Code for creating and using the SPC model of a plenoptic camera with known geometry.

The current implementation can be run with both MATLAB and GNU Octave. It will be rewritten for Python, hopefully soon.

In case you want to give reference to any of the published papers:

• refer to [ACIVS12] and [MIUN13] for the general concept of the SPC model,
• refer to [SPIE13] and [IC3D12] for the spatial resolution extractor applicable to the common field of view,
• refer to [ICASSP14] and [ICIP14] for the spatial resolution extractor applicable to the whole field of view,
• refer to [ICIP15] for the angular and depth resolution extractors.

The functionality for generating an SPC model for a camera system is implemented in the following files:

* Generate_LCm.m
* Generate_LCm_decoupled.m
* Generate_Aperture.m
* Aperture_m.m
* Generate_Lens.m
* Lens_m.m

Each file contains a function with the same name as the file.

The first function, Generate_LCm.m generates the initial set of light cones for the image sensor pixels. The angular span of the generated light cones is defined with respect to the given light-acceptance-angle of the sensor pixel as a physical property of the image sensor pixel. More info about the parameters can be found in the header of the file.

The function Generate_LCm_decoupled(), contains the functionality for generating the initial set of light cones on the sensor pixel, and assumes that all lenslets in a micro-lens array are decoupled from their neighbouring lenslets. This means that each lenslet affects only the pixels behind that particular lenslet, see e.g. [SPIE13] for details. More info about the parameters can be found in the header of the file.

The function Generate_Aperture() generates an aperture from given values.
Then Aperture_m() applies that aperture to a set of light cones. In this implementation the aperture describes the part of the lens that light can pass through, as otherwise the lens is assumed to be infinitely wide. More info about the parameters can be found in the header of the file.

The function Generate_Lens() is then used to generate a lens or a lens array from given values. Then the function Lens_m() is used to apply this lens or lens-array to the light cones generated above and trimmed by the aperture. More info about the parameters can be found in the header of the file.

The use of the functions just described are illustrated in a set of example files:

* PC2.m
* Lytro.m
* R29.m

All implementations are given as 1-dimensional optimizations.

In PC2.m I use the set of the previously defined functions to generate the SPC model of a plenoptic camera. An image sensor and a microlens-array with known geometry and spacing build the structure of the plenoptic camera.

In Lytro.m I've implemented the original Lytro camera as an example of
plenoptic camera implementation. More info about the parameters can be found in the header of the file. See [ICASSP14] for more details.

R29.m is my implementation of the Raytrix R29 plenoptic camera, which is used to generate the results in [ICIP14].

So far the special and depth resolution have been the interesting properties.

First I look at the spatial resolution profile through depth, or, as I call it, the lateral resolution. Then it follows with depth and angular resolution.

The following scripts are described:

* Base_m.m
* ResDistPrincipalRayModel_CFoV.m
* ResDistSPC_CFoV.m
* StitchedResDistLytro.m
* StitchedResDistR29.m
* ERR.m

Base_m.m is a function for projecting a set of light cones on a given base plane. This functionality is used e.g. inside the aperture to find the part of the light cone that can pass through the aperture geometry.

ResDistPrincipalRayModel_CFoV.m calculates the minimum resolvability distance in the common field of view of all the microlenses using the principal-ray-model. The resolvability distance is calculated for several depth planes. The principal ray model is implemented using the SPC model, when the aperture is at the center of the microlenses and in the size of a pin-hole. The results have been used in papers [SPIE13] and [ICIP14]. More info about the parameters can be found in the header of the file.

ResDistSPC_CFoV.m calculates the minimum resolvability distance in the common field of view (CFoV) of all the microlenses using the SPC model. The resolvability distance is calculated for several depth planes. More info about the parameters can be found in the header of the file.

StitchedResDistLytro.m generates the SPC model of a Lytro plenoptic camera and then calculates the minimum-resolvability-distance for several depth planes. The surface area to look for the minimum-resolvability-distance goes outside the common field of view (CFoV), using an incremental approach. This is described in detail in paper [ICASSP14].

StitchedResDistR29.m generates the SPC model of an R29 plenoptic camera and then calculates the minimum-resolvability-distance for several depth planes. The surface area to look for the minimum-resolvability-distance goes outside the common field of view (CFoV), using an incremental approach. This is described in detail in papers [ICASSP14] and [ICIP14].

ERR.m, the Effective Resolution Ratio calculates and plots the normalized-spatial-resolution for R29 plenoptic camera using the minimum-resolvability-distance values previously calculated in StitchedResDistR29.m. It also calculates and plots the normalized-spatial-resolution for a plenoptic camera with three-focal length microlens array structure, using the analytical approach.

Here I look at the depth resolution extractor. The following script is described:

* DepthRes.m

DepthRes.mextracts the location of the resolvable depth planes for a plenoptic 2.0 (or a focused lenoptic) camera. It considers only the central row of the pixels on the image sensor and so it is one dimensional.

More info about the SPC model can be found in [ACIVS12], [IC3D12] and [MIUN13].

[SPIE13] Mitra Damghanian, Roger Olsson, Mårten Sjöström, Hector Navarro Fructuoso, and Manuel Martinez-Corral. "Investigating the lateral resolution in a plenoptic capturing system using the SPC model." In IS&T/SPIE Electronic Imaging, pp. 86600T-86600T. International Society for Optics and Photonics, 2013. URL: http://miun.diva-portal.org/smash/record.jsf?pid=diva2:607155

[ICIP14] Mitra Damghanian, Roger Olsson, Mårten Sjöström, Arne Erdmann, and Christian Perwass. "Spatial resolution in a multi-focus plenoptic camera." IEEE International Conference on Image Processing (ICIP), 2014, pp: 1932-1936. URL: http://miun.diva-portal.org/smash/record.jsf?pid=diva2:762088

[ICASSP14] Mitra Damghanian, Roger Olsson, and Mårten Sjöström. "Performance analysis in Lytro camera: Empirical and model based approaches to assess refocusing quality." ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, IEEE conference proceedings, 2014, 559-563 (2014). URL: http://miun.diva-portal.org/smash/record.jsf?pid=diva2:706716

[ICIP15] Mitra Damghanian, Roger Olsson, Mårten Sjöström. "Depth and angular resolution in plenoptic cameras." Accepted in: IEEE International Conference on Image Processing (ICIP), Québec, Canada, Sep2015.

[ACIVS12] Mitra Damghanian, Roger Olsson, and Mårten Sjöström. "The Sampling Pattern Cube–A Representation and Evaluation Tool for Optical Capturing Systems." In Advanced Concepts for Intelligent Vision Systems, pp. 120-131. Springer Berlin Heidelberg, 2012. URL: http://miun.diva-portal.org/smash/record.jsf?pid=diva2:555237

[IC3D12] Mitra Damghanian, Roger Olsson, and Marten Sjostrom. "Extraction of the lateral resolution in a plenoptic camera using the SPC model." In 3D Imaging (IC3D), 2012 International Conference on, pp. 1-5. IEEE, 2012. URL: http://miun.diva-portal.org/smash/record.jsf?pid=diva2:582321

[MIUN13] Mitra Damghanian. “The sampling pattern cube: A framework for representation and evaluation of plenoptic capturing systems,” Licentiate thesis No 99, Mid Sweden University, Department of Information and Communication Systems, 2013. URL: http://miun.diva-portal.org/smash/record.jsf?pid=diva2:626787