[Insight-users] Gradient descent and local minima?

[motes motes]

On Mon, Feb 1, 2010 at 3:36 PM, Kevin H. Hobbs <hobbsk at ohiou.edu> wrote:
> On 02/01/2010 07:53 AM, motes motes wrote:
>> I am currently using the gradient descent optimizer and the
>> MeanSquaresImageToImageMetric in an image registration apllication
>> used for CD scans of lungs.
>>
>> But how do I know that the minima reached is not just a local minima
>> instead of the global minima?
>
> The short answer is that one can never know if a multi-dimensional
> optimization has reached the global minimum.
>
> The best you can do is show that repeated optimizations with different
> initial conditions reach the "same" final point, and that that point is
> no worse than any other point found.
>
>



Ok but its not possible to argument that if the fixed and moving
images don't differ too much the minima found will most likely be
global? This I have read somewhere but I actually don't understand
why.