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// Copyright (c) 2007, 2008, 2009, 2011 libmv authors.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
#include "libmv/tracking/klt_region_tracker.h"
#include "libmv/image/convolve.h"
#include "libmv/image/image.h"
#include "libmv/image/sample.h"
#include "libmv/logging/logging.h"
namespace libmv {
// Compute the gradient matrix noted by Z and the error vector e. See Good
// Features to Track.
//
// TODO(keir): The calls to SampleLinear() do boundary checking that should
// instead happen outside the loop. Since this is the innermost loop, the extra
// bounds checking hurts performance.
static void ComputeTrackingEquation(const Array3Df& image_and_gradient1,
const Array3Df& image_and_gradient2,
double x1,
double y1,
double x2,
double y2,
int half_width,
float* gxx,
float* gxy,
float* gyy,
float* ex,
float* ey) {
*gxx = *gxy = *gyy = 0;
*ex = *ey = 0;
for (int r = -half_width; r <= half_width; ++r) {
for (int c = -half_width; c <= half_width; ++c) {
float xx1 = x1 + c;
float yy1 = y1 + r;
float xx2 = x2 + c;
float yy2 = y2 + r;
float I = SampleLinear(image_and_gradient1, yy1, xx1, 0);
float J = SampleLinear(image_and_gradient2, yy2, xx2, 0);
float gx = SampleLinear(image_and_gradient2, yy2, xx2, 1);
float gy = SampleLinear(image_and_gradient2, yy2, xx2, 2);
*gxx += gx * gx;
*gxy += gx * gy;
*gyy += gy * gy;
*ex += (I - J) * gx;
*ey += (I - J) * gy;
}
}
}
static bool RegionIsInBounds(const FloatImage& image1,
double x,
double y,
int half_window_size) {
// Check the minimum coordinates.
int min_x = floor(x) - half_window_size - 1;
int min_y = floor(y) - half_window_size - 1;
if (min_x < 0.0 || min_y < 0.0) {
return false;
}
// Check the maximum coordinates.
int max_x = ceil(x) + half_window_size + 1;
int max_y = ceil(y) + half_window_size + 1;
if (max_x > image1.cols() || max_y > image1.rows()) {
return false;
}
// Ok, we're good.
return true;
}
bool KltRegionTracker::Track(const FloatImage& image1,
const FloatImage& image2,
double x1,
double y1,
double* x2,
double* y2) const {
if (!RegionIsInBounds(image1, x1, y1, half_window_size)) {
LG << "Fell out of image1's window with x1=" << x1 << ", y1=" << y1
<< ", hw=" << half_window_size << ".";
return false;
}
Array3Df image_and_gradient1;
Array3Df image_and_gradient2;
BlurredImageAndDerivativesChannels(image1, sigma, &image_and_gradient1);
BlurredImageAndDerivativesChannels(image2, sigma, &image_and_gradient2);
int i;
float dx = 0, dy = 0;
for (i = 0; i < max_iterations; ++i) {
// Check that the entire image patch is within the bounds of the images.
if (!RegionIsInBounds(image2, *x2, *y2, half_window_size)) {
LG << "Fell out of image2's window with x2=" << *x2 << ", y2=" << *y2
<< ", hw=" << half_window_size << ".";
return false;
}
// Compute gradient matrix and error vector.
float gxx, gxy, gyy, ex, ey;
ComputeTrackingEquation(image_and_gradient1,
image_and_gradient2,
x1,
y1,
*x2,
*y2,
half_window_size,
&gxx,
&gxy,
&gyy,
&ex,
&ey);
// Solve the tracking equation
//
// [gxx gxy] [dx] = [ex]
// [gxy gyy] [dy] = [ey]
//
// for dx and dy. Borrowed from Stan Birchfield's KLT implementation.
float determinant = gxx * gyy - gxy * gxy;
dx = (gyy * ex - gxy * ey) / determinant;
dy = (gxx * ey - gxy * ex) / determinant;
// Update the position with the solved displacement.
*x2 += dx;
*y2 += dy;
// Check for the quality of the solution, but not until having already
// updated the position with our best estimate. The reason to do the update
// anyway is that the user already knows the position is bad, so we may as
// well try our best.
if (determinant < min_determinant) {
// The determinant, which indicates the trackiness of the point, is too
// small, so fail out.
LG << "Determinant " << determinant << " is too small; failing tracking.";
return false;
}
LG << "x=" << *x2 << ", y=" << *y2 << ", dx=" << dx << ", dy=" << dy
<< ", det=" << determinant;
// If the update is small, then we probably found the target.
if (dx * dx + dy * dy < min_update_squared_distance) {
LG << "Successful track in " << i << " iterations.";
return true;
}
}
// Getting here means we hit max iterations, so tracking failed.
LG << "Too many iterations; max is set to " << max_iterations << ".";
return false;
}
} // namespace libmv
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