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上篇讲述了一维FFT的GPU实现(FFT算法实现——基于GPU的基2快速傅里叶变换),后来我又由于需要做了一下二维FFT,大概思路如下。
首先看的肯定是公式:
如上面公式所描述的,2维FFT只需要拆分成行FFT,和列FFT就行了,其中我在下面的实现是假设原点在F(0,0),由于我的代码需要原点在中心,所以在最后我将原点移动到了中心。
下面是原点F(0,0)的2维FFT的伪代码:
//C2DFFT //被执行2DFFT的是一个N*N的矩阵,在source_2d中按行顺序储存 //水平方向FFT for (int i=0;i<N;i++) { fft1(&source_2d[i*N],&source_2d_1[i*N],N); } //转置列成行 for (int i=0;i<N*N;i++) { int x = i%N; int y = i/N; int index = x*N+y; source_2d[index] = source_2d_1[i]; } //垂直FFT for(int i=0;i<N;i++) { fft1(&source_2d[i*N],&source_2d_1[i*N],N); } //转置回来 for (int i=0;i<N*N;i++) { int x = i%N; int y = i/N; int index = x*N+y; source_2d[index] = source_2d_1[i]; }
GPU实现无非把这些东西转换到GPU上。
我基于OpenGL的fragment shader来计算fft;数据都存放在纹理或者FBO里面。和1维fft不同的是,NXN的数据里面,只是对当前列或者当前排做一维FFT,所以bit反转表只需要一个1*N的buffer就可以了。对应的蝴蝶图数据也只需要1*N即可。所以我们有如下的分配:
static ofFbo _fbo_bitrev_table; static ofFbo _origin_butterfly_2d; _fbo_bitrev_table.allocate(N,1,GL_RGBA32F); _origin_butterfly_2d.allocate(N,1,GL_RGBA32F);
首先要做的是把长度为N的bit反转表求出来,这个只需要求一次,所以在最开始的时候就用CPU求出来:
for(int i=0;i<N;i++) { _bitrev_index_2d.setColor(i,0,ofFloatColor(bit_rev(i,N-1),0,0,0)); } _bitrev_index_2d.update(); //翻转后的索引 _fbo_bitrev_table.begin(); _bitrev_index_2d.draw(0,0,N,1); _fbo_bitrev_table.end();
然后初始化最初的蝴蝶图,这个和1维FFT是一样的,只是长度不同而已:
for(int i=0;i<N;i++) { //初始化二维蝴蝶图 if(i%2==0) { _data_2d.setColor(i,0,ofFloatColor(0.f,2.f,0,i+1)); } else { _data_2d.setColor(i,0,ofFloatColor(1.f,2.f,0,i-1)); } } _data_2d.update(); /////////////////2D初始化///////////////// //初始化2D蝴蝶图 _weight_index_2d[0].begin(); _data_2d.draw(0,0,N,1); _weight_index_2d[0].end(); //备份2D初始蝴蝶图,用于下一次新的计算 _origin_butterfly_2d.begin(); _data_2d.draw(0,0,N,1); _origin_butterfly_2d.end();
辅助函数:
static unsigned int bit_rev(unsigned int v, unsigned int maxv) { unsigned int t = log(maxv + 1)/log(2); unsigned int ret = 0; unsigned int s = 0x80000000>>(31); for (unsigned int i = 0; i < t; ++i) { unsigned int r = v&(s << i); ret |= (r << (t-i-1)) >> (i); } return ret; } static void bit_reverse_copy(RBVector2 src[], RBVector2 des[], int len) { for (int i = 0; i < len;i++) { des[bit_rev(i, len-1)] = src[i]; } }
下面定义计算2维IFFT的函数:
void GPUFFT::ifft_2d(ofFbo& in,ofFbo& out,int size);
其中in是输入,out是输出,size就是N,由初始化的时候传入了一次,在这里写是为了方便调试的时候临时改变尺寸。
Ifft本身的代码和上面形式一样,内容变成了各种shader计算:
void GPUFFT::ifft_2d(ofFbo& in,ofFbo& out,int size) { //禁用Alpha混合,否则绘制到FBO会混合Alpha,造成数据丢失 ofDisableAlphaBlending(); //水平FFT _weight_index_2d[_cur_2d].begin(); _origin_butterfly_2d.draw(0,0,N,1); _weight_index_2d[_cur_2d].end(); _fbo_in_bitreved_2d.begin(); _bit_reverse_shader_2d.begin(); _bit_reverse_shader_2d.setUniform3f("iResolution",N,N,0); _bit_reverse_shader_2d.setUniform1i("N",N); _bit_reverse_shader_2d.setUniform1i("dir",1); _bit_reverse_shader_2d.setUniformTexture("tex_origin",in.getTextureReference(),1); _bit_reverse_shader_2d.setUniformTexture("tex_bitreverse_table",_fbo_bitrev_table.getTextureReference(),2); ofRect(0,0,N,N); _bit_reverse_shader_2d.end(); _fbo_in_bitreved_2d.end(); //翻转后的数据 _res_back_2d[_cur_2d].begin(); _fbo_in_bitreved_2d.draw(0,0,N,N); _res_back_2d[_cur_2d].end(); for(int i = 1;i<N;i*=2) { _res_back_2d[1-_cur_2d].begin(); ofClear(0,0,0,0); _gpu_fft_shader_2d.begin(); _gpu_fft_shader_2d.setUniform1i("size",N); _gpu_fft_shader_2d.setUniform1i("n_step",i); _gpu_fft_shader_2d.setUniform3f("iResolution",N,N,0); _gpu_fft_shader_2d.setUniform1i("dir",1); _gpu_fft_shader_2d.setUniformTexture("tex_index_weight",_weight_index_2d[_cur_2d].getTextureReference(),1); _gpu_fft_shader_2d.setUniformTexture("tex_res_back",_res_back_2d[_cur_2d].getTextureReference(),2); //_gpu_fft_shader_2d.setUniformTexture("test",imag_test.getTextureReference(),4); ofRect(0,0,N,N); _gpu_fft_shader_2d.end(); _res_back_2d[1-_cur_2d].end(); _weight_index_2d[1-_cur_2d].begin(); ofClear(0,0,0,0); _weight_index_shader_2d.begin(); _weight_index_shader_2d.setUniform1i("size",N); _weight_index_shader_2d.setUniform1i("n_step",i); _weight_index_shader_2d.setUniform3f("iResolution",N,1,0); _weight_index_shader_2d.setUniform1i("dir",1); _weight_index_shader_2d.setUniformTexture("tex_input",_weight_index_2d[_cur_2d].getTextureReference(),1); ofRect(0,0,N,1); _weight_index_shader_2d.end(); _weight_index_2d[1-_cur_2d].end(); _cur_2d = 1 - _cur_2d; } //for ifft _res_back_2d[1-_cur_2d].begin(); _res_back_2d[_cur_2d].draw(0,0,N,N); _res_back_2d[1-_cur_2d].end(); _res_back_2d[_cur_2d].begin(); _ifft_div_shader_2d.begin(); _ifft_div_shader_2d.setUniform1i("N",N); _ifft_div_shader_2d.setUniform3f("iResolution",N,N,0); _ifft_div_shader_2d.setUniformTexture("tex_rgb",_res_back_2d[1-_cur_2d].getTextureReference(),1); ofRect(0,0,N,N); _ifft_div_shader_2d.end(); _res_back_2d[_cur_2d].end(); //垂直FFT //垂直方向的所有都是计算都按照垂直方向来 _weight_index_2d[_cur_2d].begin(); _origin_butterfly_2d.draw(0,0,N,1); _weight_index_2d[_cur_2d].end(); //这一步不会将垂直水平化 _fbo_in_bitreved_2d.begin(); _bit_reverse_shader_2d.begin(); _bit_reverse_shader_2d.setUniform3f("iResolution",N,N,0); _bit_reverse_shader_2d.setUniform1i("N",N); _bit_reverse_shader_2d.setUniform1i("dir",2); _bit_reverse_shader_2d.setUniformTexture("tex_origin",_res_back_2d[_cur_2d].getTextureReference(),1); _bit_reverse_shader_2d.setUniformTexture("tex_bitreverse_table",_fbo_bitrev_table.getTextureReference(),2); ofRect(0,0,N,N); _bit_reverse_shader_2d.end(); _fbo_in_bitreved_2d.end(); //翻转后的数据 _res_back_2d[_cur_2d].begin(); _fbo_in_bitreved_2d.draw(0,0,N,N); _res_back_2d[_cur_2d].end(); for(int i = 1;i<N;i*=2) { _res_back_2d[1-_cur_2d].begin(); ofClear(0,0,0,0); _gpu_fft_shader_2d.begin(); _gpu_fft_shader_2d.setUniform1i("size",N); _gpu_fft_shader_2d.setUniform1i("n_step",i); _gpu_fft_shader_2d.setUniform3f("iResolution",N,N,0); _gpu_fft_shader_2d.setUniform1i("dir",2); _gpu_fft_shader_2d.setUniformTexture("tex_index_weight",_weight_index_2d[_cur_2d].getTextureReference(),1); _gpu_fft_shader_2d.setUniformTexture("tex_res_back",_res_back_2d[_cur_2d].getTextureReference(),2); //_gpu_fft_shader_2d.setUniformTexture("test",imag_test.getTextureReference(),4); ofRect(0,0,N,N); _gpu_fft_shader_2d.end(); _res_back_2d[1-_cur_2d].end(); _weight_index_2d[1-_cur_2d].begin(); ofClear(0,0,0,0); _weight_index_shader_2d.begin(); _weight_index_shader_2d.setUniform1i("size",N); _weight_index_shader_2d.setUniform1i("n_step",i); _weight_index_shader_2d.setUniform3f("iResolution",N,1,0); _weight_index_shader_2d.setUniform1i("dir",2); _weight_index_shader_2d.setUniformTexture("tex_input",_weight_index_2d[_cur_2d].getTextureReference(),1); ofRect(0,0,N,1); _weight_index_shader_2d.end(); _weight_index_2d[1-_cur_2d].end(); _cur_2d = 1 - _cur_2d; } //for ifft _res_back_2d[1-_cur_2d].begin(); _res_back_2d[_cur_2d].draw(0,0,N,N); _res_back_2d[1-_cur_2d].end(); _res_back_2d[_cur_2d].begin(); _ifft_div_shader_2d.begin(); _ifft_div_shader_2d.setUniform1i("N",N); _ifft_div_shader_2d.setUniform3f("iResolution",N,N,0); _ifft_div_shader_2d.setUniformTexture("tex_rgb",_res_back_2d[1-_cur_2d].getTextureReference(),1); ofRect(0,0,N,N); _ifft_div_shader_2d.end(); _res_back_2d[_cur_2d].end(); out.begin(); _res_back_2d[_cur_2d].draw(0,0,N,N); out.end(); //恢复Alpha混合 //ofEnableAlphaBlending(); }
现在来看shader内容:
_bit_reverse_shader_2d
这个shader用于将整个N*N的数据全部按照行或者按照列进行翻装,使之满足执行fft的条件:
#version 130 uniform sampler2D tex_origin; //1xN查找表,用于查找索引对应的bitreverse数 uniform sampler2D tex_bitreverse_table; //1 for x direction,2 for y direction uniform int dir; uniform int N; uniform vec3 iResolution; out vec4 outColor; void main() { vec2 tex_coord = gl_FragCoord.xy/iResolution.xy; vec2 table_index; table_index.y = 0.5; if(dir==1) table_index.x = tex_coord.x; else table_index.x = tex_coord.y; float bitreverse = texture(tex_bitreverse_table,table_index).r; vec2 origin_index; if(dir==1) { //x方向 origin_index.y = tex_coord.y; origin_index.x = (bitreverse+0.5)/N; } else { //y方向 origin_index.x = tex_coord.x; origin_index.y = (bitreverse+0.5)/N; } vec2 param = texture(tex_origin,origin_index).xy; outColor = vec4(param,0,1); }
_gpu_fft_shader_2d
这是fft执行计算的部分,同样分为按行和按列:
#version 130 //NX1 uniform sampler2D tex_index_weight; //NXN uniform sampler2D tex_res_back; uniform sampler2D test; uniform int size; uniform int n_step; //1 for x direction,2 for y direction uniform int dir; uniform vec3 iResolution; out vec4 outColor; void main() { vec2 tex_coord = gl_FragCoord.xy/iResolution.xy; vec2 first_index; if(dir==1) { first_index.y = 0.5; first_index.x = tex_coord.x; } else { first_index.y = 0.5; first_index.x = tex_coord.y; } float cur_x = gl_FragCoord.x - 0.5; float cur_y = gl_FragCoord.y - 0.5; vec2 outv; vec4 temp = texture(tex_index_weight,first_index); //ifft vec2 weight = vec2(cos(temp.r/temp.g*2*3.141592653),-sin(temp.r/temp.g*2*3.141592653)); //fft //vec2 weight = vec2(cos(temp.r/temp.g*2*3.141592653),sin(temp.r/temp.g*2*3.141592653)); vec2 _param2_index; if(dir==1) { _param2_index.x = (temp.a + 0.5)/size; _param2_index.y = tex_coord.y; } else { _param2_index.x = tex_coord.x; _param2_index.y = (temp.a + 0.5)/size; } vec2 param1 = texture(tex_res_back,tex_coord).rg; vec2 param2 = texture(tex_res_back,_param2_index).rg; float tex_coord_n1; float tex_coord_n2; if(dir==1) { tex_coord_n1 = cur_x; } else { tex_coord_n1 = cur_y; } tex_coord_n2 = temp.a; if(tex_coord_n1<tex_coord_n2) { outv.r = param1.r + param2.r*weight.r-weight.g*param2.g; outv.g = param1.g +weight.r*param2.g + weight.g*param2.r; } else { outv.r = param2.r + param1.r*weight.r-weight.g*param1.g; outv.g = param2.g +weight.r*param1.g + weight.g*param1.r; } outColor = vec4(outv,0,1); }
_weight_index_shader_2d
更新蝴蝶图索引:
#version 130 uniform sampler2D tex_input; uniform int size; uniform int n_total; //start with 2 uniform int n_step; //1 for x direction,2 for y direction uniform int dir; uniform vec3 iResolution; out vec4 outColor; void main() { vec2 tex_coord = gl_FragCoord.xy/iResolution.xy; vec4 fetch = texture(tex_input,tex_coord); float cur_x = gl_FragCoord.x - 0.5; float cur_y = gl_FragCoord.y - 0.5; vec4 outv; float tex_coord_n; if(dir==1) { //x dir tex_coord_n = cur_x; } else { //y dir tex_coord_n = cur_x; } //updata weight vec2 pre_w = fetch.rg; float i = pre_w.r; float n = pre_w.g; float new_i; float new_n; new_i = i; new_n = n*2; if(int(tex_coord_n)%(n_step*4) > n_step*2-1) { new_i += n_step*2; } outv.r = new_i; outv.g = new_n; //outv.rg = tex_coord; //updata index vec2 pre_index = fetch.ba; int x = int(pre_index.x); int y = int(pre_index.y); int ni = n_step*2; float new_tex_coord_n = tex_coord_n; if((int(tex_coord_n)/ni)%2==0) { new_tex_coord_n += ni; } else { new_tex_coord_n -= ni; } outv.b = 0; outv.a = new_tex_coord_n; outColor = outv; //outColor = vec4(tex_coord_n,tex_coord_n%n_step,tex_coord_n%n_step,tex_coord_n%n_step); }
最后的
_ifft_div_shader_2d
是为了计算ifft,将每个计算结果除以一个N:
#version 130 uniform sampler2D tex_rgb; uniform int N; uniform vec3 iResolution; out vec4 outColor; void main() { vec2 tex_coord = gl_FragCoord.xy/iResolution.xy; vec2 outv; vec4 c = texture(tex_rgb,tex_coord); outv.r = c.r/N; outv.g = c.g/N; outColor = vec4(outv,0,1); }
最后,out里面就是结果了。
对于将原点移动到中心多了以下shader:
vec4 c; if(tex_coord.x>0.5&&tex_coord.y>0.5) { c = texture(tex_rgb,tex_coord-vec2(0.5,0.5)); } if(tex_coord.x>0.5&&tex_coord.y<0.5) { c = texture(tex_rgb,tex_coord+vec2(-0.5,0.5)); } if(tex_coord.x<0.5&&tex_coord.y>0.5) { c = texture(tex_rgb,tex_coord+vec2(0.5,-0.5)); } if(tex_coord.x<0.5&&tex_coord.y<0.5) { c = texture(tex_rgb,tex_coord+vec2(0.5,0.5)); } outColor = c;
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原文地址:http://www.cnblogs.com/wubugui/p/4521174.html