Lecture 6: Structure Enhancement

Question 1

How are intensity gradients computed on discrete images?

Answer 1

using first- and second-order derivatives. Derivatives of digital functions like images can be defined in terms of finite differences

Question 2

What are forward, backward and central differences?

Answer 2

forward: Difference with value of next point.
f’(x) = f(x+1) - f(x)

backward: Difference with value of the previous point
f’(x) = f(x) + f(x-1)

central differences
f’(x) = (f(x+1)-f(x-1))/2

Question 3

How about second order derivatives?

Answer 3

f’‘(x) = f(x+1) - 2f(x) + f(x-1)

Question 4

Which basic edge detection algorithms do you know?

Answer 4

1. Sobel
2. Prewitt
3. Laplacian of Gaussian
4. Canny Gaussian
5. Roberts
6. Fuzzy

Question 5

Explain how convolutional filters can be used for edge detection and describe the design of the kernels.

Answer 5

1. All operations can be implemented as 3x3 spatial convolution filters with appropriate weigths
2. For two or more variables, the dimension are considered individually

Question 6

How does the Laplacian-of-Gaussian approach accomplish the enhancement of structures at different scales?

Answer 6

Use filters of difference sizes.

• Intensity changes are not independent of image scale, so differently sized operators are required
• Zero crossing of the second derivative can be used equivalently for detecting sudden intensity changes
• Standard deviation controls the size of the structures the LoG responds to.
• The intensity of structures at scales much smaller than standard deviation will be reduced.

Question 7

What is the relationship between the zero-crossings and the standard deviation of the LoG filter?

Answer 7

The behavior of the LoG zero crossing edge detector is largely governed by the standard
deviation of the Gaussian used in the LoG filter. The higher this value is set, the more
smaller features will be smoothed out of existence, and hence fewer zero crossings will be
produced.
This parameter can be set to remove unwanted detail or noise as desired. The idea that at
different smoothing levels different sized features become prominent is referred to as `scale’.

Question 8

What is the general concept of vesselness filtering?

Answer 8

It is used to detect tube-like structures. Ideal tubular structure in 3D has the following properties:

lambda1 = 0
lambda1 &laquo_space;lambda 2
lambda2 = lambda3

filter is used for enhancing the visualization of vasculature. The filter is applied at an image voxel level and is based on the eigenvalue decomposition of the local hessian matrix of the image

Question 9

How can the eigenvalues be used to distinguish between different local structures?

Answer 9

Eigenvectors of the Hessian point into the principal directions (orthonormal directions that are invariant up to a scaling factor when mapped by the Hessian).
The ellipsoid specified by eigenvectors and eigenvalues locally describes the second order structure of the image:

Question 10

What kind of structures can be enhanced with the generalized objectness filter?

Answer 10

Generalizations to an objectness filter allows to enhance plate-like or blob-lime structures

Question 11

Why is it useful to

incorporate the Frobenius norm-based term into the measure?

Answer 11

Frobenius norm is used to exclude responses in background noise

Question 12

How can convolutional neural networks be used to enhance specific structures or to perform semantic segmentation?

Answer 12

Design network as a bunch of convolutional layers with internal downsampling and upsampling.

Downsampling can be achieved via pooling or strided convolutions.

Upsampling by unpooling or strided transpose convolution

Question 13

What’s the drawback of the sliding window approach?

Answer 13

very inefficient as each pixel is classified separately and overlapping patches do not reuse shared

Question 14

Explain the concept of unpooling or up-convolution operations!

Answer 14

The unpooling operation is used to revert the effect of the max pooling operation.

Max pooling ca be reverted by remembering the location of the maximum element and restoring the position in the corresponding unpooling layer

Question 15

What are 1x1 convolutions and why may they be

useful?

Answer 15

1. Can be used to alter the number of channels of the input volume to a desired number of output channels
2. Can reduce dimensionality in the filter dimension
3. Can be used in general to change the filter space dimensionality (Increase or decrease)

Question 16

What is the intention of batch normalization and how does it generally work?

Answer 16

• Batch consists of a single image due to memory limitations of the GPU
• Batch normalization is used for faster convergence

As small changes of network activations will be amplified when the network becomes deeper, the activation distributions should be stabilized/normalized. That is accomplished by computing the mean and variance among the activations of each mini-batch.
Using batch normalization allows for higher learning rates and potentially decreases the need for dropout.

Question 17

How is this concept translated to 3D? How can sparse 2D annotations be used to train a 3D model?

Answer 17

Sparsely annotated 2D training data of a few slices and augmentation is used to train a 3D
model!

Question 18

Why are skip-connections useful?

Answer 18

These skip-connections preserve higher resolution features, which are merged with more
abstract features to get more accurate results.