Some Corrections and Deletion of Slides

presentation/finalpresentation.Rmd

@@ -34,7 +34,7 @@ xaringanExtra::use_panelset()
 ```
 
 
-# Depth Estimation
+# Depth: the third dimension
 
 * Traditional photographs are two dimensional projections of a three dimensional scene.
 
@@ -94,27 +94,6 @@ $$k(x,y) = \frac{C_{h,r}}{2\pi h^2} e^{-\frac{x^2 + y^2}{2h^2}} \times \text{I}_
 
   $$k(x,y) = \frac{C_{h,r}}{2\pi}\frac{h}{(x^2 + y^2 + h^2)^{3/2}}\times \text{I}_{\{x^2 + y^2 \ \leq \ r^2\}}$$
 
----
-
-# Image Blurring Model
-
-* The blurred image can be viewed as **convolution** of original sharp image and blur kernel. 
-
-* The observed blurred image $\boldsymbol{b}$ can be modeled in terms of its gradients $\boldsymbol{x}$ as - 
-
-  $$\boldsymbol{y} = \boldsymbol{k} \ \otimes \ \boldsymbol{x} \ + \ \boldsymbol{n}$$
-Where,
-
-  * $\boldsymbol{k}$ is blur kernel and $\boldsymbol{x}$ is gradient of *true latent image*.
-
-  * $\boldsymbol{n}$ is gradient of noise and $\otimes$ denotes the *valid convolution* operator.
-
-* Expressing the model in frequency domain as - 
-
-$$\boldsymbol{Y_{\omega} = K_{\omega}X_{\omega} + N_{\omega}}  \  \ \  \forall \ \boldsymbol{\omega} = (\omega_1,\omega_2)$$  
-* We assume Nandy's Auto regressive prior on DFT coefficients $\boldsymbol{X_{\omega}}$.
-
-
 ---
 
 # Maximum Likelihood Estimation of Blur Kernel Parameters
@@ -234,21 +213,23 @@ knitr::include_graphics("pimg/couple.png")
 
 # Challenges in Post-Segmentation ML Estimation
 
-* Our ML estimation procedure requires images of rectangular shapes.
+* ML estimation procedure requires images of rectangular shapes.
 
 * But image segments obtained by SAM are of irregular shape.
 
 --
 
 * Obvious solution is to pad or fill with zeros to make rectangular array.
 
-* This approach leads to bias towards selecting small values of radius $r$.
-
 ```{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"}
 
 knitr::include_graphics("pimg/zero_pad.png")
 ```
 
+--
+
+* This approach leads to bias towards selecting small values of radius $r$.
+
 ---
 
 ## Experiment
@@ -309,8 +290,6 @@ knitr::include_graphics("pimg/ap1.png")
 
 * Apply estimation procedure to these sub regions.
 
---
-
 * Discards a large proportion of available data depending on how irregular segment it is.
 
 ```{r ,warning=FALSE,echo=FALSE,out.width='70%',out.height="30%",fig.align='center',echo=FALSE,fig.cap= "Figure: Irregular segments identified by SAM"}

presentation/finalpresentation.html

@@ -44,7 +44,7 @@
 </style>
 
 
-# Depth Estimation
+# Depth: the third dimension
 
 * Traditional photographs are two dimensional projections of a three dimensional scene.
 
@@ -101,27 +101,6 @@
 
   `$$k(x,y) = \frac{C_{h,r}}{2\pi}\frac{h}{(x^2 + y^2 + h^2)^{3/2}}\times \text{I}_{\{x^2 + y^2 \ \leq \ r^2\}}$$`
 
----
-
-# Image Blurring Model
-
-* The blurred image can be viewed as **convolution** of original sharp image and blur kernel. 
-
-* The observed blurred image `\(\boldsymbol{b}\)` can be modeled in terms of its gradients `\(\boldsymbol{x}\)` as - 
-
-  `$$\boldsymbol{y} = \boldsymbol{k} \ \otimes \ \boldsymbol{x} \ + \ \boldsymbol{n}$$`
-Where,
-
-  * `\(\boldsymbol{k}\)` is blur kernel and `\(\boldsymbol{x}\)` is gradient of *true latent image*.
-
-  * `\(\boldsymbol{n}\)` is gradient of noise and `\(\otimes\)` denotes the *valid convolution* operator.
-
-* Expressing the model in frequency domain as - 
-
-`$$\boldsymbol{Y_{\omega} = K_{\omega}X_{\omega} + N_{\omega}}  \  \ \  \forall \ \boldsymbol{\omega} = (\omega_1,\omega_2)$$`  
-* We assume Nandy's Auto regressive prior on DFT coefficients `\(\boldsymbol{X_{\omega}}\)`.
-
-
 ---
 
 # Maximum Likelihood Estimation of Blur Kernel Parameters
@@ -232,21 +211,23 @@
 
 # Challenges in Post-Segmentation ML Estimation
 
-* Our ML estimation procedure requires images of rectangular shapes.
+* ML estimation procedure requires images of rectangular shapes.
 
 * But image segments obtained by SAM are of irregular shape.
 
 --
 
 * Obvious solution is to pad or fill with zeros to make rectangular array.
 
-* This approach leads to bias towards selecting small values of radius `\(r\)`.
-
 <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>
 
+--
+
+* This approach leads to bias towards selecting small values of radius `\(r\)`.
+
 ---
 
 ## Experiment
@@ -307,8 +288,6 @@
 
 * Apply estimation procedure to these sub regions.
 
---
-
 * Discards a large proportion of available data depending on how irregular segment it is.
 
 <div class="figure" style="text-align: center">