Pose estimation with SIFT and homography

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I think you should be a little more specific in your question.

If your asking how to obtain the rotation and translation (extrinsic parameters) of the camera using an homography, this problem is known as Homography Decomposition. For instance, if you want to insert an augmented object in your book, you will need these parameters (simply computing the perpendicular vector to X and Y will lead to errors).

Notice that to estimate the R and t from the homography you will need the instrinsic parameters of the camera, which can obtained using the calibration method present in OpenCV. These parameters will remain the same for all sequences of the camera.

Finally, you need to implement a couple of equations to extract the extrinsic parameters, they are well described in this great paper by Zhang:

A Flexible New Technique for Camera Calibration

Of course, this depends in what you really want to do in your application. I hope this can help.

If I am not mistaken, one way for you to get the Z axis is to find a perpendicular vector to X axis, or Y axis. Here is a handy Java code to find a perpendicular vector.

// Point pt0, pt1: define the line you want to find a perpendicular vector from.
// Point intersect: is the point of intersection between that line and the perpendicular vector.
// double vectorLength: the lenght in pixels of perpendicular vector.    

double angle = Math.PI/2; // 90 degrees
double perpendicularCos = Math.cos(angle); // or just use '= 0' because angle is 90º
double perpendicularSin = Math.sin(angle); // or just use '= 1' because angle is 90º
double d = pointsDist(pt0, pt1); // distance in pixels between 2 points.

// (x,y) define a vector of length vectorLength perpendicular to (pt0,pt1)
double x = intersec.x - ((pt1.x - pt0.x) * perpendicularCos - (pt1.y - pt0.y) * arrowSin) * (vectorLength / d);    
double y = intersec.y - ((pt1.y - pt0.y) * perpendicularCos + (pt1.x - pt0.x) * arrowSin) * (vectorLength / d);