[Rtk-users] Rtk-users Digest, Vol 26, Issue 5

[Jan Hoskovec]

Hi Andy,

I'm sorry not to have replied earlier. For the precisions you wanted,

1) your intuition is right, the upper and lower integration limits are
the values you are "expecting", the values delimiting the angular
range you want to cover (whatever is the actual sampling).

2) The division by two is there because in my approach, the "zone of
influence" of each sampled projections begins and ends halfway between
the sampled value of the gantry angle and the next / preceding sample.
The weights of other than first and last samples simplify to " (next
angle - previous angle) / 2" for me.

Hope this would help (unless, of course, you've found a better option
during the weekend :-) ).

Cheers,

Jan

2014-10-25 15:41 GMT+02:00 Andy Shieh <hsieandy at gmail.com>:
> Hi Jan,
>
> Thanks for sharing.
> This does seem useful to me, but I'm not sure if I understand your method
> correctly.
>
> For your lower and upper integration limit, do you mean the limit values for
> the angular range that you are "expecting"?
> For example if you are expecting a 0-180 deg scan (although the first and
> last angles might not be 0 and 180 due to sampling), lower/upper integration
> limit would be 0 and 180 deg?
>
> And why is the division 2 needed there?
> I thought in rtkFDKWeightProjectionFilter.txx, the gap value used for the
> weighting is "nextAngle - previousAngle" for a certain projection.
> In this case I would expect Gap_first to be
>
> Gap_first = second_angle - lower_integration_limit
> (As the lower integration limit is kind of like the "virtual angle"
> preceding the first angle?)
>
> Thanks for your help :)
>
> Cheers,
> Andy
>
>
>>
>> Date: Fri, 24 Oct 2014 17:21:27 +0200
>> From: Jan Hoskovec <jean.hoskovec at gmail.com>
>> To: Andy Shieh <hsieandy at gmail.com>
>> Cc: "rtk-users at public.kitware.com" <rtk-users at public.kitware.com>
>> Subject: Re: [Rtk-users] itFirstAngle and itLastAngle in
>>         rtkParkerShortScanImageFilter.txt
>> Message-ID:
>>
>> <CANtP0QSnh70uETrdyTjg=u3HaUth4kRwDVfhMmKL=DhwrwzNLg at mail.gmail.com>
>> Content-Type: text/plain; charset=UTF-8
>>
>> Hi Andy,
>>
>> I was recently dealing with a similar problem in a different context
>> (180? backprojection with irregular sampling and how to handle the
>> first and last gaps) and what worked for me was
>>
>> Gap_first = (second angle - first angle) / 2 - lower integration limit
>>
>> and, analogically,
>>
>> Gap_last = upper integration limit - (last angle - second last angle) / 2
>>
>> with the integration limits being arbitrary set where I wanted them.
>> The idea behind this was that a continuous projection value we are
>> miming in the discrete integral should always be represented by the
>> closest projection we have, with a known angular segment to cover.
>>
>> However, that was a DBP-type algorithm, for which the exact
>> integration limits are extremely important, it may be different in the
>> context of a short scan. But just in case you might find this
>> useful...
>>
>> Cheers,
>>
>> Jan
>
>
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