Final Presentation Commit

presentation/finalpresentation.Rmd

@@ -133,6 +133,8 @@ knitr::include_graphics("pimg/sigexpall.png")
 
 # How to estimate Spatially Varying blur ?
 
+* Real world images often exhibit spatially varying blur implying pixel to pixel varying blur level.
+
 --
 
 ```{r ,warning=FALSE,echo=FALSE,out.width='44%',fig.align='center',echo=FALSE}
@@ -144,6 +146,8 @@ knitr::include_graphics("pimg/moon.png")
 
 # How to estimate Spatially Varying blur ?
 
+* Real world images often exhibit spatially varying blur implying pixel to pixel varying blur level.
+
 ```{r ,warning=FALSE,echo=FALSE,out.width='44%',fig.align='center',echo=FALSE}
 
 knitr::include_graphics("pimg/moon_kern.png")
@@ -153,8 +157,6 @@ knitr::include_graphics("pimg/moon_kern.png")
 
 # Spatially Varying Blur Estimation
 
-* Real world images often exhibit spatially varying blur implying pixel to pixel varying blur level.
-
 * Assume locally constant blur within a small patch around each pixel.
 
 --
@@ -227,7 +229,7 @@ knitr::include_graphics("pimg/couple.png")
 
 * Obvious solution is to pad or fill with zeros to make rectangular array.
 
-```{r ,warning=FALSE,echo=FALSE,out.width='60%',out.height="40%",fig.align='center',echo=FALSE,fig.cap= "Figure: Zero padding to make rectangular array"}
+```{r ,warning=FALSE,echo=FALSE,out.width='65%',out.height="40%",fig.align='center',echo=FALSE}
 
 knitr::include_graphics("pimg/zero_pad.png")
 ```
@@ -346,7 +348,7 @@ $$L(\boldsymbol{\theta}) \propto \frac{1}{\sqrt{\text{det}(\sigma^2 \boldsymbol{
 
 # Decorrelation Loss
 
-* For an observed blurred image $\boldsymbol{y}$, suppose the true blur kernel is $\boldsymbol{k_{\theta_0}}$.
+* For an observed blurred image gradient $\boldsymbol{y}$, suppose the true blur kernel is $\boldsymbol{k_{\theta_0}}$.
 
 --
 
@@ -356,10 +358,6 @@ $$L(\boldsymbol{\theta}) \propto \frac{1}{\sqrt{\text{det}(\sigma^2 \boldsymbol{
 
 --
 
-* Because, convolution using $\boldsymbol{k}$ increases the correlation among image gradients.
-
---
-
 * We simulated defocus blur on a $255\times 255$ image using disc kernel with $r_{true} = 3$.
 
 * Plotted ACF of both horizontal and vertical gradients after deconvoluting using $r = 2,3,4$. 
@@ -386,17 +384,11 @@ knitr::include_graphics("pimg/decorr2.png")
 
 # Decorrelation Loss
 
-* For deconvolution step we used conditional mean of $\boldsymbol{X_{\omega}}$ given $\boldsymbol{Y_{\omega}}$ and $\boldsymbol{K_{\omega}}$ i.e.
-
-$$\mathbb{E}[\boldsymbol{X_{\omega}}|\boldsymbol{Y_{\omega}},\boldsymbol{K_{\omega}}] = \frac{\sigma^2g_{\omega}\boldsymbol{K_{\omega}Y_{\omega}}}{\eta^2h_{\omega} + \sigma^2g_{\omega}|\boldsymbol{K_{\omega}}|^2}$$
-
-* Take Inverse DFT to obtain deconvoluted horizontal and vertical gradients denoted by $\boldsymbol{x_{h,\theta}}$ and $\boldsymbol{x_{v,\theta}}$.
-
---
 
 * Consider sum of squared ACF in both along and across direction of gradients as loss function denoted by 
 
 $$\text{Decorr}(\boldsymbol{\theta}) = \text{Decorr}(\boldsymbol{x_{h,\theta}},\boldsymbol{x_{v,\theta}})$$
+$\ \ \ \ \text{ }$ Where, $\boldsymbol{x_{h,\theta}}$ and $\boldsymbol{x_{v,\theta}}$ denotes deconvoluted horizontal and vertical gradients respectively.
 
 * It captures the amount of correlation present in image gradients after deblurring using $\boldsymbol{k_\theta}$.
 
@@ -405,6 +397,11 @@ $$\text{Decorr}(\boldsymbol{\theta}) = \text{Decorr}(\boldsymbol{x_{h,\theta}},\
 * $\text{Decorr}(\boldsymbol{\theta})$ should be minimum for true value of $\boldsymbol{\theta}$.
 
 $$\hat{\boldsymbol{\theta}} = \underset{\boldsymbol{\theta}}{\text{argmin}} \ \text{Decorr}(\boldsymbol{x_{h,\theta}},\boldsymbol{x_{v,\theta}})$$
+--
+
+* For deconvolution step we used conditional mean of $\boldsymbol{X_{\omega}}$ given $\boldsymbol{Y_{\omega}}$ and $\boldsymbol{K_{\omega}}$ i.e.
+
+$$\mathbb{E}[\boldsymbol{X_{\omega}}|\boldsymbol{Y_{\omega}},\boldsymbol{K_{\omega}}] = \frac{\sigma^2g_{\omega}\boldsymbol{K_{\omega}Y_{\omega}}}{\eta^2h_{\omega} + \sigma^2g_{\omega}|\boldsymbol{K_{\omega}}|^2}$$
 
 ---
 
@@ -512,15 +509,7 @@ knitr::include_graphics("pimg/refocus1.png")
 
 ---
 
-# Discussion
-
-* We proposed a new method to estimate spatially varying blur based on single image of the scene.
-
---
-
-* Due to issue of zero padding with ML estimation, we developed an ad hoc procedure based on Decorrelation Loss.
-
---
+# Comment
 
 * Estimated blur maps clearly depict differences in blur levels & boundaries between objects in image.
 
@@ -534,17 +523,15 @@ knitr::include_graphics("pimg/refocus1.png")
 
 --
 
-* Choice of $\kappa$ can be incorporated in estimation procedure.
+* Further improvement is possible by choosing suitable tuning parameter.
 
---
-
 * Hard to isolate effects of tuning parameter because of their confounding effect.
 
 ---
 
-# Discussion
+# Computation time
 
-* A significant reduction in computing time.
+* This results in a significant reduction in computing time.
 
 * Because instead of estimating for all pixel separately we are estimating only for segments.
 
@@ -554,9 +541,11 @@ knitr::include_graphics("pimg/refocus1.png")
 
 * SAM takes around 3 minutes for segmentation on GPU run time.
 
+* Pixel by pixel blur estimation takes around 1 hr 30 minutes only for initial step.
+
 --
 
-* Pixel by pixel blur estimation takes around 1 hr 30 minutes only for initial step.
+* A R package implementing our estimation procedure is available on github : [DepthR](https://github.com/ShrayanRoy/DepthR)
 
 ---
 
@@ -577,6 +566,8 @@ https://digitalcommons.isical.ac.in/doctoral-theses/7/
 
 * Xiang Zhu et al. “Estimating Spatially Varying Defocus Blur From A Single Image”. In: (2013). issn: 1941-0042. url: http://dx.doi.org/10.1109/TIP.2013.2279316.
 
+*  William Hadley Richardson. “Bayesian-Based Iterative Method of Image Restoration". In: (1972). doi: http://dx.doi.org/10.1145/1276377.127646
+
 ---
 
 class: center, middle

presentation/finalpresentation.html

@@ -137,6 +137,8 @@
 
 # How to estimate Spatially Varying blur ?
 
+* Real world images often exhibit spatially varying blur implying pixel to pixel varying blur level.
+
 --
 
 <img src="pimg/moon.png" width="44%" style="display: block; margin: auto;" />
@@ -145,14 +147,14 @@
 
 # How to estimate Spatially Varying blur ?
 
+* Real world images often exhibit spatially varying blur implying pixel to pixel varying blur level.
+
 <img src="pimg/moon_kern.png" width="44%" style="display: block; margin: auto;" />
 
 ---
 
 # Spatially Varying Blur Estimation
 
-* Real world images often exhibit spatially varying blur implying pixel to pixel varying blur level.
-
 * Assume locally constant blur within a small patch around each pixel.
 
 --
@@ -225,10 +227,7 @@
 
 * Obvious solution is to pad or fill with zeros to make rectangular array.
 
-<div class="figure" style="text-align: center">
-<img src="pimg/zero_pad.png" alt="Figure: Zero padding to make rectangular array" width="60%" height="40%" />
-<p class="caption">Figure: Zero padding to make rectangular array</p>
-</div>
+<img src="pimg/zero_pad.png" width="65%" height="40%" style="display: block; margin: auto;" />
 
 --
 
@@ -344,7 +343,7 @@
 
 # Decorrelation Loss
 
-* For an observed blurred image `\(\boldsymbol{y}\)`, suppose the true blur kernel is `\(\boldsymbol{k_{\theta_0}}\)`.
+* For an observed blurred image gradient `\(\boldsymbol{y}\)`, suppose the true blur kernel is `\(\boldsymbol{k_{\theta_0}}\)`.
 
 --
 
@@ -354,10 +353,6 @@
 
 --
 
-* Because, convolution using `\(\boldsymbol{k}\)` increases the correlation among image gradients.
-
---
-
 * We simulated defocus blur on a `\(255\times 255\)` image using disc kernel with `\(r_{true} = 3\)`.
 
 * Plotted ACF of both horizontal and vertical gradients after deconvoluting using `\(r = 2,3,4\)`. 
@@ -381,17 +376,11 @@
 
 # Decorrelation Loss
 
-* For deconvolution step we used conditional mean of `\(\boldsymbol{X_{\omega}}\)` given `\(\boldsymbol{Y_{\omega}}\)` and `\(\boldsymbol{K_{\omega}}\)` i.e.
-
-`$$\mathbb{E}[\boldsymbol{X_{\omega}}|\boldsymbol{Y_{\omega}},\boldsymbol{K_{\omega}}] = \frac{\sigma^2g_{\omega}\boldsymbol{K_{\omega}Y_{\omega}}}{\eta^2h_{\omega} + \sigma^2g_{\omega}|\boldsymbol{K_{\omega}}|^2}$$`
-
-* Take Inverse DFT to obtain deconvoluted horizontal and vertical gradients denoted by `\(\boldsymbol{x_{h,\theta}}\)` and `\(\boldsymbol{x_{v,\theta}}\)`.
-
---
 
 * Consider sum of squared ACF in both along and across direction of gradients as loss function denoted by 
 
 `$$\text{Decorr}(\boldsymbol{\theta}) = \text{Decorr}(\boldsymbol{x_{h,\theta}},\boldsymbol{x_{v,\theta}})$$`
+`\(\ \ \ \ \text{ }\)` Where, `\(\boldsymbol{x_{h,\theta}}\)` and `\(\boldsymbol{x_{v,\theta}}\)` denotes deconvoluted horizontal and vertical gradients respectively.
 
 * It captures the amount of correlation present in image gradients after deblurring using `\(\boldsymbol{k_\theta}\)`.
 
@@ -400,6 +389,11 @@
 * `\(\text{Decorr}(\boldsymbol{\theta})\)` should be minimum for true value of `\(\boldsymbol{\theta}\)`.
 
 `$$\hat{\boldsymbol{\theta}} = \underset{\boldsymbol{\theta}}{\text{argmin}} \ \text{Decorr}(\boldsymbol{x_{h,\theta}},\boldsymbol{x_{v,\theta}})$$`
+--
+
+* For deconvolution step we used conditional mean of `\(\boldsymbol{X_{\omega}}\)` given `\(\boldsymbol{Y_{\omega}}\)` and `\(\boldsymbol{K_{\omega}}\)` i.e.
+
+`$$\mathbb{E}[\boldsymbol{X_{\omega}}|\boldsymbol{Y_{\omega}},\boldsymbol{K_{\omega}}] = \frac{\sigma^2g_{\omega}\boldsymbol{K_{\omega}Y_{\omega}}}{\eta^2h_{\omega} + \sigma^2g_{\omega}|\boldsymbol{K_{\omega}}|^2}$$`
 
 ---
 
@@ -489,15 +483,7 @@
 
 ---
 
-# Discussion
-
-* We proposed a new method to estimate spatially varying blur based on single image of the scene.
-
---
-
-* Due to issue of zero padding with ML estimation, we developed an ad hoc procedure based on Decorrelation Loss.
-
---
+# Comment
 
 * Estimated blur maps clearly depict differences in blur levels & boundaries between objects in image.
 
@@ -511,17 +497,15 @@
 
 --
 
-* Choice of `\(\kappa\)` can be incorporated in estimation procedure.
+* Further improvement is possible by choosing suitable tuning parameter.
 
---
-
 * Hard to isolate effects of tuning parameter because of their confounding effect.
 
 ---
 
-# Discussion
+# Computation time
 
-* A significant reduction in computing time.
+* This results in a significant reduction in computing time.
 
 * Because instead of estimating for all pixel separately we are estimating only for segments.
 
@@ -531,9 +515,11 @@
 
 * SAM takes around 3 minutes for segmentation on GPU run time.
 
+* Pixel by pixel blur estimation takes around 1 hr 30 minutes only for initial step.
+
 --
 
-* Pixel by pixel blur estimation takes around 1 hr 30 minutes only for initial step.
+* A R package implementing our estimation procedure is available on github : [DepthR](https://github.com/ShrayanRoy/DepthR)
 
 ---
 
@@ -554,6 +540,8 @@
 
 * Xiang Zhu et al. “Estimating Spatially Varying Defocus Blur From A Single Image”. In: (2013). issn: 1941-0042. url: http://dx.doi.org/10.1109/TIP.2013.2279316.
 
+*  William Hadley Richardson. “Bayesian-Based Iterative Method of Image Restoration". In: (1972). doi: http://dx.doi.org/10.1145/1276377.127646
+
 ---
 
 class: center, middle