for (std::vector < Point2d >::iterator pit = rit->points.begin ();
pit != rit->points.end (); pit++)
{
CV_IMAGE_ELEM (SWTImage, float, pit->y, pit->x) =
std::min (pit->SWT, median);
}
}
}
bool
Point2dSort (const Point2d & lhs, const Point2d & rhs)
{
return lhs.SWT < rhs.SWT;
}
std::vector < std::vector < Point2d >
>findLegallyConnectedComponents (IplImage * SWTImage,
IplImage * ColorImage,
std::vector < Ray > &rays)
{
boost::unordered_map < int, int >
map;
boost::unordered_map < int,
Point2d >
revmap;
typedef
boost::adjacency_list <
boost::vecS,
boost::vecS,
boost::undirectedS >
Graph;
int
num_vertices = 0;
// Number vertices for graph. Associate each point with number
for (int row = 0; row < SWTImage->height; row++)
{
float *
ptr = (float *) (SWTImage->imageData + row * SWTImage->widthStep);
for (int col = 0; col < SWTImage->width; col++)
{
if (*ptr > 0)
{
map[row * SWTImage->width + col] = num_vertices;
Point2d p;
p.x = col;
p.y = row;
revmap[num_vertices] = p;
num_vertices++;
}
ptr++;
}
}
Graph g (num_vertices);
for (int row = 0; row < SWTImage->height; row++)
{
float *
ptr = (float *) (SWTImage->imageData + row * SWTImage->widthStep);
for (int col = 0; col < SWTImage->width; col++)
{
if (*ptr > 0)
{
// check pixel to the right, right-down, down, left-down
// now only checking right and right-down to avoid diagonal elements connexion
int
this_pixel = map[row * SWTImage->width + col];
if (col + 1 < SWTImage->width)
{
float
right = CV_IMAGE_ELEM (SWTImage, float, row, col + 1);
if (right > 0
&&
((float)
(std::max ((*ptr), right) /
std::min ((*ptr), right)) <= 3.0))
boost::add_edge (this_pixel,
map.at (row * SWTImage->width + col + 1),
g);
}
if (row + 1 < SWTImage->height)
{
if (col + 1 < SWTImage->width)
{
float
right_down =
CV_IMAGE_ELEM (SWTImage, float, row + 1, col + 1);
if (right_down > 0
&&
((float)
(std::max ((*ptr), right_down) /
std::min ((*ptr), right_down)) <= 3.0))
boost::add_edge (this_pixel,
map.at ((row + 1) * SWTImage->width +
col + 1), g);
}
/* float
down = CV_IMAGE_ELEM (SWTImage, float, row + 1, col);
if (down > 0
&&
((float)
(std::max ((*ptr), down) / std::min ((*ptr), down)) <=
3.0))
boost::add_edge (this_pixel,
map.at ((row + 1) * SWTImage->width +
col), g);
if (col - 1 >= 0)
{
float
left_down =