Low pass filters are integrator that is used for filtering , smoothing the  image. While high pass filters are differentiator for getting edges (gf: Sobel, LoG all edge detection) and these operate on numerical values of transformed or raw image data. Same understanding with wavelets too (starting point)...

ODE (ordinary differential equation) and PDE are used for reconstruction . Having the differential operators in the matrix form.

Numerical recipes in C , will let you know how to build the matrix/block matrix and process it in the continuous to discrete domain .

DIP by Anil K Jain (more on z-tranform)  , Gonzales and Woods ,William Pratt

Hello, following topics my help u.

1. Image Enhancements

2. Wavelet processing

3. Sampling and Quantization

DIP by Gonzales and Woods may help u lot

Hello, following topics my help u.

1. Image Enhancements

2. Wavelet processing

3. Sampling and Quantization

DIP by Gonzales and Woods may help u lot

The following literature can be referred.

Luc Florack and Hans van Assen."Multiplicative calculus in biomedical image analysis", Journal of Mathematical Imaging and Vision, DOI: 10.1007/s10851-011-0275-1, 2011.

Well the derivatives and laplacians play an important role, along with the differential equations. More importantly the diffusion equations are widely used. I would recommend a coursera course by shapiro.

https://www.coursera.org/course/images

I we interpret calculus broadly to include real analysis, for instance, some suggestions are:

1. Calculus of variations in one (e.g., snakes) and several dimensions (e.g., TV-minimization, thin plate splines.)

2. Partial differential equations (e.g., level set methods, fast marching and scale space theory)

3. Functions of bounded variation (e.g., TV-minimization, the Rudin -Osher-Fatemi model).

My examples are not exhaustive, of course.

Not sure if your assignment also includes image measurements and more computer-vision-like problems, but there are several image processing and computer vision problems that require least squares solutions. I'm no expert on this, but maybe this page might give a nice overview of different mathematical approaches to this problem: http://www.imagingshop.com/linear-and-nonlinear-least-squares-with-math-net/

One particularly popular example application of least-squares is in bundle adjustment, where you only have a set of image coordinates of the same set of scene points in several photos, taken from different positions (with possibly different cameras) and you need to estimate: 6 dimensional camera position and orientation for each photo, focal length for each photo (or sometimes this can be assumed the same) as well as the actual 3D locations of all the image points used. Several Least-squares solutions have been proposed that try to minimize the 'reprojection error of the estimated 3D points', compared to the coordinates of the measured point locations in the images. Most methods use iterations with a Jacobian matrix to speed up convergence. This Jacobian can either be numerically estimated or mathematically derived and simplified from knowledge of the underlying problem.

A nice example of a nonlinear least-squares solution to a more simple image analysis problem, by Hesch and Roumeliotis, can be found here: http://www-users.cs.umn.edu/~joel/_files/Joel_Hesch_ICCV11.pdf,

Where only the 6D camera pose needs to be estimated with known 3D points, camera parameters and image coordinates. This is just one of many solutions proposed to the same problem, but I found this one particularly elegant and practical, and it's close to state-of-the art in accuracy.

Another example of the use of least squares is in 'optic flow' or 'stereo-disparity' calculation between two images (also useful for 3D scene reconstruction). Different factors can be included in the cost function that needs to be minimized, such as image-intensity-constancy, color constancy, image derivative, continuity, etc. I can't think of a particular example method as there are so many different ones out there, which all have their own benefits and limitations (none of them is perfect). Probably best to check the latest computer vision conferences and journals, such as CVPR 2015.

you can see this...

http://www.springer.com/us/book/9780387217666

Calculus is a systematic algebraic method to deal with small changes in the objects properties .This is done by differential calculus or by integral calculus where ever needed.

Once you understand this abstract application of calculus and its formulation ,you can perform similar application in image processing ,such as analysing videos or any other moving objects .Calculus may be used in finding the rate of change in pixels along a line in images which will calculate the frequency .