Dear Alaeldin

One good solution to solve your problem would be to use an optimal interpolation technique for merging data which overlap. I suppose that the different images were taken at different times and that the geophysical parameter evolved with time. Thus by imposing a spatial and temporal correlation function, with a temporal radius covering the elapsed time between the first an last image and a spacial scale corresponding to some  pixel, you can obtain a single merged analysis. But first check the consistency of your images (of course) and choose a guess (for instance the time average of your three images).

If the objective analysis seems too complicated, you can simplify your problem by taking an algebric averaging with some time ponderation of the data in order to give more information to the image which is closer to the time of your analysis. Of course  this depends on which satellite variable you are working on!

Hope this can help you!

G.C.

 Dear Aladdin S,

You have to see the spatial, spectral, and temporal resolution of the image. and then, one way of good solution to solve your problems would be to use the image processing technique to bring same scale of all the three images or near to each other, so that you can overlay all the three images. Alternatively, you may use the covariance of geo-statistical methods in order to obtain more reliable predicted value of the parameters derived from the images. Many of the scholars used the hybrid image processing and overlay techniques to merge the data to see the land use / land cover dynamics, landscape environmental changes and climate changes with define time interval. 

For example, Landsat TM data (30M spatial resolution) and IRS LISS II data (36M spatial resolution), and different seasonal / temporal (cropping season and harvesting seasons)  data is used for land use studies.

There are many scholars conducted the same kind of studies using geophysical and environmental variables. (huge literatures are available in the open access sources for the immediate reference).

M.Palaniyandi

You have given us the conceptual task, so the aswer has the same character...:)

Using spectral properties the missing 20% coverage could be modeled  by creating, for example, the linear regression equation based on common parts of an images A and B. The same solution can be applied to the second pair of images. Next you can calculate disparity maps for whole area of interest. 

SK

Dear Aladadin S,

    I guess you are talking about stereo matching, therefore the epipolar image of A from the AB pair and A from AC pair are different. You may always need the transformation parameters for the fusion (between the original image and the epipolar image), as well as the rpc parameters. two ways:

1) do forward intersection with AC pair, reproject the value to AB pair to form another disparity image. fuse them, you might be able to check the consistency of the overlap points (3 ray points).

2) do it externally, do forward intersection for both AB and AC pair, and fuse the the resulting DSM.

Hope it helps.

Rongjun

Dear Caniaux and Palaniyandi

Thank you so much about your answers. However, I think it would be helpful to give some more information about the data that I am working on.

I have tri- stereo [(a) forward Off-nadir + (b) quasi + (c) backward Off-nadir] VHR satellite RS images (1 Pan+4 MS-bands). I believe, they have almost the same acquisition time and scale.

To generate the disparity maps, I have rectified the three images (generate 3 Epipolar images) so all the corresponding pixels lay on the same line. The product of the applied matching technique (for example) for the forward Off-nadir image (a) **as a base image** is: (ab) disparity map and (ac)-disparity map.

The images were acquired over an urban area, so the occlusion effect is severe. The regular interpolation in dense urban areas will dramatically reduce the quality of the generated disparity map; thus, fusing these two disparity maps will overcome this problem.

I agree with Dr. Caniaux that optimal interpolation technique will provide the required fusion (merging). However, this technique requires the geophysical parameters to be known at lease the airbase (B) between the acquired images which is not constant for line sensor like the case of the frame sensors.

I would like to model the relationship of the two disparity maps (ac & ab) without involving too much parameters related to the acquisition geometry. Now, I am dealing with epipolar images not the raw images. I believe the relationship is linear (D_ac = m* D_ab + C). But the experiments do not support that.

Regarding Dear Qin:

The answer is very clear and effective; however, I would like to NOT use the RPC's to avoid extra calculation like the forward intersect and Bunuel adjustment.

Thank you for all the participants.

hope I have described the situation clearly

Ala

Dear Ala,

following your idea, the relationship of the disparity map should not be linear, but somehow like this 1/D_ac = m*(1/D_ab) + c

hope it helps.

best,

Rongjun

Dear Qin

thank you so much. your answer is what I was expecting ( a math Model describing the relationship).

So, do you have/know any literature /paper that support or explain what you have pointed out?     it would be very appreciated

Regards

Ala

Dear Ala,

    I just refer to the perspective epipolar geometry, if you do some calculation based on this (i mean you do calculation on the perspective model for the same occasion), you will probably get this conclusion, but at least it should not be linear, as the disparity is inversely proportional to the scale factor.

Rongjun

Dear

there are a large number of softwares can do that such as envi, arc map

regards