1 /*
2 * Copyright (c) 2016-2020 Arm Limited.
3 *
4 * SPDX-License-Identifier: MIT
5 *
6 * Permission is hereby granted, free of charge, to any person obtaining a copy
7 * of this software and associated documentation files (the "Software"), to
8 * deal in the Software without restriction, including without limitation the
9 * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
10 * sell copies of the Software, and to permit persons to whom the Software is
11 * furnished to do so, subject to the following conditions:
12 *
13 * The above copyright notice and this permission notice shall be included in all
14 * copies or substantial portions of the Software.
15 *
16 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
17 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
18 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
19 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
20 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
21 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
22 * SOFTWARE.
23 */
24 #include "src/core/NEON/kernels/NELKTrackerKernel.h"
25
26 #include "arm_compute/core/Coordinates.h"
27 #include "arm_compute/core/Error.h"
28 #include "arm_compute/core/Helpers.h"
29 #include "arm_compute/core/ITensor.h"
30 #include "arm_compute/core/TensorInfo.h"
31 #include "arm_compute/core/Validate.h"
32 #include "arm_compute/core/Window.h"
33 #include "src/core/AccessWindowStatic.h"
34 #include "src/core/helpers/AutoConfiguration.h"
35 #include "src/core/helpers/WindowHelpers.h"
36
37 #include <arm_neon.h>
38 #include <cmath>
39
40 using namespace arm_compute;
41
42 /** Constants used for Lucas-Kanade Algorithm */
43 constexpr int W_BITS = 14;
44 constexpr float D0 = 1 << W_BITS;
45 constexpr float DETERMINANT_THRESHOLD = 1.0e-07f; // Threshold for the determinant. Used for lost tracking criteria
46 constexpr float EIGENVALUE_THRESHOLD = 1.0e-04f; // Thresholds for minimum eigenvalue. Used for lost tracking criteria
47 constexpr float FLT_SCALE = 1.0f / (1 << 20);
48
49 namespace
50 {
51 enum class BilinearInterpolation
52 {
53 BILINEAR_OLD_NEW,
54 BILINEAR_SCHARR
55 };
56
57 template <typename T>
INT_ROUND(T x,int n)58 constexpr int INT_ROUND(T x, int n)
59 {
60 return (x + (1 << (n - 1))) >> n;
61 }
62
63 template <typename T>
get_pixel(const ITensor * tensor,int xi,int yi,int iw00,int iw01,int iw10,int iw11,int scale)64 inline int get_pixel(const ITensor *tensor, int xi, int yi, int iw00, int iw01, int iw10, int iw11, int scale)
65 {
66 const auto px00 = *reinterpret_cast<const T *>(tensor->buffer() + tensor->info()->offset_element_in_bytes(Coordinates(xi, yi)));
67 const auto px01 = *reinterpret_cast<const T *>(tensor->buffer() + tensor->info()->offset_element_in_bytes(Coordinates(xi + 1, yi)));
68 const auto px10 = *reinterpret_cast<const T *>(tensor->buffer() + tensor->info()->offset_element_in_bytes(Coordinates(xi, yi + 1)));
69 const auto px11 = *reinterpret_cast<const T *>(tensor->buffer() + tensor->info()->offset_element_in_bytes(Coordinates(xi + 1, yi + 1)));
70
71 return INT_ROUND(px00 * iw00 + px01 * iw01 + px10 * iw10 + px11 * iw11, scale);
72 }
73
compute_bilinear_interpolation(int16x8_t top_row,int16x8_t bottom_row,int16x4_t w00,int16x4_t w01,int16x4_t w10,int16x4_t w11,int32x4_t shift)74 inline int32x4_t compute_bilinear_interpolation(int16x8_t top_row, int16x8_t bottom_row, int16x4_t w00, int16x4_t w01, int16x4_t w10, int16x4_t w11, int32x4_t shift)
75 {
76 // Get the left column of upper row
77 const int16x4_t px00 = vget_low_s16(top_row);
78
79 // Get the right column of upper row
80 const int16x4_t px01 = vext_s16(px00, vget_high_s16(top_row), 1);
81
82 // Get the left column of lower row
83 const int16x4_t px10 = vget_low_s16(bottom_row);
84
85 // Get the right column of right row
86 const int16x4_t px11 = vext_s16(px10, vget_high_s16(bottom_row), 1);
87
88 // Apply the bilinear filter
89 return vqrshlq_s32(vmull_s16(px00, w00) + vmull_s16(px01, w01) + vmull_s16(px10, w10) + vmull_s16(px11, w11), shift);
90 }
91 } // namespace
92
init_keypoints(int start,int end)93 void NELKTrackerKernel::init_keypoints(int start, int end)
94 {
95 if(_level == _num_levels - 1)
96 {
97 const float level_scale = pow(_pyramid_scale, _level);
98
99 for(int i = start; i < end; ++i)
100 {
101 _old_points_internal->at(i).x = _old_points->at(i).x * level_scale;
102 _old_points_internal->at(i).y = _old_points->at(i).y * level_scale;
103 _old_points_internal->at(i).tracking_status = true;
104
105 NELKInternalKeypoint keypoint_to_track;
106
107 if(_use_initial_estimate)
108 {
109 keypoint_to_track.x = _new_points_estimates->at(i).x * level_scale;
110 keypoint_to_track.y = _new_points_estimates->at(i).y * level_scale;
111 keypoint_to_track.tracking_status = (_new_points_estimates->at(i).tracking_status == 1);
112 }
113 else
114 {
115 keypoint_to_track.x = _old_points_internal->at(i).x;
116 keypoint_to_track.y = _old_points_internal->at(i).y;
117 keypoint_to_track.tracking_status = true;
118 }
119
120 _new_points_internal->at(i) = keypoint_to_track;
121 }
122 }
123 else
124 {
125 for(int i = start; i < end; ++i)
126 {
127 _old_points_internal->at(i).x /= _pyramid_scale;
128 _old_points_internal->at(i).y /= _pyramid_scale;
129 _new_points_internal->at(i).x /= _pyramid_scale;
130 _new_points_internal->at(i).y /= _pyramid_scale;
131 }
132 }
133 }
134
compute_spatial_gradient_matrix(const NELKInternalKeypoint & keypoint,int32_t * bilinear_ix,int32_t * bilinear_iy)135 std::tuple<int, int, int> NELKTrackerKernel::compute_spatial_gradient_matrix(const NELKInternalKeypoint &keypoint, int32_t *bilinear_ix, int32_t *bilinear_iy)
136 {
137 int iA11 = 0;
138 int iA12 = 0;
139 int iA22 = 0;
140
141 int32x4_t nA11 = vdupq_n_s32(0);
142 int32x4_t nA12 = vdupq_n_s32(0);
143 int32x4_t nA22 = vdupq_n_s32(0);
144
145 float keypoint_int_x = 0;
146 float keypoint_int_y = 0;
147
148 const float wx = std::modf(keypoint.x, &keypoint_int_x);
149 const float wy = std::modf(keypoint.y, &keypoint_int_y);
150
151 const int iw00 = roundf((1.0f - wx) * (1.0f - wy) * D0);
152 const int iw01 = roundf(wx * (1.0f - wy) * D0);
153 const int iw10 = roundf((1.0f - wx) * wy * D0);
154 const int iw11 = D0 - iw00 - iw01 - iw10;
155
156 const int16x4_t nw00 = vdup_n_s16(iw00);
157 const int16x4_t nw01 = vdup_n_s16(iw01);
158 const int16x4_t nw10 = vdup_n_s16(iw10);
159 const int16x4_t nw11 = vdup_n_s16(iw11);
160
161 // Convert stride from uint_t* to int16_t*
162 const size_t row_stride = _old_scharr_gx->info()->strides_in_bytes()[1] / 2;
163 const Coordinates top_left_window_corner(static_cast<int>(keypoint_int_x) - _window_dimension / 2, static_cast<int>(keypoint_int_y) - _window_dimension / 2);
164 auto idx = reinterpret_cast<const int16_t *>(_old_scharr_gx->buffer() + _old_scharr_gx->info()->offset_element_in_bytes(top_left_window_corner));
165 auto idy = reinterpret_cast<const int16_t *>(_old_scharr_gy->buffer() + _old_scharr_gy->info()->offset_element_in_bytes(top_left_window_corner));
166 static const int32x4_t nshifter_scharr = vdupq_n_s32(-W_BITS);
167
168 for(int ky = 0; ky < _window_dimension; ++ky, idx += row_stride, idy += row_stride)
169 {
170 int kx = 0;
171
172 // Calculate elements in blocks of four as long as possible
173 for(; kx <= _window_dimension - 4; kx += 4)
174 {
175 // Interpolation X
176 const int16x8_t ndx_row1 = vld1q_s16(idx + kx);
177 const int16x8_t ndx_row2 = vld1q_s16(idx + kx + row_stride);
178
179 const int32x4_t nxval = compute_bilinear_interpolation(ndx_row1, ndx_row2, nw00, nw01, nw10, nw11, nshifter_scharr);
180
181 // Interpolation Y
182 const int16x8_t ndy_row1 = vld1q_s16(idy + kx);
183 const int16x8_t ndy_row2 = vld1q_s16(idy + kx + row_stride);
184
185 const int32x4_t nyval = compute_bilinear_interpolation(ndy_row1, ndy_row2, nw00, nw01, nw10, nw11, nshifter_scharr);
186
187 // Store the intermediate data so that we don't need to recalculate them in later stage
188 vst1q_s32(bilinear_ix + kx + ky * _window_dimension, nxval);
189 vst1q_s32(bilinear_iy + kx + ky * _window_dimension, nyval);
190
191 // Accumulate Ix^2
192 nA11 = vmlaq_s32(nA11, nxval, nxval);
193 // Accumulate Ix * Iy
194 nA12 = vmlaq_s32(nA12, nxval, nyval);
195 // Accumulate Iy^2
196 nA22 = vmlaq_s32(nA22, nyval, nyval);
197 }
198
199 // Calculate the leftover elements
200 for(; kx < _window_dimension; ++kx)
201 {
202 const int32_t ixval = get_pixel<int16_t>(_old_scharr_gx, top_left_window_corner.x() + kx, top_left_window_corner.y() + ky,
203 iw00, iw01, iw10, iw11, W_BITS);
204 const int32_t iyval = get_pixel<int16_t>(_old_scharr_gy, top_left_window_corner.x() + kx, top_left_window_corner.y() + ky,
205 iw00, iw01, iw10, iw11, W_BITS);
206
207 iA11 += ixval * ixval;
208 iA12 += ixval * iyval;
209 iA22 += iyval * iyval;
210
211 bilinear_ix[kx + ky * _window_dimension] = ixval;
212 bilinear_iy[kx + ky * _window_dimension] = iyval;
213 }
214 }
215
216 iA11 += vgetq_lane_s32(nA11, 0) + vgetq_lane_s32(nA11, 1) + vgetq_lane_s32(nA11, 2) + vgetq_lane_s32(nA11, 3);
217 iA12 += vgetq_lane_s32(nA12, 0) + vgetq_lane_s32(nA12, 1) + vgetq_lane_s32(nA12, 2) + vgetq_lane_s32(nA12, 3);
218 iA22 += vgetq_lane_s32(nA22, 0) + vgetq_lane_s32(nA22, 1) + vgetq_lane_s32(nA22, 2) + vgetq_lane_s32(nA22, 3);
219
220 return std::make_tuple(iA11, iA12, iA22);
221 }
222
compute_image_mismatch_vector(const NELKInternalKeypoint & old_keypoint,const NELKInternalKeypoint & new_keypoint,const int32_t * bilinear_ix,const int32_t * bilinear_iy)223 std::pair<int, int> NELKTrackerKernel::compute_image_mismatch_vector(const NELKInternalKeypoint &old_keypoint, const NELKInternalKeypoint &new_keypoint, const int32_t *bilinear_ix,
224 const int32_t *bilinear_iy)
225 {
226 int ib1 = 0;
227 int ib2 = 0;
228
229 int32x4_t nb1 = vdupq_n_s32(0);
230 int32x4_t nb2 = vdupq_n_s32(0);
231
232 // Compute weights for the old keypoint
233 float old_keypoint_int_x = 0;
234 float old_keypoint_int_y = 0;
235
236 const float old_wx = std::modf(old_keypoint.x, &old_keypoint_int_x);
237 const float old_wy = std::modf(old_keypoint.y, &old_keypoint_int_y);
238
239 const int iw00_old = roundf((1.0f - old_wx) * (1.0f - old_wy) * D0);
240 const int iw01_old = roundf(old_wx * (1.0f - old_wy) * D0);
241 const int iw10_old = roundf((1.0f - old_wx) * old_wy * D0);
242 const int iw11_old = D0 - iw00_old - iw01_old - iw10_old;
243
244 const int16x4_t nw00_old = vdup_n_s16(iw00_old);
245 const int16x4_t nw01_old = vdup_n_s16(iw01_old);
246 const int16x4_t nw10_old = vdup_n_s16(iw10_old);
247 const int16x4_t nw11_old = vdup_n_s16(iw11_old);
248
249 // Compute weights for the new keypoint
250 float new_keypoint_int_x = 0;
251 float new_keypoint_int_y = 0;
252
253 const float new_wx = std::modf(new_keypoint.x, &new_keypoint_int_x);
254 const float new_wy = std::modf(new_keypoint.y, &new_keypoint_int_y);
255
256 const int iw00_new = roundf((1.0f - new_wx) * (1.0f - new_wy) * D0);
257 const int iw01_new = roundf(new_wx * (1.0f - new_wy) * D0);
258 const int iw10_new = roundf((1.0f - new_wx) * new_wy * D0);
259 const int iw11_new = D0 - iw00_new - iw01_new - iw10_new;
260
261 const int16x4_t nw00_new = vdup_n_s16(iw00_new);
262 const int16x4_t nw01_new = vdup_n_s16(iw01_new);
263 const int16x4_t nw10_new = vdup_n_s16(iw10_new);
264 const int16x4_t nw11_new = vdup_n_s16(iw11_new);
265
266 const int row_stride = _input_new->info()->strides_in_bytes()[1];
267 const Coordinates top_left_window_corner_old(static_cast<int>(old_keypoint_int_x) - _window_dimension / 2, static_cast<int>(old_keypoint_int_y) - _window_dimension / 2);
268 const Coordinates top_left_window_corner_new(static_cast<int>(new_keypoint_int_x) - _window_dimension / 2, static_cast<int>(new_keypoint_int_y) - _window_dimension / 2);
269 const uint8_t *old_ptr = _input_old->buffer() + _input_old->info()->offset_element_in_bytes(top_left_window_corner_old);
270 const uint8_t *new_ptr = _input_new->buffer() + _input_new->info()->offset_element_in_bytes(top_left_window_corner_new);
271 static const int32x4_t nshifter_tensor = vdupq_n_s32(-(W_BITS - 5));
272
273 for(int ky = 0; ky < _window_dimension; ++ky, new_ptr += row_stride, old_ptr += row_stride)
274 {
275 int kx = 0;
276
277 // Calculate elements in blocks of four as long as possible
278 for(; kx <= _window_dimension - 4; kx += 4)
279 {
280 // Interpolation old tensor
281 const int16x8_t nold_row1 = vreinterpretq_s16_u16(vmovl_u8(vld1_u8(old_ptr + kx)));
282 const int16x8_t nold_row2 = vreinterpretq_s16_u16(vmovl_u8(vld1_u8(old_ptr + kx + row_stride)));
283
284 const int32x4_t noldval = compute_bilinear_interpolation(nold_row1, nold_row2, nw00_old, nw01_old, nw10_old, nw11_old, nshifter_tensor);
285
286 // Interpolation new tensor
287 const int16x8_t nnew_row1 = vreinterpretq_s16_u16(vmovl_u8(vld1_u8(new_ptr + kx)));
288 const int16x8_t nnew_row2 = vreinterpretq_s16_u16(vmovl_u8(vld1_u8(new_ptr + kx + row_stride)));
289
290 const int32x4_t nnewval = compute_bilinear_interpolation(nnew_row1, nnew_row2, nw00_new, nw01_new, nw10_new, nw11_new, nshifter_tensor);
291
292 // Calculate It gradient, i.e. pixelwise difference between old and new tensor
293 const int32x4_t diff = vsubq_s32(nnewval, noldval);
294
295 // Load the Ix and Iy gradient computed in the previous stage
296 const int32x4_t nxval = vld1q_s32(bilinear_ix + kx + ky * _window_dimension);
297 const int32x4_t nyval = vld1q_s32(bilinear_iy + kx + ky * _window_dimension);
298
299 // Caculate Ix * It and Iy * It, and accumulate the results
300 nb1 = vmlaq_s32(nb1, diff, nxval);
301 nb2 = vmlaq_s32(nb2, diff, nyval);
302 }
303
304 // Calculate the leftover elements
305 for(; kx < _window_dimension; ++kx)
306 {
307 const int32_t ival = get_pixel<uint8_t>(_input_old, top_left_window_corner_old.x() + kx, top_left_window_corner_old.y() + ky,
308 iw00_old, iw01_old, iw10_old, iw11_old, W_BITS - 5);
309 const int32_t jval = get_pixel<uint8_t>(_input_new, top_left_window_corner_new.x() + kx, top_left_window_corner_new.y() + ky,
310 iw00_new, iw01_new, iw10_new, iw11_new, W_BITS - 5);
311
312 const int32_t diff = jval - ival;
313
314 ib1 += diff * bilinear_ix[kx + ky * _window_dimension];
315 ib2 += diff * bilinear_iy[kx + ky * _window_dimension];
316 }
317 }
318
319 ib1 += vgetq_lane_s32(nb1, 0) + vgetq_lane_s32(nb1, 1) + vgetq_lane_s32(nb1, 2) + vgetq_lane_s32(nb1, 3);
320 ib2 += vgetq_lane_s32(nb2, 0) + vgetq_lane_s32(nb2, 1) + vgetq_lane_s32(nb2, 2) + vgetq_lane_s32(nb2, 3);
321
322 return std::make_pair(ib1, ib2);
323 }
324
NELKTrackerKernel()325 NELKTrackerKernel::NELKTrackerKernel()
326 : _input_old(nullptr), _input_new(nullptr), _old_scharr_gx(nullptr), _old_scharr_gy(nullptr), _new_points(nullptr), _new_points_estimates(nullptr), _old_points(nullptr), _old_points_internal(),
327 _new_points_internal(), _termination(Termination::TERM_CRITERIA_EPSILON), _use_initial_estimate(false), _pyramid_scale(0.0f), _epsilon(0.0f), _num_iterations(0), _window_dimension(0), _level(0),
328 _num_levels(0), _valid_region()
329 {
330 }
331
border_size() const332 BorderSize NELKTrackerKernel::border_size() const
333 {
334 return BorderSize(1);
335 }
336
configure(const ITensor * input_old,const ITensor * input_new,const ITensor * old_scharr_gx,const ITensor * old_scharr_gy,const IKeyPointArray * old_points,const IKeyPointArray * new_points_estimates,IKeyPointArray * new_points,INELKInternalKeypointArray * old_points_internal,INELKInternalKeypointArray * new_points_internal,Termination termination,bool use_initial_estimate,float epsilon,unsigned int num_iterations,size_t window_dimension,size_t level,size_t num_levels,float pyramid_scale)337 void NELKTrackerKernel::configure(const ITensor *input_old, const ITensor *input_new, const ITensor *old_scharr_gx, const ITensor *old_scharr_gy,
338 const IKeyPointArray *old_points, const IKeyPointArray *new_points_estimates, IKeyPointArray *new_points,
339 INELKInternalKeypointArray *old_points_internal, INELKInternalKeypointArray *new_points_internal,
340 Termination termination, bool use_initial_estimate, float epsilon, unsigned int num_iterations, size_t window_dimension,
341 size_t level, size_t num_levels, float pyramid_scale)
342
343 {
344 ARM_COMPUTE_ERROR_ON_DATA_TYPE_CHANNEL_NOT_IN(input_old, 1, DataType::U8);
345 ARM_COMPUTE_ERROR_ON_DATA_TYPE_CHANNEL_NOT_IN(input_new, 1, DataType::U8);
346 ARM_COMPUTE_ERROR_ON_DATA_TYPE_CHANNEL_NOT_IN(old_scharr_gx, 1, DataType::S16);
347 ARM_COMPUTE_ERROR_ON_DATA_TYPE_CHANNEL_NOT_IN(old_scharr_gy, 1, DataType::S16);
348
349 _input_old = input_old;
350 _input_new = input_new;
351 _old_scharr_gx = old_scharr_gx;
352 _old_scharr_gy = old_scharr_gy;
353 _old_points = old_points;
354 _new_points_estimates = new_points_estimates;
355 _new_points = new_points;
356 _old_points_internal = old_points_internal;
357 _new_points_internal = new_points_internal;
358 _termination = termination;
359 _use_initial_estimate = use_initial_estimate;
360 _epsilon = epsilon;
361 _window_dimension = window_dimension;
362 _level = level;
363 _num_levels = num_levels;
364 _pyramid_scale = pyramid_scale;
365 _num_levels = num_levels;
366
367 // Set maximum number of iterations used for convergence
368 const size_t max_iterations = 1000;
369 _num_iterations = (termination == Termination::TERM_CRITERIA_EPSILON) ? max_iterations : num_iterations;
370
371 Window window;
372 window.set(Window::DimX, Window::Dimension(0, old_points->num_values()));
373 window.set(Window::DimY, Window::Dimension(0, 1));
374
375 _valid_region = intersect_valid_regions(
376 input_old->info()->valid_region(),
377 input_new->info()->valid_region(),
378 old_scharr_gx->info()->valid_region(),
379 old_scharr_gy->info()->valid_region());
380
381 update_window_and_padding(window,
382 AccessWindowStatic(input_old->info(), _valid_region.start(0), _valid_region.start(1),
383 _valid_region.end(0), _valid_region.end(1)),
384 AccessWindowStatic(input_new->info(), _valid_region.start(0), _valid_region.start(1),
385 _valid_region.end(0), _valid_region.end(1)),
386 AccessWindowStatic(old_scharr_gx->info(), _valid_region.start(0), _valid_region.start(1),
387 _valid_region.end(0), _valid_region.end(1)),
388 AccessWindowStatic(old_scharr_gy->info(), _valid_region.start(0), _valid_region.start(1),
389 _valid_region.end(0), _valid_region.end(1)));
390
391 INEKernel::configure(window);
392 }
393
run(const Window & window,const ThreadInfo & info)394 void NELKTrackerKernel::run(const Window &window, const ThreadInfo &info)
395 {
396 ARM_COMPUTE_UNUSED(info);
397 ARM_COMPUTE_ERROR_ON_UNCONFIGURED_KERNEL(this);
398 ARM_COMPUTE_ERROR_ON_INVALID_SUBWINDOW(INEKernel::window(), window);
399
400 ARM_COMPUTE_ERROR_ON(_input_old->buffer() == nullptr);
401 ARM_COMPUTE_ERROR_ON(_input_new->buffer() == nullptr);
402 ARM_COMPUTE_ERROR_ON(_old_scharr_gx->buffer() == nullptr);
403 ARM_COMPUTE_ERROR_ON(_old_scharr_gy->buffer() == nullptr);
404
405 const int list_end = window.x().end();
406 const int list_start = window.x().start();
407
408 init_keypoints(list_start, list_end);
409
410 const int buffer_size = _window_dimension * _window_dimension;
411 std::vector<int32_t> bilinear_ix(buffer_size);
412 std::vector<int32_t> bilinear_iy(buffer_size);
413
414 const int half_window = _window_dimension / 2;
415
416 auto is_invalid_keypoint = [&](const NELKInternalKeypoint & keypoint)
417 {
418 const int x = std::floor(keypoint.x);
419 const int y = std::floor(keypoint.y);
420
421 return (x - half_window < _valid_region.start(0)) || (x + half_window >= _valid_region.end(0) - 1) || (y - half_window < _valid_region.start(1)) || (y + half_window >= _valid_region.end(1) - 1);
422 };
423
424 for(int list_indx = list_start; list_indx < list_end; ++list_indx)
425 {
426 NELKInternalKeypoint &old_keypoint = _old_points_internal->at(list_indx);
427 NELKInternalKeypoint &new_keypoint = _new_points_internal->at(list_indx);
428
429 if(!old_keypoint.tracking_status)
430 {
431 continue;
432 }
433
434 if(is_invalid_keypoint(old_keypoint))
435 {
436 if(_level == 0)
437 {
438 new_keypoint.tracking_status = false;
439 }
440
441 continue;
442 }
443
444 // Compute spatial gradient matrix
445 int iA11 = 0;
446 int iA12 = 0;
447 int iA22 = 0;
448
449 std::tie(iA11, iA12, iA22) = compute_spatial_gradient_matrix(old_keypoint, bilinear_ix.data(), bilinear_iy.data());
450
451 const float A11 = iA11 * FLT_SCALE;
452 const float A12 = iA12 * FLT_SCALE;
453 const float A22 = iA22 * FLT_SCALE;
454
455 // Calculate minimum eigenvalue
456 const float sum_A11_A22 = A11 + A22;
457 const float discriminant = sum_A11_A22 * sum_A11_A22 - 4.0f * (A11 * A22 - A12 * A12);
458 // Divide by _window_dimension^2 to reduce the floating point accummulation error
459 const float minimum_eigenvalue = (sum_A11_A22 - std::sqrt(discriminant)) / (2.0f * _window_dimension * _window_dimension);
460
461 // Determinant
462 const double D = A11 * A22 - A12 * A12;
463
464 // Check if it is a good point to track
465 if(minimum_eigenvalue < EIGENVALUE_THRESHOLD || D < DETERMINANT_THRESHOLD)
466 {
467 // Invalidate tracked point
468 if(_level == 0)
469 {
470 new_keypoint.tracking_status = false;
471 }
472
473 continue;
474 }
475
476 float prev_delta_x = 0.0f;
477 float prev_delta_y = 0.0f;
478
479 for(unsigned int j = 0; j < _num_iterations; ++j)
480 {
481 if(is_invalid_keypoint(new_keypoint))
482 {
483 if(_level == 0)
484 {
485 new_keypoint.tracking_status = false;
486 }
487
488 break;
489 }
490
491 // Compute image mismatch vector
492 int ib1 = 0;
493 int ib2 = 0;
494
495 std::tie(ib1, ib2) = compute_image_mismatch_vector(old_keypoint, new_keypoint, bilinear_ix.data(), bilinear_iy.data());
496
497 double b1 = ib1 * FLT_SCALE;
498 double b2 = ib2 * FLT_SCALE;
499
500 // Compute motion vector -> A^-1 * -b
501 const float delta_x = (A12 * b2 - A22 * b1) / D;
502 const float delta_y = (A12 * b1 - A11 * b2) / D;
503
504 // Update the new position
505 new_keypoint.x += delta_x;
506 new_keypoint.y += delta_y;
507
508 const float mag2 = delta_x * delta_x + delta_y * delta_y;
509
510 // Check if termination criteria is EPSILON and if it is satisfied
511 if(mag2 <= _epsilon && (_termination == Termination::TERM_CRITERIA_EPSILON || _termination == Termination::TERM_CRITERIA_BOTH))
512 {
513 break;
514 }
515
516 // Check convergence analyzing the previous delta
517 if(j > 0 && std::fabs(delta_x + prev_delta_x) < 0.01f && std::fabs(delta_y + prev_delta_y) < 0.01f)
518 {
519 new_keypoint.x -= delta_x * _pyramid_scale;
520 new_keypoint.y -= delta_y * _pyramid_scale;
521 break;
522 }
523
524 prev_delta_x = delta_x;
525 prev_delta_y = delta_y;
526 }
527 }
528
529 if(_level == 0)
530 {
531 for(int list_indx = list_start; list_indx < list_end; ++list_indx)
532 {
533 const NELKInternalKeypoint &new_keypoint = _new_points_internal->at(list_indx);
534
535 _new_points->at(list_indx).x = roundf(new_keypoint.x);
536 _new_points->at(list_indx).y = roundf(new_keypoint.y);
537 _new_points->at(list_indx).tracking_status = new_keypoint.tracking_status ? 1 : 0;
538 }
539 }
540 }
541