Basic image transformation of image tilt correction equation

Basic image transformation of image tilt correction equation

three basic image transformation matrices are

1Translation Transformation Matrix

2Scaling Matrix

           

3Rotation transformation Matrix

the advantage of using matrix to express matrix rotation is that the expression is more concise,more convenient for further transformations.For example, a transform that has a translation transformation,and a zoom transform .,and a rotating transformation .,then the matrix is used to represent these transformation combinations,the equivalent of a combination of matrix multiplication action,Finally, it can be formed into a matrix.

How did the rotation transformation matrix come about??proof as follows

(x, y) a point in the original image

(x ', y ') a point in the post-rotation diagram

a angle of rotation

change x, y to the sine cosine representation

x = RCOSB

y = rsinb

Remember R =Bto beASIN (X/R)  (ASINrepresents the inverse cosine)

the x ' = RCOs (b + a), y ' = Rsin (b+a)

the triangle and the difference formula are used here .

X ' = RCOs (b+a) = RCOSACOSB–RSINASINB = Xcosa–ysina

Y ' = Rsin (b+a) = RSINACOSB + Rsinbcosa = Xsina + ycosa

the way to the rectangle is the conclusion .

the conclusion is not very beautiful..put(x, Y)converted to (RCOSB, RSINB)and the difference formula is the key.

Basic image transformation of image tilt correction equation