you should not tranform camera frustum to object space, as you should avoid matrix transformations just to test an object. you should create the frustum in the space that is common for examined objects, what object space usualy isnt. Compute the frustum in world space, and have aabs of objects defined in world space too. this way you can imidiately examine aabs position distance towards the planes of frustum.
A plane is defined by a point and a normal . Since I suspect you build the view matrix by eye position, which is in world space, you have the point for the 4 side planes, all left is near plane and far plane world space point. Near and far perspective value are world space sclaras as well. just take the direction vector of camera : At-Eye, normalize it, and multiply it with near scalar and far scalar, add result to eye position, to get the points of near and far plane. You are now left to compute normals for the six planes in world space, the at-eye vector is just very suitable to compute 2 normals of near and far plane in world space.
For the 4 side planes to get world space normal, you should find the near plane 4 corner points and far plane 4 corner points, subtract them to get edges of plane and compute cross product of those two edges to get normal.
for near plane (the same for far plane) get the near value as a vector (0,0,n) and use FOV value and tan() goniometric function to compute the vector to add it with (4 variation ,x +/-,y +/-),
so you get
and add those four to eye postionm this way wou have four near plane croners in world space.