KAZE系列筆記：
1. OpenCV學習筆記（27）KAZE 算法原理與源碼分析（一）非線性擴散濾波
2. OpenCV學習筆記（28）KAZE 算法原理與源碼分析（二）非線性尺度空間構建
3. OpenCV學習筆記（29）KAZE 算法原理與源碼分析（三）特徵檢測與描述
4. OpenCV學習筆記（30）KAZE 算法原理與源碼分析（四）KAZE特徵的性能分析與比較
5. OpenCV學習筆記（31）KAZE 算法原理與源碼分析（五）KAZE的性能優化及與SIFT的比較
KAZE算法資源：
1. 論文： http://www.robesafe.com/personal/pablo.alcantarilla/papers/Alcantarilla12eccv.pdf
2. 項目主頁：http://www.robesafe.com/personal/pablo.alcantarilla/kaze.html
3. 作者代碼：http://www.robesafe.com/personal/pablo.alcantarilla/code/kaze_features_1_4.tar
（需要boost庫，另外其計時函數的使用比較複雜，可以用OpenCV的cv::getTickCount代替）
4. Computer Vision Talks的評測：http://computer-vision-talks.com/2013/03/porting-kaze-features-to-opencv/
5. Computer Vision Talks 博主Ievgen Khvedchenia將KAZE集成到OpenCV的cv::Feature2D類，但需要重新編譯OpenCV，並且沒有實現算法參數調整和按Mask過濾特徵點的功能：https://github.com/BloodAxe/opencv/tree/kaze-features
6. 我在Ievgen的項目庫中提取出KAZE，封裝成繼承cv::Feature2D的類，無需重新編譯OpenCV，實現了參數調整和Mask過濾的功能: https://github.com/yuhuazou/kaze_opencv (2013-03-28更新，對KAZE代碼進行了優化)
7. Matlab 版的接口程序，封裝了1.0版的KAZE代碼：https://github.com/vlfeat/vlbenchmarks/blob/unstable/%2BlocalFeatures/Kaze.m
2.3 與其他特徵算法的比較
2.3.1 與OpenCV API的融合
KAZE算法作者在其項目主頁提供了源碼，其中包括KAZE的核心算法庫以及KAZE特徵的提取、匹配和比較等例程，是基於OpenCV實現的。Computer Vision Talks的博主Ievgen Khvedchenia不久前將KAZE代碼融合到OpenCV的cv::Feature2D API中，不過他是OpenCV項目的維護者之一，他的目標是在未來的OpenCV版本中加入KAZE。使用他的KAZE類需要重新編譯OpenCV，並且目前只是簡單地嵌入、還不能調整KAZE類的參數，也不支持Mask過濾。
因爲想盡快測試和比較KAZE算法的性能，又不想重新編譯OpenCV，我在Ievgen的項目庫中將KAZE相關的代碼抽離出來，改造爲一個相對獨立的cv::KAZE類，繼承於cv::Feature2D類。這樣就可以方便地在OpenCV中使用，並能夠通過一致的接口與其它特徵算法進行比較。cv::KAZE類包括如下文件：
|--KAZE
| kaze_features.cpp // Class that warps KAZE to cv::Feature2D
| kaze_features.h
| kaze.cpp // Implementation of KAZE
| kaze.h
| kaze_config.cpp // Configuration variables and options
| kaze_config.h
| kaze_ipoint.cpp // Class that defines a point of interest
| kaze_ipoint.h
| kaze_nldiffusion_functions.cpp // Functions for non-linear diffusion applications
| kaze_nldiffusion_functions.h
| kaze_utils.cpp // Some useful functions
| kaze_utils.h
其中kaze_feature.h和kaze_feature.cpp是繼承cv::Feature2D的cv::KAZE類，通過這個類將KAZE核心算法庫與OpenCV的Feature2D類關聯起來。其具體代碼如下：
#ifndef _KAZE_FEATURES_H_
#define _KAZE_FEATURES_H_
////////////////////////////////////////////////////////////////////
// Extract from ..\opencv\modules\features2d\src\precomp.hpp
//
#ifdef HAVE_CVCONFIG_H
#include "cvconfig.h"
#endif
#include "opencv2/features2d/features2d.hpp"
#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/imgproc/imgproc_c.h"
#include "opencv2/core/internal.hpp"
#include <algorithm>
#ifdef HAVE_TEGRA_OPTIMIZATION
#include "opencv2/features2d/features2d_tegra.hpp"
#endif
//
////////////////////////////////////////////////////////////////////
#include "kaze_config.h"
/*!
KAZE features implementation.
!! Note that it has NOT been warped to cv::Algorithm in oder to avoid rebuilding OpenCV
So most functions of cv::Algorithm can not be used in cv::KAZE
http://www.robesafe.com/personal/pablo.alcantarilla/papers/Alcantarilla12eccv.pdf
*/
namespace cv
{
class CV_EXPORTS_W KAZE : public Feature2D
{
public:
CV_WRAP explicit KAZE();
KAZE(toptions &_options);
// returns the descriptor size in bytes
int descriptorSize() const;
// returns the descriptor type
int descriptorType() const;
// Compute the KAZE features and descriptors on an image
void operator()( InputArray image, InputArray mask, vector<KeyPoint>& keypoints,
OutputArray descriptors, bool useProvidedKeypoints=false ) const;
// Compute the KAZE features with mask
void operator()(InputArray image, InputArray mask, vector<KeyPoint>& keypoints) const;
// Compute the KAZE features and descriptors on an image WITHOUT mask
void operator()(InputArray image, vector<KeyPoint>& keypoints, OutputArray descriptors) const;
//AlgorithmInfo* info() const;
protected:
void detectImpl( const Mat& image, vector<KeyPoint>& keypoints, const Mat& mask=Mat() ) const;
// !! NOT recommend to use because KAZE descriptors ONLY work with KAZE features
void computeImpl( const Mat& image, vector<KeyPoint>& keypoints, Mat& descriptors ) const;
CV_PROP_RW int nfeatures;
private:
toptions options;
};
typedef KAZE KazeFeatureDetector;
//typedef KAZE KazeDescriptorExtractor; // NOT available because KAZE descriptors ONLY work with KAZE features
}
#endif
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/** Authors: Ievgen Khvedchenia */
/** Modified: Yuhua Zou, 2013-03-20 */
#include <iterator>
#include "kaze_features.h"
#include "kaze.h"
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
#define DEGREE_TO_RADIAN(x) ((x) * CV_PI / 180.0)
#define RADIAN_TO_DEGREE(x) ((x) * 180.0 / CV_PI)
namespace cv
{
/***
* Convertions between cv::Keypoint and KAZE::Ipoint
*/
static inline void convertPoint(const cv::KeyPoint& kp, Ipoint& aux)
{
aux.xf = kp.pt.x;
aux.yf = kp.pt.y;
aux.x = fRound(aux.xf);
aux.y = fRound(aux.yf);
//cout << "SURF size: " << kpts_surf1_[i].size*.5 << endl;
aux.octave = kp.octave;
// Get the radius for visualization
aux.scale = kp.size*.5/2.5;
aux.angle = DEGREE_TO_RADIAN(kp.angle);
//aux.descriptor_size = 64;
}
static inline void convertPoint(const Ipoint& src, cv::KeyPoint& kp)
{
kp.pt.x = src.xf;
kp.pt.y = src.yf;
kp.angle = RADIAN_TO_DEGREE(src.angle);
kp.response = src.dresponse;
kp.octave = src.octave;
kp.size = src.scale;
}
/***
* runByPixelsMask() for KAZE Ipoint
*/
class MaskPredicate
{
public:
MaskPredicate( const Mat& _mask ) : mask(_mask) {}
bool operator() (const Ipoint& key_pt) const
{
return mask.at<uchar>( (int)(key_pt.yf + 0.5f), (int)(key_pt.xf + 0.5f) ) == 0;
}
private:
const Mat mask;
MaskPredicate& operator=(const MaskPredicate&);
};
void runByPixelsMask( std::vector<Ipoint>& keypoints, const Mat& mask )
{
if( mask.empty() )
return;
keypoints.erase(std::remove_if(keypoints.begin(), keypoints.end(), MaskPredicate(mask)), keypoints.end());
}
/***
* Implementation of cv::KAZE
*/
KAZE::KAZE()
{
}
KAZE::KAZE(toptions &_options)
{
options = _options;
}
int KAZE::descriptorSize() const
{
return options.extended ? 128 : 64;
}
int KAZE::descriptorType() const
{
return CV_32F;
}
void KAZE::operator()(InputArray _image, InputArray _mask, vector<KeyPoint>& _keypoints,
OutputArray _descriptors, bool useProvidedKeypoints) const
{
bool do_keypoints = !useProvidedKeypoints;
bool do_descriptors = _descriptors.needed();
if( (!do_keypoints && !do_descriptors) || _image.empty() )
return;
cv::Mat img1_8, img1_32;
// Convert to gray scale iamge and float image
if (_image.getMat().channels() == 3)
cv::cvtColor(_image, img1_8, CV_RGB2GRAY);
else
_image.getMat().copyTo(img1_8);
img1_8.convertTo(img1_32, CV_32F, 1.0/255.0,0);
// Construct KAZE
toptions opt = options;
opt.img_width = img1_32.cols;
opt.img_height = img1_32.rows;
::KAZE kazeEvolution(opt);
// Create nonlinear scale space
kazeEvolution.Create_Nonlinear_Scale_Space(img1_32);
// Feature detection
std::vector<Ipoint> kazePoints;
if (do_keypoints)
{
kazeEvolution.Feature_Detection(kazePoints);
if (!_mask.empty())
{
runByPixelsMask(kazePoints, _mask.getMat());
}
}
else
{
kazePoints.resize(_keypoints.size());
for (size_t i = 0; i < kazePoints.size(); i++)
{
convertPoint(_keypoints[i], kazePoints[i]);
}
}
// Descriptor generation
if (do_descriptors)
{
kazeEvolution.Feature_Description(kazePoints);
cv::Mat& descriptors = _descriptors.getMatRef();
descriptors.create(kazePoints.size(), descriptorSize(), descriptorType());
for (size_t i = 0; i < kazePoints.size(); i++)
{
std::copy(kazePoints[i].descriptor.begin(), kazePoints[i].descriptor.end(), (float*)descriptors.row(i).data);
}
}
// Transfer from KAZE::Ipoint to cv::KeyPoint
if (do_keypoints)
{
_keypoints.resize(kazePoints.size());
for (size_t i = 0; i < kazePoints.size(); i++)
{
convertPoint(kazePoints[i], _keypoints[i]);
}
}
}
void KAZE::operator()(InputArray image, InputArray mask, vector<KeyPoint>& keypoints ) const
{
(*this)(image, mask, keypoints, noArray(), false);
}
void KAZE::operator()(InputArray image, vector<KeyPoint>& keypoints, OutputArray descriptors) const
{
(*this)(image, noArray(), keypoints, descriptors, false);
}
void KAZE::detectImpl( const Mat& image, vector<KeyPoint>& keypoints, const Mat& mask) const
{
(*this)(image, mask, keypoints, noArray(), false);
}
void KAZE::computeImpl( const Mat& image, vector<KeyPoint>& keypoints, Mat& descriptors) const
{
(*this)(image, Mat(), keypoints, descriptors, false); // Regenerate keypoints no matter keypoints is empty or not
}
}
下面是基於cv::KAZE類的特徵提取與圖像匹配例程及結果圖：
// KazeOpenCV.cpp : 定義控制檯應用程序的入口點。
//
#include "predep.h"
#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/highgui/highgui.hpp"
#include "opencv2/calib3d/calib3d.hpp"
#include "KAZE/kaze_features.h"
#pragma comment( lib, cvLIB("core") )
#pragma comment( lib, cvLIB("imgproc") )
#pragma comment( lib, cvLIB("highgui") )
#pragma comment( lib, cvLIB("flann") )
#pragma comment( lib, cvLIB("features2d") )
#pragma comment( lib, cvLIB("calib3d") )
using namespace std;
using namespace cv;
int main(int argc, char** argv[])
{
Mat img_1 = imread("box.png");
Mat img_2 = imread("box_in_scene.png");
std::vector<KeyPoint> keypoints_1, keypoints_2;
Mat descriptors_1, descriptors_2;
toptions opt;
opt.extended = true; // 1 - 128-bit vector, 0 - 64-bit vector, default: 0
opt.verbosity = true; // 1 - show detail information while caculating KAZE, 0 - unshow, default: 0
KAZE detector_1(opt);
KAZE detector_2(opt);
double t2 = 0.0, t1 = 0.0, tkaze = 0.0;
int64 start_t1 = cv::getTickCount();
//-- Detect keypoints and calculate descriptors
detector_1(img_1, keypoints_1, descriptors_1);
detector_2(img_2, keypoints_2, descriptors_2);
t2 = cv::getTickCount();
tkaze = 1000.0 * (t2 - start_t1) / cv::getTickFrequency();
cout << "\n\n-- Total detection time (ms): " << tkaze << endl;
printf("-- Keypoint number of img_1 : %d \n", keypoints_1.size() );
printf("-- Keypoint number of img_2 : %d \n", keypoints_2.size() );
//-- Matching descriptor vectors using FLANN matcher
FlannBasedMatcher matcher;
vector< DMatch > matches;
matcher.match( descriptors_1, descriptors_2, matches );
double max_dist = 0; double min_dist = 100;
//-- Quick calculation of max and min distances between keypoints
for( int i = 0; i < descriptors_1.rows; i++ )
{
double dist = matches[i].distance;
if( dist < min_dist ) min_dist = dist;
if( dist > max_dist ) max_dist = dist;
}
//-- Find initial good matches (i.e. whose distance is less than 2*min_dist )
vector< DMatch > good_matches, inliers;
for( int i = 0; i < descriptors_1.rows; i++ )
{
if( matches[i].distance < 2*min_dist )
{
good_matches.push_back( matches[i]);
}
}
cout << "-- Computing homography (RANSAC)..." << endl;
//-- Get the keypoints from the good matches
vector<Point2f> points1( good_matches.size() );
vector<Point2f> points2( good_matches.size() );
for( size_t i = 0; i < good_matches.size(); i++ )
{
points1[i] = keypoints_1[ good_matches[i].queryIdx ].pt;
points2[i] = keypoints_2[ good_matches[i].trainIdx ].pt;
}
//-- Computing homography (RANSAC) and find inliers
vector<uchar> flags(points1.size(), 0);
Mat H = findHomography( points1, points2, CV_RANSAC, 3.0, flags );
//cout << H << endl << endl;
for (int i = 0; i < good_matches.size(); i++)
{
if (flags[i])
{
inliers.push_back( good_matches[i] );
}
}
//-- Draw Keypoints
Mat img_1k, img_2k;
drawKeypoints(img_1, keypoints_1, img_1k, Scalar::all(-1), DrawMatchesFlags::DRAW_RICH_KEYPOINTS);
drawKeypoints(img_2, keypoints_2, img_2k, Scalar::all(-1), DrawMatchesFlags::DRAW_RICH_KEYPOINTS);
//-- Draw inliers
Mat img_matches;
drawMatches( img_1, keypoints_1, img_2, keypoints_2,
inliers, img_matches, Scalar::all(-1), Scalar::all(-1),
vector<char>(), DrawMatchesFlags::NOT_DRAW_SINGLE_POINTS );
printf("-- Number of Matches : %d \n", good_matches.size() );
printf("-- Number of Inliers : %d \n", inliers.size() );
printf("-- Match rate : %f \n", inliers.size() / (float)good_matches.size() );
//-- Localize the object
//-- Get the corners from the image_1 ( the object to be "detected" )
vector<Point2f> obj_corners;
obj_corners.push_back( Point2f(0,0) );
obj_corners.push_back( Point2f(img_1.cols,0) );
obj_corners.push_back( Point2f(img_1.cols,img_1.rows) );
obj_corners.push_back( Point2f(0,img_1.rows) );
if (!H.empty())
{
vector<Point2f> scene_corners;
perspectiveTransform(obj_corners, scene_corners, H);
//-- Draw lines between the corners (the mapped object in the scene - image_2 )
int npts = scene_corners.size();
for (int i=0; i<npts; i++)
line( img_matches, scene_corners[i] + Point2f( img_1.cols, 0),
scene_corners[(i+1)%npts] + Point2f( img_1.cols, 0), Scalar(0,0,255), 2 );
}
//-- Show detected matches
cout << "-- Show detected matches." << endl;
namedWindow("Image 1",CV_WINDOW_NORMAL);
namedWindow("Image 2",CV_WINDOW_NORMAL);
namedWindow("Good Matches",CV_WINDOW_NORMAL);
imshow( "Image 1", img_1k );
imshow( "Image 2", img_2k );
imshow( "Good Matches", img_matches );
waitKey(0);
destroyAllWindows();
return 0;
}
2.3.2 KAZE特徵的性能測試與比較
KAZE論文中給出了若干實驗圖表數據，與SURF、SIFT和STAR相比，KAZE有更好的尺度和旋轉不變性，並且穩定、可重複檢測。主要的實驗包括：
（1） 重複檢測試驗
這裏主要從旋轉縮放、視角變換、噪聲干擾、模糊圖像、壓縮圖像等方面進行了測試，可以看出KAZE的可重複性明顯優於其它特徵。
（2） 特徵檢測與匹配試驗
這裏也是從旋轉縮放、視角變換、噪聲干擾、模糊圖像、壓縮圖像等方面進行了測試，給出了特徵匹配的Precision-Recall圖。使用的匹配算法是最近鄰匹配。這裏可以看出，在圖像模糊、噪聲干擾和壓縮重構等造成的信息丟失的情況下，KAZE特徵的魯棒性明顯優於其它特徵。
（3） 表面形變目標的特徵匹配
這裏可以看出基於g2傳導函數的KAZE特徵性能最好。
（4） 檢測效率測試
這裏可以看出KAZE的特徵檢測時間高於SURF和STAR，但與SIFT相近。這裏比較花時間的是非線性尺度空間的構建。
作者提出通過多線程並行計算進行AOS求解的方法來加快運行速度，在實現代碼中，他們用boost/thread庫進行AOS求解和尋找局部極大值點。不過我通過測試發現這並沒有明顯提高運行速度，可能是因爲他們的代碼中，分發的多個線程最後要用thread.join()等待所有計算線程結束，然後才能繼續後續運算。這個join的使用反而可能會降低運行速度。
Computer Vision Talks博客不久前對KAZE算法進行了評測，並與其它特徵進行了性能比較。這裏我根據Ievgen在github上的OpenCV-Features-Comparison代碼進行了更深入的測試，進一步顯示了KAZE特徵在尺度縮放、旋轉變換、亮度變化和高斯模糊等情況下的優良性能。
(1) Percent of correct matches
(2) Percent of matches
(3) Match ratio
(4) Mean distance
(5) Homography error
不過KAZE在運行時間上的短板的確很明顯，遠高於其他特徵。特別是，論文的實驗顯示KAZE和SIFT的檢測速度相差並不大。但在我的實驗中，KAZE的檢測時間是SIFT的10倍，而且SIFT比SURF還快一倍！這可能是OpenCV的實現代碼中對SIFT做了較大的優化。具體還需要再研究下OpenCV的代碼。
最後分享一下上述圖表的Matlab代碼：
%%
% MATLAB script for the visualization of the results of OpenCV-Features-Comparison
% Copyright (c) by Yuhua Zou.
% Email: yuhuazou AT gmail DOT com OR chenyusiyuan AT 126 DOT com
%
close all;
clear all;
clc;
% workroot: directory which contains files as follows:
% HomographyError.txt
% MatchingRatio.txt
% MeanDistance.txt
% PercentOfCorrectMatches.txt
% PercentOfMatches.txt
% Performance.txt
%
workroot='.\5\';
files=dir([workroot,'*.txt']);
% use the file name as the figure name, stored in a cell 'nameFigure'
nameFigure = cell(1,length(files));
for i=1:length(files),
% get file name and create a correspoinding figure
filename = files(i,1).name;
nameFigure{i} = filename(1:end-4);
figure('Name',nameFigure{i},'Position',[20 40 1240 780]);
% initialize 2 cells to store title name and legends of each plot
nameTitle{1} = '';
nameLegend{1} = '';
% open file
file = fullfile(workroot,filename);
fid = fopen(file,'r');
% process 'Performance.txt' individually
if strcmp(nameFigure{i},'Performance') ,
nl = 0;
data = 0;
%% analyze each line
tline = fgetl(fid);
while ischar(tline),
nl = nl + 1;
tline(tline == '"') = '';
if nl == 1,
nameTitle{ 1 } = tline;
elseif nl == 2,
args = regexp(tline,'\t','split');
nameLegend = args(2:end);
elseif ~isempty(tline),
args = regexp(tline,'\t','split');
cols = length(args) - 1;
tick = args{1};
nameTick{nl-2} = tick;
for n = 1:cols, data(nl-2,n) = str2num( args{n+1} ); end
end
tline = fgetl(fid);
end
% plotting
for k=1:2,
subplot(2,1,k);
[data_sorted,idx] = sort(data(:,k),'ascend');
h = barh( data_sorted ); % get the handle to change bar color
xlabel('Time (ms)'); ylabel('Algorithms');
title(nameLegend{ k }, 'FontWeight', 'bold');
set(gca, 'yticklabel', nameTick(idx), 'FontSize', 7);
% set(gca,'yticklabel','','FontSize',7); % unshow y-axis ticks
%% attach the value to the right side of each bar
x = get(h, 'XData');
y = get(h, 'YData');
horiGap = 0.01 * ( max(y) - min(y) );
for c=1:length(x),
text( y(c) + horiGap, x(c), num2str(y(c), '%0.3f'),...
'HorizontalAlignment','left','VerticalAlignment','middle',...
'FontSize',7);
end
%% Change the color of each bar
ch = get(h,'Children'); % get children of the bar group
fvd = get(ch,'Faces'); % get faces data
fvcd = get(ch,'FaceVertexCData'); % get face vertex cdata
% [zs, izs] = sortrows(datak,1); % sort the rows ascending by first columns
for c = 1:length(data_sorted)
fvcd(fvd(c,:)) = idx(c); % adjust the face vertex cdata to be that of the row
end
set(ch,'FaceVertexCData',fvcd) % set to new face vertex cdata
% you can search 'FaceVertexCData' in MATLAB Help for more info.
end
else
%% process other documents
nDataRow = 0; % rows of numerical data in each plot
nPlot = 0; % number of plots
data{1} = 0; % all numerical data in current document
%% analyze each line
tline = fgetl(fid);
while ischar(tline) && ~strcmp(tline, -1),
% split the line into strings by '\t'
args = regexp(tline,'\t','split');
if strcmp(args{end},''), args = args(1:end-1); end; % remove the last empty one
% the line which contains only one string
% is recognized as the beginning of a new plot
% the string is stored as plot title
% which represents the transformation type
if length(args) == 1,
nDataRow = 0;
nPlot = nPlot + 1;
tline(tline == '"') = '';
nameTitle{ nPlot } = tline;
else
% the line with several '"'s under the 'plot title' line
% stores legends of the plot
% which represent feature methods
if ~isempty( find( tline=='"', 1 ) ),
tline(tline == '"') = '';
nameLegend{ nPlot } = args(2:end);
else
% the line without '""'s contains numerical data
% which represent experiment data
nDataRow = nDataRow + 1;
for n = 1:length(args),
data{ nPlot }(nDataRow,n) = str2double( args{n} );
end
end
end
tline = fgetl(fid);
end
%% plotting
cmap = colormap( jet( length( nameLegend{1} ) ) ); % cmap: table of line color
for p = 1:nPlot,
subplot(ceil(nPlot/2), 2, p);
xdata = data{p}(:,1);
ydata = data{p}(:,2:end);
for r=1:size(ydata,2)
plot(xdata, ydata(:,r), 'Color', cmap(r,:), 'LineWidth',2); hold on; % draw each line with different color
end
title(nameTitle{p},'FontWeight','bold');
if p == 1, legend(nameLegend{p},'Location','Best','FontSize',7); end
xlim([min(xdata(:)-0.1*max(xdata(:))), 1.1*max(xdata(:))]);
ylim([0, 1.1*max(ydata(:))]);
end
end
fclose(fid);
end
KAZE特徵分析的系列筆記到此暫告一段落了，我覺得如果能夠在非線性尺度空間的構建和特徵檢測方面對算法做出優化和改進、提高其實時性，KAZE 將大有用武之地。筆記倉促寫完，還有很多不足和問題，歡迎大家指正和討論，謝謝！