'Programming/Computer Vision'에 해당되는 글 3건

  1. 2009.09.15 8 point 알고리즘
  2. 2009.05.02 AutoAlbum
  3. 2009.05.02 Computer Vision at MSR Cambridge

3 x 3 matrix인 Fundamenta matrix F는 8개의 corresponding point가 주어질 경우, unique하게 결정될 수 있다.
<!-- MATH ${\tt m}=[x \, y \, 1]^\top,{\tt m'}=[x' y' 1]^\top$ -->
<!-- MATH ${\bf f}=[F_{11} F_{12} F_{13} F_{21} F_{22} F_{23} F_{31} F_{32} F_{33} ]^\top$ -->
라고 하자.
<!-- MATH \begin{equation} {\bf A} {\bf f}= 0 \end{equation} -->
위 식을 이용하여, 두 점과 f는 아래와 같이 나타낼 수 있다.
<!-- MATH \begin{equation} \left[ \begin{array}{ccccccccc} x x' & y x' & x' & x y' & y y' & y' & x & y & 1 \end{array} \right] {\bf f} = 0 \end{equation} -->
위 식을 사용하여 아래의 식을 생성한다.(마지막 항인 1은 생략이 가능하다.)
사용자 삽입 이미지
이 때, A는 8개의 corresponding point  pair를 이용하여 만든 matrix이다.
위 식에 의해, f는 A를 Singular Value Decomposition(SVD)를 통해서 계산될 수 있다.
A matrix는 SVD에 의해서 USVT로 decompose되고, f는 V matrix의 last column이 된다.

출처 : http://www.cs.unc.edu/~marc/tutorial/node54.html

아래는 위의 내용을 OpenCV로 작성해본 코드이다.
F33은 1이므로, 위 식의 A matrix에서 마지막 column은 제거하였다.

CvMat* A = cvCreateMat(8, 8, CV_32FC1);
CvMat* S = cvCreateMat(8, 1, CV_32FC1);
CvMat* U = cvCreateMat(8, 8, CV_32FC1);
CvMat* V = cvCreateMat(8, 8, CV_32FC1);

// assign A matrix
float* pA = A->data.fl;

// point assign code here
// pA[i * 8 + j] = x;

cvSVD(A, S, U, V);

// f is a vector containing the elements of fundamenta matrix F
// float* pV = V->data.fl;
// pV[i * 8 + 7] ...


cvReleaseMat(&U);
cvReleaseMat(&S);
cvReleaseMat(&V);
cvReleaseMat(&A);

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AutoAlbum




A system for automatically summarizing your digital photographs to make them easier to find.

 

Quick Links

About AutoAlbum & PhotoTOC

It is getting increasingly popular for consumers to buy a digital camera and take thousands of photos of daily life. Most consumers simply dump these photos into one directory, analogous to dumping developed prints into a shoebox. A typical user generates thousands of photos a year. Finding a photo in this shoebox directory is difficult. AutoAlbum and PhotoTOC are browsing user interfaces that help solve this problem. AutoAlbum was the original UI, while PhotoTOC is a new, updated UI. PhotoTOC consists of two panes. Thumbnails of all images in the shoebox directory is shown on the right pane, as a big contact sheet. PhotoTOC automatically clusters these images. One representative photograph from every cluster is shown on the left pane. When the user clicks on a representative photograph, the right pane scrolls to show that same photograph in the center of the window. The user can then find his/her photograph with minimal scrolling on the right-hand pane. Both AutoAlbum and PhotoTOC use two forms of metadata to help cluster the photos: the creation time of the photo and the order that the photos were taken. Under some circumstances, the creation time of the photo is preserved after download from the camera to the PC. In those cases, PhotoTOC can cluster on the creation time and ignore the content. In other cases, the creation time is destroyed (e.g., by downloading with a serial cable, or camera running out of batteries). However, the order of the photographs is still often preserved, via either download time or file name. In this second case, PhotoTOC uses the content of the photos to cluster, but creates clusters that obey the photographic order. In the demo, the combination of these two clustering techniques are used: first, time-based clustering uses the creation date of the file to form albums. If the creation date of the file is not the creation date of the photo, time-based clustering will produce very large clusters. So, any very large cluster will get broken down by content-based clustering that obeys the order of the photographs.

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