1 // Three-lobed Lanczos, the most common choice.
2 #define LANCZOS_RADIUS 3.0
10 #include <Eigen/Sparse>
11 #include <Eigen/SparseQR>
12 #include <Eigen/OrderingMethods>
14 #include "effect_chain.h"
15 #include "effect_util.h"
18 #include "resample_effect.h"
21 using namespace Eigen;
37 return 1.0f - fabs(x);
43 float lanczos_weight(float x, float a)
48 return sinc(M_PI * x) * sinc(M_PI * x / a);
52 // Euclid's algorithm, from Wikipedia.
53 unsigned gcd(unsigned a, unsigned b)
63 template<class DestFloat>
64 unsigned combine_samples(const Tap<float> *src, Tap<DestFloat> *dst, unsigned src_size, unsigned num_src_samples, unsigned max_samples_saved)
66 // Cut off near-zero values at both sides.
67 unsigned num_samples_saved = 0;
68 while (num_samples_saved < max_samples_saved &&
69 num_src_samples > 0 &&
70 fabs(src[0].weight) < 1e-6) {
75 while (num_samples_saved < max_samples_saved &&
76 num_src_samples > 0 &&
77 fabs(src[num_src_samples - 1].weight) < 1e-6) {
82 for (unsigned i = 0, j = 0; i < num_src_samples; ++i, ++j) {
83 // Copy the sample directly; it will be overwritten later if we can combine.
85 dst[j].weight = convert_float<float, DestFloat>(src[i].weight);
86 dst[j].pos = convert_float<float, DestFloat>(src[i].pos);
89 if (i == num_src_samples - 1) {
90 // Last sample; cannot combine.
93 assert(num_samples_saved <= max_samples_saved);
94 if (num_samples_saved == max_samples_saved) {
95 // We could maybe save more here, but other rows can't, so don't bother.
99 float w1 = src[i].weight;
100 float w2 = src[i + 1].weight;
101 if (w1 * w2 < 0.0f) {
102 // Differing signs; cannot combine.
106 float pos1 = src[i].pos;
107 float pos2 = src[i + 1].pos;
110 fp16_int_t pos, total_weight;
112 combine_two_samples(w1, w2, pos1, pos2, src_size, &pos, &total_weight, &sum_sq_error);
114 // If the interpolation error is larger than that of about sqrt(2) of
115 // a level at 8-bit precision, don't combine. (You'd think 1.0 was enough,
116 // but since the artifacts are not really random, they can get quite
117 // visible. On the other hand, going to 0.25f, I can see no change at
118 // all with 8-bit output, so it would not seem to be worth it.)
119 if (sum_sq_error > 0.5f / (255.0f * 255.0f)) {
123 // OK, we can combine this and the next sample.
125 dst[j].weight = total_weight;
129 ++i; // Skip the next sample.
132 return num_samples_saved;
135 // Normalize so that the sum becomes one. Note that we do it twice;
136 // this sometimes helps a tiny little bit when we have many samples.
138 void normalize_sum(Tap<T>* vals, unsigned num)
140 for (int normalize_pass = 0; normalize_pass < 2; ++normalize_pass) {
142 for (unsigned i = 0; i < num; ++i) {
143 sum += to_fp64(vals[i].weight);
145 for (unsigned i = 0; i < num; ++i) {
146 vals[i].weight = from_fp64<T>(to_fp64(vals[i].weight) / sum);
151 // Make use of the bilinear filtering in the GPU to reduce the number of samples
152 // we need to make. This is a bit more complex than BlurEffect since we cannot combine
153 // two neighboring samples if their weights have differing signs, so we first need to
154 // figure out the maximum number of samples. Then, we downconvert all the weights to
155 // that number -- we could have gone for a variable-length system, but this is simpler,
156 // and the gains would probably be offset by the extra cost of checking when to stop.
158 // The greedy strategy for combining samples is optimal.
159 template<class DestFloat>
160 unsigned combine_many_samples(const Tap<float> *weights, unsigned src_size, unsigned src_samples, unsigned dst_samples, Tap<DestFloat> **bilinear_weights)
162 int src_bilinear_samples = 0;
163 for (unsigned y = 0; y < dst_samples; ++y) {
164 unsigned num_samples_saved = combine_samples<DestFloat>(weights + y * src_samples, NULL, src_size, src_samples, UINT_MAX);
165 src_bilinear_samples = max<int>(src_bilinear_samples, src_samples - num_samples_saved);
168 // Now that we know the right width, actually combine the samples.
169 *bilinear_weights = new Tap<DestFloat>[dst_samples * src_bilinear_samples];
170 for (unsigned y = 0; y < dst_samples; ++y) {
171 Tap<DestFloat> *bilinear_weights_ptr = *bilinear_weights + y * src_bilinear_samples;
172 unsigned num_samples_saved = combine_samples(
173 weights + y * src_samples,
174 bilinear_weights_ptr,
177 src_samples - src_bilinear_samples);
178 assert(int(src_samples) - int(num_samples_saved) == src_bilinear_samples);
179 normalize_sum(bilinear_weights_ptr, src_bilinear_samples);
181 return src_bilinear_samples;
184 // Compute the sum of squared errors between the ideal weights (which are
185 // assumed to fall exactly on pixel centers) and the weights that result
186 // from sampling at <bilinear_weights>. The primary reason for the difference
187 // is inaccuracy in the sampling positions, both due to limited precision
188 // in storing them (already inherent in sending them in as fp16_int_t)
189 // and in subtexel sampling precision (which we calculate in this function).
191 double compute_sum_sq_error(const Tap<float>* weights, unsigned num_weights,
192 const Tap<T>* bilinear_weights, unsigned num_bilinear_weights,
195 // Find the effective range of the bilinear-optimized kernel.
196 // Due to rounding of the positions, this is not necessarily the same
197 // as the intended range (ie., the range of the original weights).
198 int lower_pos = int(floor(to_fp64(bilinear_weights[0].pos) * size - 0.5));
199 int upper_pos = int(ceil(to_fp64(bilinear_weights[num_bilinear_weights - 1].pos) * size - 0.5)) + 2;
200 lower_pos = min<int>(lower_pos, lrintf(weights[0].pos * size - 0.5));
201 upper_pos = max<int>(upper_pos, lrintf(weights[num_weights - 1].pos * size - 0.5) + 1);
203 float* effective_weights = new float[upper_pos - lower_pos];
204 for (int i = 0; i < upper_pos - lower_pos; ++i) {
205 effective_weights[i] = 0.0f;
208 // Now find the effective weights that result from this sampling.
209 for (unsigned i = 0; i < num_bilinear_weights; ++i) {
210 const float pixel_pos = to_fp64(bilinear_weights[i].pos) * size - 0.5f;
211 const int x0 = int(floor(pixel_pos)) - lower_pos;
212 const int x1 = x0 + 1;
213 const float f = lrintf((pixel_pos - (x0 + lower_pos)) / movit_texel_subpixel_precision) * movit_texel_subpixel_precision;
217 assert(x0 < upper_pos - lower_pos);
218 assert(x1 < upper_pos - lower_pos);
220 effective_weights[x0] += to_fp64(bilinear_weights[i].weight) * (1.0 - f);
221 effective_weights[x1] += to_fp64(bilinear_weights[i].weight) * f;
224 // Subtract the desired weights to get the error.
225 for (unsigned i = 0; i < num_weights; ++i) {
226 const int x = lrintf(weights[i].pos * size - 0.5f) - lower_pos;
228 assert(x < upper_pos - lower_pos);
230 effective_weights[x] -= weights[i].weight;
233 double sum_sq_error = 0.0;
234 for (unsigned i = 0; i < num_weights; ++i) {
235 sum_sq_error += effective_weights[i] * effective_weights[i];
238 delete[] effective_weights;
244 ResampleEffect::ResampleEffect()
247 offset_x(0.0f), offset_y(0.0f),
248 zoom_x(1.0f), zoom_y(1.0f),
249 zoom_center_x(0.5f), zoom_center_y(0.5f)
251 register_int("width", &output_width);
252 register_int("height", &output_height);
254 // The first blur pass will forward resolution information to us.
255 hpass = new SingleResamplePassEffect(this);
256 CHECK(hpass->set_int("direction", SingleResamplePassEffect::HORIZONTAL));
257 vpass = new SingleResamplePassEffect(NULL);
258 CHECK(vpass->set_int("direction", SingleResamplePassEffect::VERTICAL));
263 void ResampleEffect::rewrite_graph(EffectChain *graph, Node *self)
265 Node *hpass_node = graph->add_node(hpass);
266 Node *vpass_node = graph->add_node(vpass);
267 graph->connect_nodes(hpass_node, vpass_node);
268 graph->replace_receiver(self, hpass_node);
269 graph->replace_sender(self, vpass_node);
270 self->disabled = true;
273 // We get this information forwarded from the first blur pass,
274 // since we are not part of the chain ourselves.
275 void ResampleEffect::inform_input_size(unsigned input_num, unsigned width, unsigned height)
277 assert(input_num == 0);
281 input_height = height;
285 void ResampleEffect::update_size()
288 ok |= hpass->set_int("input_width", input_width);
289 ok |= hpass->set_int("input_height", input_height);
290 ok |= hpass->set_int("output_width", output_width);
291 ok |= hpass->set_int("output_height", input_height);
293 ok |= vpass->set_int("input_width", output_width);
294 ok |= vpass->set_int("input_height", input_height);
295 ok |= vpass->set_int("output_width", output_width);
296 ok |= vpass->set_int("output_height", output_height);
300 // The offset added due to zoom may have changed with the size.
301 update_offset_and_zoom();
304 void ResampleEffect::update_offset_and_zoom()
308 // Zoom from the right origin. (zoom_center is given in normalized coordinates,
310 float extra_offset_x = zoom_center_x * (1.0f - 1.0f / zoom_x) * input_width;
311 float extra_offset_y = (1.0f - zoom_center_y) * (1.0f - 1.0f / zoom_y) * input_height;
313 ok |= hpass->set_float("offset", extra_offset_x + offset_x);
314 ok |= vpass->set_float("offset", extra_offset_y - offset_y); // Compensate for the bottom-left origin.
315 ok |= hpass->set_float("zoom", zoom_x);
316 ok |= vpass->set_float("zoom", zoom_y);
321 bool ResampleEffect::set_float(const string &key, float value) {
322 if (key == "width") {
323 output_width = value;
327 if (key == "height") {
328 output_height = value;
334 update_offset_and_zoom();
339 update_offset_and_zoom();
342 if (key == "zoom_x") {
347 update_offset_and_zoom();
350 if (key == "zoom_y") {
355 update_offset_and_zoom();
358 if (key == "zoom_center_x") {
359 zoom_center_x = value;
360 update_offset_and_zoom();
363 if (key == "zoom_center_y") {
364 zoom_center_y = value;
365 update_offset_and_zoom();
371 SingleResamplePassEffect::SingleResamplePassEffect(ResampleEffect *parent)
373 direction(HORIZONTAL),
378 last_input_width(-1),
379 last_input_height(-1),
380 last_output_width(-1),
381 last_output_height(-1),
382 last_offset(0.0 / 0.0), // NaN.
383 last_zoom(0.0 / 0.0) // NaN.
385 register_int("direction", (int *)&direction);
386 register_int("input_width", &input_width);
387 register_int("input_height", &input_height);
388 register_int("output_width", &output_width);
389 register_int("output_height", &output_height);
390 register_float("offset", &offset);
391 register_float("zoom", &zoom);
393 glGenTextures(1, &texnum);
396 SingleResamplePassEffect::~SingleResamplePassEffect()
398 glDeleteTextures(1, &texnum);
401 string SingleResamplePassEffect::output_fragment_shader()
404 sprintf(buf, "#define DIRECTION_VERTICAL %d\n", (direction == VERTICAL));
405 return buf + read_file("resample_effect.frag");
408 // Using vertical scaling as an example:
410 // Generally out[y] = w0 * in[yi] + w1 * in[yi + 1] + w2 * in[yi + 2] + ...
412 // Obviously, yi will depend on y (in a not-quite-linear way), but so will
413 // the weights w0, w1, w2, etc.. The easiest way of doing this is to encode,
414 // for each sample, the weight and the yi value, e.g. <yi, w0>, <yi + 1, w1>,
415 // and so on. For each y, we encode these along the x-axis (since that is spare),
416 // so out[0] will read from parameters <x,y> = <0,0>, <1,0>, <2,0> and so on.
418 // For horizontal scaling, we fill in the exact same texture;
419 // the shader just interprets it differently.
420 void SingleResamplePassEffect::update_texture(GLuint glsl_program_num, const string &prefix, unsigned *sampler_num)
422 unsigned src_size, dst_size;
423 if (direction == SingleResamplePassEffect::HORIZONTAL) {
424 assert(input_height == output_height);
425 src_size = input_width;
426 dst_size = output_width;
427 } else if (direction == SingleResamplePassEffect::VERTICAL) {
428 assert(input_width == output_width);
429 src_size = input_height;
430 dst_size = output_height;
435 // For many resamplings (e.g. 640 -> 1280), we will end up with the same
436 // set of samples over and over again in a loop. Thus, we can compute only
437 // the first such loop, and then ask the card to repeat the texture for us.
438 // This is both easier on the texture cache and lowers our CPU cost for
439 // generating the kernel somewhat.
440 float scaling_factor;
441 if (fabs(zoom - 1.0f) < 1e-6) {
442 num_loops = gcd(src_size, dst_size);
443 scaling_factor = float(dst_size) / float(src_size);
445 // If zooming is enabled (ie., zoom != 1), we turn off the looping.
446 // We _could_ perhaps do it for rational zoom levels (especially
447 // things like 2:1), but it doesn't seem to be worth it, given that
448 // the most common use case would seem to be varying the zoom
449 // from frame to frame.
451 scaling_factor = zoom * float(dst_size) / float(src_size);
453 slice_height = 1.0f / num_loops;
454 unsigned dst_samples = dst_size / num_loops;
456 // Sample the kernel in the right place. A diagram with a triangular kernel
457 // (corresponding to linear filtering, and obviously with radius 1)
458 // for easier ASCII art drawing:
464 // x---x---x x x---x---x---x
466 // Scaling up (in this case, 2x) means sampling more densely:
472 // x-x-x-x-x-x x x x-x-x-x-x-x-x-x
474 // When scaling up, any destination pixel will only be influenced by a few
475 // (in this case, two) neighboring pixels, and more importantly, the number
476 // will not be influenced by the scaling factor. (Note, however, that the
477 // pixel centers have moved, due to OpenGL's center-pixel convention.)
478 // The only thing that changes is the weights themselves, as the sampling
479 // points are at different distances from the original pixels.
481 // Scaling down is a different story:
487 // --x------ x --x-------x--
489 // Again, the pixel centers have moved in a maybe unintuitive fashion,
490 // although when you consider that there are multiple source pixels around,
491 // it's not so bad as at first look:
497 // --x-------x-------x-------x--
499 // As you can see, the new pixels become averages of the two neighboring old
500 // ones (the situation for Lanczos is of course more complex).
502 // Anyhow, in this case we clearly need to look at more source pixels
503 // to compute the destination pixel, and how many depend on the scaling factor.
504 // Thus, the kernel width will vary with how much we scale.
505 float radius_scaling_factor = min(scaling_factor, 1.0f);
506 int int_radius = lrintf(LANCZOS_RADIUS / radius_scaling_factor);
507 int src_samples = int_radius * 2 + 1;
508 Tap<float> *weights = new Tap<float>[dst_samples * src_samples];
509 float subpixel_offset = offset - lrintf(offset); // The part not covered by whole_pixel_offset.
510 assert(subpixel_offset >= -0.5f && subpixel_offset <= 0.5f);
511 for (unsigned y = 0; y < dst_samples; ++y) {
512 // Find the point around which we want to sample the source image,
513 // compensating for differing pixel centers as the scale changes.
514 float center_src_y = (y + 0.5f) / scaling_factor - 0.5f;
515 int base_src_y = lrintf(center_src_y);
517 // Now sample <int_radius> pixels on each side around that point.
518 for (int i = 0; i < src_samples; ++i) {
519 int src_y = base_src_y + i - int_radius;
520 float weight = lanczos_weight(radius_scaling_factor * (src_y - center_src_y - subpixel_offset), LANCZOS_RADIUS);
521 weights[y * src_samples + i].weight = weight * radius_scaling_factor;
522 weights[y * src_samples + i].pos = (src_y + 0.5) / float(src_size);
526 // Now make use of the bilinear filtering in the GPU to reduce the number of samples
527 // we need to make. Try fp16 first; if it's not accurate enough, we go to fp32.
528 // Our tolerance level for total error is a bit higher than the one for invididual
529 // samples, since one would assume overall errors in the shape don't matter as much.
530 const float max_error = 2.0f / (255.0f * 255.0f);
531 Tap<fp16_int_t> *bilinear_weights_fp16;
532 src_bilinear_samples = combine_many_samples(weights, src_size, src_samples, dst_samples, &bilinear_weights_fp16);
533 Tap<float> *bilinear_weights_fp32 = NULL;
534 bool fallback_to_fp32 = false;
535 double max_sum_sq_error_fp16 = 0.0;
536 for (unsigned y = 0; y < dst_samples; ++y) {
537 double sum_sq_error_fp16 = compute_sum_sq_error(
538 weights + y * src_samples, src_samples,
539 bilinear_weights_fp16 + y * src_bilinear_samples, src_bilinear_samples,
541 max_sum_sq_error_fp16 = std::max(max_sum_sq_error_fp16, sum_sq_error_fp16);
542 if (max_sum_sq_error_fp16 > max_error) {
547 if (max_sum_sq_error_fp16 > max_error) {
548 fallback_to_fp32 = true;
549 src_bilinear_samples = combine_many_samples(weights, src_size, src_samples, dst_samples, &bilinear_weights_fp32);
552 // Encode as a two-component texture. Note the GL_REPEAT.
553 glActiveTexture(GL_TEXTURE0 + *sampler_num);
555 glBindTexture(GL_TEXTURE_2D, texnum);
557 glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
559 glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
561 glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);
563 if (fallback_to_fp32) {
564 glTexImage2D(GL_TEXTURE_2D, 0, GL_RG32F, src_bilinear_samples, dst_samples, 0, GL_RG, GL_FLOAT, bilinear_weights_fp32);
566 glTexImage2D(GL_TEXTURE_2D, 0, GL_RG16F, src_bilinear_samples, dst_samples, 0, GL_RG, GL_HALF_FLOAT, bilinear_weights_fp16);
571 delete[] bilinear_weights_fp16;
572 delete[] bilinear_weights_fp32;
575 void SingleResamplePassEffect::set_gl_state(GLuint glsl_program_num, const string &prefix, unsigned *sampler_num)
577 Effect::set_gl_state(glsl_program_num, prefix, sampler_num);
579 assert(input_width > 0);
580 assert(input_height > 0);
581 assert(output_width > 0);
582 assert(output_height > 0);
584 if (input_width != last_input_width ||
585 input_height != last_input_height ||
586 output_width != last_output_width ||
587 output_height != last_output_height ||
588 offset != last_offset ||
590 update_texture(glsl_program_num, prefix, sampler_num);
591 last_input_width = input_width;
592 last_input_height = input_height;
593 last_output_width = output_width;
594 last_output_height = output_height;
595 last_offset = offset;
599 glActiveTexture(GL_TEXTURE0 + *sampler_num);
601 glBindTexture(GL_TEXTURE_2D, texnum);
604 set_uniform_int(glsl_program_num, prefix, "sample_tex", *sampler_num);
606 set_uniform_int(glsl_program_num, prefix, "num_samples", src_bilinear_samples);
607 set_uniform_float(glsl_program_num, prefix, "num_loops", num_loops);
608 set_uniform_float(glsl_program_num, prefix, "slice_height", slice_height);
610 // Instructions for how to convert integer sample numbers to positions in the weight texture.
611 set_uniform_float(glsl_program_num, prefix, "sample_x_scale", 1.0f / src_bilinear_samples);
612 set_uniform_float(glsl_program_num, prefix, "sample_x_offset", 0.5f / src_bilinear_samples);
614 float whole_pixel_offset;
615 if (direction == SingleResamplePassEffect::VERTICAL) {
616 whole_pixel_offset = lrintf(offset) / float(input_height);
618 whole_pixel_offset = lrintf(offset) / float(input_width);
620 set_uniform_float(glsl_program_num, prefix, "whole_pixel_offset", whole_pixel_offset);
622 // We specifically do not want mipmaps on the input texture;
623 // they break minification.
624 Node *self = chain->find_node_for_effect(this);
625 glActiveTexture(chain->get_input_sampler(self, 0));
627 glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);