I've a vector of points from a grey section of an image and written like this:
std::vector<Point> vectorg;
for(i = 0; i <= hei - 1; i++) {
for(j = 0; j <= wid - 1; j++) {
if(mask(i,j) == 128) {
vectorg.push_back(Point(j,i));
}
}
}
Knowing what coordinates stored in certain cell is possible by:
cout << vectorg[0].x;
cout << vectorg[0].y;
The question is now the other way around, is it possible to know which cell holds certain coordinates?
Thanks a lot, I'm new here also with opencv programming, I'll be in your care.
Just do the following:
#include <algorithm>
// ...
Point p(searchedX, searchedY);
std::vector<Point>::iterator element = std::find(vectorg.begin(), vectorg.end(), p);
if (element != vectorg.end()) {
cout << (*element).x << endl;
cout << (*element).y << endl;
} else {
cout << "The point is not in the vector" << endl;
}
It may be overkill, but a way to do it (without doing a greedy exhaustive search) would be to build a FLANN index that will store the position of your points.
The feature matrix is made of the coordinates of your points.
Since OpenCV knows how to convert a vector to a matrix, you should be able to use your current vector as is.
Then, if you want only one point, just ask for the 1 nearest neighbour in the query (k parameter).
The bonus is, if you decide later that you need to have also the closest points in the neighborhood, just raise the value of k.
Sorry for the late response, and thanks for the answers, they inspired me indirectly.
I found an easy way to do it. This is by making another Mat which holds the numbers where the coordinates were saved.
std::vector<Point> vectorg;
cv::Mat_<int> Index =Mat_<int>::zeros(hei,wid);
for(i = 0; i <= hei - 1; i++) {
for(j = 0; j <= wid - 1; j++) {
if(mask(i,j) == 128) {
vectorg.push_back(Point(j,i));
Index(vector[count])=count;
count++;
}
}
}
This way I can know which cell holds certain coordinates by simply:
cout<<Index(36,362); //as example
Thanks a lot, I'll be in your care next time.
Related
I am trying to compute $\partial{J}{q_i}$ in drake C++ for manipulator and as per my search, the best approach seems to be using autodiff function. I was not able to fully understand autodiff approach from the resources that I found, so I apologize if my approach is not clear enough. I have used my understanding from some already asked questions mentioned on the forum regarding auto diff as well as https://drake.mit.edu/doxygen_cxx/classdrake_1_1multibody_1_1_multibody_plant.html as reference.
As I want to calculate $\partial{J}{q_i}$, the return type will be a tensor i.e. 3 * 7 * 7(or 6 * 7 * 7 depending on the spatial jacobian). I can think of using std::vectorEigen::MatrixXd to allocate the output or alternatively just doing one $q_i$ at a time and computing the respective jacobian for the auto diff. In either case, I was struggling to pass it in the initializing the jacobian function.
I did the following to initialize autodiff
std::unique_ptr<multibody::MultibodyPlant<AutoDiffXd>> mplant_autodiff = systems::System<double>::ToAutoDiffXd(mplant);
std::unique_ptr<systems::Context<AutoDiffXd>> mContext_autodiff = mplant_autodiff->CreateDefaultContext();
mContext_autodiff->SetTimeStateAndParametersFrom(*mContext);
const multibody::Frame<AutoDiffXd>* mFrame_EE_autodiff = &mplant_autodiff->GetBodyByName(mEE_link).body_frame();
const multibody::Frame<AutoDiffXd>* mWorld_Frame_autodiff = &(mplant_autodiff->world_frame());
//Initialize the q as autodiff vector
drake::AutoDiffVecXd q_autodiff = drake::math::InitializeAutoDiff(mq_robot);
MatrixX<AutoDiffXd> mJacobian_autodiff; // Linear Jacobian matrix.
mplant_autodiff->SetPositions(context_autodiff.get(), q_autodiff);
mplant_autodiff->CalcJacobianTranslationalVelocity(*mContext_autodiff,
multibody::JacobianWrtVariable::kQDot,
*mFrame_EE_autodiff,
Eigen::Vector3d::Zero(),
*mWorld_Frame_autodiff,
*mWorld_Frame_autodiff,
&mJacobian_autodiff
);
However, as far as I understand, InitializeAutoDiff initializes to the identity matrix, whereas I want to $\partial{J}{q_i}$, so is there is a better way to do it. In addition, I get error messages when I try to call the jacobian matrix. Is there a way to address this problem both for $\partial{J}{q_i}$ for each q_i and changing q_i in a for loop or directly getting the result in a tensor. My apologies if I am doing something total tangent to the correct approach. I thank you in anticipation.
However, as far as I understand, InitializeAutoDiff initializes to the identity matrix, whereas I want to $\partial{J}{q_i}$, so is there is a better way to do it
That is correct. When you call InitializeAutoDiff and compute mJacobian_autodiff, you get a matrix of AutoDiffXd. Each AutoDiffXd has a value() function that stores the double value, and a derivatives() storing the gradient as an Eigen::VectorXd. We have
mJacobian(i, j).value() = J(i, j)
mJacobian_autodiff(i, j).derivatives()(k) = ∂J(i, j)/∂q(k)
So if you want to create a std::vecot<Eigen::MatrixXd> such that the k'th entry of this vector stores the matrix ∂J/∂q(k), then here is a code
std::vector<Eigen::MatrixXd> dJdq(q_autodiff.rows());
for (int i = 0; i < q_autodiff.rows(); ++i) {
dJdq[i].resize(mJacobian_autodiff.rows(), mJacobian_autodiff.cols());
}
for (int i = 0; i < q_autodiff.rows(); ++i) {
// dJidq stores the gradient of the ∂J.col(i)/∂q, namely dJidq(j, k) = ∂J(j, i)/∂q(k)
auto dJidq = ExtractGradient(mJacobian_autodiff.col(i));
for (int j = 0; j < static_cast<int>(dJdq.size()); ++j) {
dJdq[j].col(i) = dJidq.col(j);
}
}
Compute ∂J/∂q(i) for a single i
If you do not want to compute ∂J/∂q(i) for all i, but only for one specific i, you can change the initialization of q_autodiff from InitializeAutoDiff to this
AutoDiffVecXd q_autodiff(q.rows());
for (int k = 0; k < q_autodiff.rows(); ++k) {
q_autodiff(k).value() = q(k)
q_autodiff(k).derivatives() = Vector1d::Zero();
if (k == i) {
q_autodiff(k).derivatives()(0) = 1;
}
}
namely q_autodiff stores the gradient ∂q/∂q(i), which is 0 for all k != i and 1 when k == i. And then you can compute mJacobian_autodiff using your current code. Now mJacobian_autodiff(m, n).derivatives() store the gradient of ∂J(m, m)/∂q(i) for that specific i. You can extract this gradient as
Eigen::Matrix dJdqi(mJacobian_autodiff.rows(), mJacobian_autodiff.cols());
for (int m = 0; m < dJdqi.rows(); ++m) {
for (int n = 0; n < dJdqi.cols(); ++n) {
dJdqi(m, n) = mJacobian_autodiff(m, n).derivatives()(0);
}
}
Hi i'm new in pointcloud library. I'm trying to show clustering result point on rviz or pcl viewer, and then show nothing. And i realize that my data show nothing too when i subcsribe and cout that. Hopefully can help my problem, thanks
This is my code for clustering and send node
void cloudReceive(const sensor_msgs::PointCloud2ConstPtr& inputMsg){
mutex_lock.lock();
pcl::fromROSMsg(*inputMsg, *inputCloud);
cout<<inputCloud<<endl;
pcl::search::KdTree<pcl::PointXYZRGB>::Ptr tree (new pcl::search::KdTree<pcl::PointXYZRGB>);
tree->setInputCloud(inputCloud);
std::vector<pcl::PointIndices> cluster_indices;
pcl::EuclideanClusterExtraction<pcl::PointXYZRGB> ec;
ec.setClusterTolerance(0.03);//2cm
ec.setMinClusterSize(200);//min points
ec.setMaxClusterSize(1000);//max points
ec.setSearchMethod(tree);
ec.setInputCloud(inputCloud);
ec.extract(cluster_indices);
if(cluster_indices.size() > 0){
std::vector<pcl::PointIndices>::const_iterator it;
int i = 0;
for (it = cluster_indices.begin(); it != cluster_indices.end(); ++it){
if(i >= 10)
break;
cloud_cluster[i]->points.clear();
std::vector<int>::const_iterator idx_it;
for (idx_it = it->indices.begin(); idx_it != it->indices.end(); idx_it++)
cloud_cluster[i]->points.push_back(inputCloud->points[*idx_it]);
cloud_cluster[i]->width = cloud_cluster[i]->points.size();
// cloud_cluster[i]->height = 1;
// cloud_cluster[i]->is_dense = true;
cout<<"PointCloud representing the Cluster: " << cloud_cluster[i]->points.size() << " data points"<<endl;
std::stringstream ss;
ss<<"cobaa_pipecom2_cluster_"<< i << ".pcd";
writer.write<pcl::PointXYZRGB> (ss.str(), *cloud_cluster[i], false);
pcl::toROSMsg(*cloud_cluster[i], outputMsg);
// cout<<"data = "<< outputMsg <<endl;
cloud_cluster[i]->header.frame_id = FRAME_ID;
pclpub[i++].publish(outputMsg);
// i++;
}
}
else
ROS_INFO_STREAM("0 clusters extracted\n");
}
And this one is the main
int main(int argc, char** argv){
for (int z = 0; z < 10; z++) {
// std::cout << " - clustering/" << z << std::endl;
cloud_cluster[z] = pcl::PointCloud<pcl::PointXYZRGB>::Ptr(new pcl::PointCloud<pcl::PointXYZRGB>);
cloud_cluster[z]->height = 1;
cloud_cluster[z]->is_dense = true;
// cloud_cluster[z]->header.frame_id = FRAME_ID;
}
ros::init(argc,argv,"clustering");
ros::NodeHandlePtr nh(new ros::NodeHandle());
pclsub = nh->subscribe("/pclsegmen",1,cloudReceive);
std::string pub_str("clustering/0");
for (int z = 0; z < 10; z++) {
pub_str[11] = z + 48;//48=0(ASCII)
// z++;
pclpub[z] = nh->advertise <sensor_msgs::PointCloud2> (pub_str, 1);
}
// pclpub = nh->advertise<sensor_msgs::PointCloud2>("/pclcluster",1);
ros::spin();
}
This isn't an exact answer, but I think it addresses your issue & may ease your debugging.
RViz can directly subscribe to a published point cloud, the one I'm assuming you're trying to see in the cloud_receive callback. If you set the Frame to whichever frame it's being published at, and add it from the available topics, you should see the points. (Easier than trying to rebroadcast it as different topics).
Also, I recommend looking at the rostopic command line tool. You can do rostopic list to check if it's being published, rostopic bw to see if it's really publishing the expected volume of data (ex bytes vs kilobytes vs megabytes), rostopic hz to see how frequently (if ever) it's publishing, and (briefly) rostopic echo to look at the data itself. (This is me assuming from your question it's more an issue with the data coming into your node).
If you're having trouble, not with data coming into the node, nor with the visualization of pointcloud data in general, but with the transformed data that's supposed to come out of the node, I would check that the clustering worked, & reduce your code moreso to just having 1 publisher publish something. You may be doing something weird. Like messing up your pointers. You could also turn on stronger compilation warnings for your node with -Wall -Wextra -Werror or step through the execution of it via gdb (launch-prefix="xterm -e gdb --args").
The solution is, i change the ASCII number into lexical_cast. Thanks for your response, i hope this can help other
for (int z = 0; z < CLOUD_QTD; z++) {
// pub_str[11] = z + 48;
std::string topicName = "/pclcluster/" + boost::lexical_cast<std::string>(z);
global::pub[z] = n.advertise <sensor_msgs::PointCloud2> (topicName, 1);
}
I am detecting and storing the boundary of a sandpile to an array and then save it as a text file for later use. the way i stored the boundary as text file is by using the wand tool, then getting the properties of the selection which gives me a table. Then converting table to array and finally storing it as text file.
after doing so i noticed that the above mentioned table only has the (X,Y) coordinates of the "junctions" on the boundary and not every pixel of the boundary.
Now when i say later use, i want to smooth out the boundary with various methods and redraw it but i am stuck at how to go from junctions to complete boundary. Below is my attempt to do it but i am seeing heavy ram usage just after the output is printed.
Thanks for any help and your time.
X=newArray(1,5,5,10);
Y=newArray(3,3,8,8);
c=newArray("c1","c2");
//answer should be g=(1,2,3,4,5,5,5,5,5,5,6,7,8,9,10, --x part
// 3,3,3,3,3,4,5,6,7,8,8,8,8,8,8) --y part
//f=slide(a,2,c);Array.print(f);
g=cmpltarray(X,Y);Array.print(g);
function cmpltarray(Tx,Ty){
for (i = 0; i < Tx.length-1; i++) {
if(Tx[i]==Tx[i+1] && Ty[i]!=Ty[i+1])
{
l=abs(Ty[i]-Ty[i+1])-1;tempy=newArray(l);tempx=newArray(l);
for (j = 0; j < l; j++) {
tempy[j]=Ty[i]+j+1;tempx[j]=Tx[i];
}
Tx=slide(Tx,(i+1),tempx);Ty=slide(Ty,(i+1),tempy);i=i+l;
}
if(Ty[i]==Ty[i+1] && Tx[i]!=Tx[i+1])
{
l=abs(Tx[i]-Tx[i+1])-1;tempy=newArray(l);tempx=newArray(l);
for (j = 0; j < l; j++) {
tempx[j]=Tx[i]+j+1;tempy[j]=Ty[i];
}
Tx=slide(Tx,(i+1),tempx);Ty=slide(Ty,(i+1),tempy);i=i+l;
}
}
return Array.concat(Tx,Ty);
}
function slide(array,n,data){
array=Array.concat(Array.slice(array,0,n),data,Array.slice(array,n,array.length));
return array;
}
my program is Directx Program that draws a container cube within it smaller cubes....these smaller cubes fall by time i hope you understand what i mean...
The program isn't complete yet ...it should draws the container only ....but it draws nothing ...only the background color is visible... i only included what i think is needed ...
this is the routines that initialize the program
bool Game::init(HINSTANCE hinst,HWND _hw){
Directx11 ::init(hinst , _hw);
return LoadContent();}
Directx11::init()
bool Directx11::init(HINSTANCE hinst,HWND hw){
_hinst=hinst;_hwnd=hw;
RECT rc;
GetClientRect(_hwnd,&rc);
height= rc.bottom - rc.top;
width = rc.right - rc.left;
UINT flags=0;
#ifdef _DEBUG
flags |=D3D11_CREATE_DEVICE_DEBUG;
#endif
HR(D3D11CreateDevice(0,_driverType,0,flags,0,0,D3D11_SDK_VERSION,&d3dDevice,&_featureLevel,&d3dDeviceContext));
if (d3dDevice == 0 || d3dDeviceContext == 0)
return 0;
DXGI_SWAP_CHAIN_DESC sdesc;
ZeroMemory(&sdesc,sizeof(DXGI_SWAP_CHAIN_DESC));
sdesc.Windowed=true;
sdesc.BufferCount=1;
sdesc.BufferDesc.Format=DXGI_FORMAT_R8G8B8A8_UNORM;
sdesc.BufferDesc.Height=height;
sdesc.BufferDesc.Width=width;
sdesc.BufferDesc.Scaling=DXGI_MODE_SCALING_UNSPECIFIED;
sdesc.BufferDesc.ScanlineOrdering=DXGI_MODE_SCANLINE_ORDER_UNSPECIFIED;
sdesc.OutputWindow=_hwnd;
sdesc.BufferDesc.RefreshRate.Denominator=1;
sdesc.BufferDesc.RefreshRate.Numerator=60;
sdesc.Flags=0;
sdesc.BufferUsage = DXGI_USAGE_RENDER_TARGET_OUTPUT;
if (m4xMsaaEnable)
{
sdesc.SampleDesc.Count=4;
sdesc.SampleDesc.Quality=m4xMsaaQuality-1;
}
else
{
sdesc.SampleDesc.Count=1;
sdesc.SampleDesc.Quality=0;
}
IDXGIDevice *Device=0;
HR(d3dDevice->QueryInterface(__uuidof(IDXGIDevice),reinterpret_cast <void**> (&Device)));
IDXGIAdapter*Ad=0;
HR(Device->GetParent(__uuidof(IDXGIAdapter),reinterpret_cast <void**> (&Ad)));
IDXGIFactory* fac=0;
HR(Ad->GetParent(__uuidof(IDXGIFactory),reinterpret_cast <void**> (&fac)));
fac->CreateSwapChain(d3dDevice,&sdesc,&swapchain);
ReleaseCOM(Device);
ReleaseCOM(Ad);
ReleaseCOM(fac);
ID3D11Texture2D *back = 0;
HR(swapchain->GetBuffer(0,__uuidof(ID3D11Texture2D),reinterpret_cast <void**> (&back)));
HR(d3dDevice->CreateRenderTargetView(back,0,&RenderTarget));
D3D11_TEXTURE2D_DESC Tdesc;
ZeroMemory(&Tdesc,sizeof(D3D11_TEXTURE2D_DESC));
Tdesc.BindFlags = D3D11_BIND_DEPTH_STENCIL;
Tdesc.ArraySize = 1;
Tdesc.Format= DXGI_FORMAT_D24_UNORM_S8_UINT;
Tdesc.Height= height;
Tdesc.Width = width;
Tdesc.Usage = D3D11_USAGE_DEFAULT;
Tdesc.MipLevels=1;
if (m4xMsaaEnable)
{
Tdesc.SampleDesc.Count=4;
Tdesc.SampleDesc.Quality=m4xMsaaQuality-1;
}
else
{
Tdesc.SampleDesc.Count=1;
Tdesc.SampleDesc.Quality=0;
}
HR(d3dDevice->CreateTexture2D(&Tdesc,0,&depthview));
HR(d3dDevice->CreateDepthStencilView(depthview,0,&depth));
d3dDeviceContext->OMSetRenderTargets(1,&RenderTarget,depth);
D3D11_VIEWPORT vp;
vp.TopLeftX=0.0f;
vp.TopLeftY=0.0f;
vp.Width = static_cast <float> (width);
vp.Height= static_cast <float> (height);
vp.MinDepth = 0.0f;
vp.MaxDepth = 1.0f;
d3dDeviceContext -> RSSetViewports(1,&vp);
return true;
SetBuild() Prepare the matrices inside the container for the smaller cubes ....i didnt program it to draw the smaller cubes yet
and this the function that draws the scene
void Game::Render(){
d3dDeviceContext->ClearRenderTargetView(RenderTarget,reinterpret_cast <const float*> (&Colors::LightSteelBlue));
d3dDeviceContext->ClearDepthStencilView(depth,D3D11_CLEAR_DEPTH | D3D11_CLEAR_STENCIL,1.0f,0);
d3dDeviceContext-> IASetInputLayout(_layout);
d3dDeviceContext-> IASetPrimitiveTopology(D3D10_PRIMITIVE_TOPOLOGY_TRIANGLELIST);
d3dDeviceContext->IASetIndexBuffer(indices,DXGI_FORMAT_R32_UINT,0);
UINT strides=sizeof(Vertex),off=0;
d3dDeviceContext->IASetVertexBuffers(0,1,&vertices,&strides,&off);
D3DX11_TECHNIQUE_DESC des;
Tech->GetDesc(&des);
Floor * Lookup; /*is a variable to Lookup inside the matrices structure (Floor Contains XMMATRX Piese[9])*/
std::vector<XMFLOAT4X4> filled; // saves the matrices of the smaller cubes
XMMATRIX V=XMLoadFloat4x4(&View),P = XMLoadFloat4x4(&Proj);
XMMATRIX vp = V * P;XMMATRIX wvp;
for (UINT i = 0; i < des.Passes; i++)
{
d3dDeviceContext->RSSetState(BuildRast);
wvp = XMLoadFloat4x4(&(B.Memory[0].Pieces[0])) * vp; // Loading The Matrix at translation(0,0,0)
HR(ShadeMat->SetMatrix(reinterpret_cast<float*> ( &wvp)));
HR(Tech->GetPassByIndex(i)->Apply(0,d3dDeviceContext));
d3dDeviceContext->DrawIndexed(build_ind_count,build_ind_index,build_vers_index);
d3dDeviceContext->RSSetState(PieseRast);
UINT r1=B.GetSize(),r2=filled.size();
for (UINT j = 0; j < r1; j++)
{
Lookup = &B.Memory[j];
for (UINT r = 0; r < Lookup->filledindeces.size(); r++)
{
filled.push_back(Lookup->Pieces[Lookup->filledindeces[r]]);
}
}
for (UINT j = 0; j < r2; j++)
{
ShadeMat->SetMatrix( reinterpret_cast<const float*> (&filled[i]));
Tech->GetPassByIndex(i)->Apply(0,d3dDeviceContext);
d3dDeviceContext->DrawIndexed(piese_ind_count,piese_ind_index,piese_vers_index);
}
}
HR(swapchain->Present(0,0));}
thanks in Advance
One bug in your program appears to be that you're using i, the index of the current pass, as an index into the filled vector, when you should apparently be using j.
Another apparent bug is that in the loop where you are supposed to be iterating over the elements of filled, you're not iterating over all of them. The value r2 is set to the size of filled before you append anything to it during that pass. During the first pass this means that nothing will be drawn by this loop. If your technique only has one pass then this means that the second DrawIndexed call in your code will never be executed.
It also appears you should be only adding matrices to filled once, regardless of the number of the passes the technique has. You should consider if your code is actually meant to work with techniques with multiple passes.
I have a graph structure where I am removing edges one by one until some conditions are met. My brain has totally stopped and i can't find an efficient way to detect if removing an edge will result in my graph splitting in two or more graphs.
The bruteforce solution would be to do an bfs until one can reach all the nodes from a random node, but that will take too much time with large graphs...
Any ideas?
Edit: After a bit of search it seems what I am trying to do is very similar to the fleury's algorithm, where I need to find if an edge is a "bridge" or not.
Edges that make a graph disconnected when removed are called 'bridges'. You can find them in O(|V|+|E|) with a single depth-first search over the whole graph. A related algorithm finds all 'articulation points' (nodes that, if removed, makes the graph disconnected) follows. Any edge between two articulation-points is a bridge (you can test that in a second pass over all edges).
//
// g: graph; v: current vertex id;
// r_p: parents (r/w); r_a: ascents (r/w); r_ap: art. points, bool array (r/w)
// n_v: bfs order-of-visit
//
void dfs_art_i(graph *g, int v, int *r_p, int *r_v, int *r_a, int *r_ap, int *n_v) {
int i;
r_v[v] = *n_v;
r_a[v] = *n_v;
(*n_v) ++;
// printf("entering %d (nv = %d)\n", v, *n_v);
for (i=0; i<g->vertices[v].n_edges; i++) {
int w = g->vertices[v].edges[i].target;
// printf("\t evaluating %d->%d: ", v, w);
if (r_v[w] == -1) {
// printf("...\n");
// This is the first time we find this vertex
r_p[w] = v;
dfs_art_i(g, w, r_p, r_v, r_a, r_ap, n_v);
// printf("\n\t ... back in %d->%d", v, w);
if (r_a[w] >= r_v[v]) {
// printf(" - a[%d] %d >= v[%d] %d", w, r_a[w], v, r_v[v]);
// Articulation point found
r_ap[i] = 1;
}
if (r_a[w] < r_a[v]) {
// printf(" - a[%d] %d < a[%d] %d", w, r_a[w], v, r_a[v]);
r_a[v] = r_a[w];
}
// printf("\n");
}
else {
// printf("back");
// We have already found this vertex before
if (r_v[w] < r_a[v]) {
// printf(" - updating ascent to %d", r_v[w]);
r_a[v] = r_v[w];
}
// printf("\n");
}
}
}
int dfs_art(graph *g, int root, int *r_p, int *r_v, int *r_a, int *r_ap) {
int i, n_visited = 0, n_root_children = 0;
for (i=0; i<g->n_vertices; i++) {
r_p[i] = r_v[i] = r_a[i] = -1;
r_ap[i] = 0;
}
dfs_art_i(g, root, r_p, r_v, r_a, r_ap, &n_visitados);
// the root can only be an AP if it has more than 1 child
for (i=0; i<g->n_vertices; i++) {
if (r_p[i] == root) {
n_root_children ++;
}
}
r_ap[root] = n_root_children > 1 ? 1 : 0;
return 1;
}
If you remove the link between vertices A and B, can't you just check that you can still reach A from B after the edge removal? That's a little better than getting to all nodes from a random node.
How do you choose the edges to be removed?
Can you tell more about your problem domain?
Just how large Is your graph? maybe BFS is just fine!
After you wrote that you are trying to find out whether an edge is a bridge or not, I suggest
you remove edges in decreasing order of their betweenness measure.
Essentially, betweenness is a measure of an edges (or vertices) centrality in a graph.
Edges with higher value of betweenness have greater potential of being a bridge in a graph.
Look it up on the web, the algorithm is called 'Girvan-Newman algorithm'.