ECE 515 Image Analysis & Computer Vision II Spring 2021
HW # 6
Turn in solutions to problems 1-3. Due 11:59 PM Thursday, 04/29.
Solutions to practice problems are not to be submitted.
1. In this problem we consider the processing of an image using a convoltion operation
with a simple 3×1 kernel. Image I shown below is applied to a filter with impulse
response h = [-1 0 1] followed by a ReLU nonlinearity, where
ReLU(x) = max(x, 0), x ∈ R
0 0 0 50 50 50 50 50 50 0 0 0
0 0 0 50 50 50 50 50 50 0 0 0
0 0 0 50 50 50 50 50 50 0 0 0
0 0 0 50 50 50 50 50 50 0 0 0
0 0 0 50 50 50 50 50 50 0 0 0
0 0 0 50 50 50 50 50 50 0 0 0
0 0 0 50 50 50 50 50 50 0 0 0
0 0 0 50 50 50 50 50 50 0 0 0
Image I h = -1 0 1
Use zero padding so that the output is of the same size as the input image (note that
zero-padding will be needed in only one of the two dimensions). Also assume a stride
of 1.
(a) Determine the output image.
(b) Explain what kind of processing using the above operations is performed, in terms
of edges, on the input image.
2. In this problem we will e
xamine the number of parameters used in a neural network
and the input-output volumes of a convolutional layer in a CNN.
(i) Consider a neural network where the input feature vector has 50 entries. There are
two hidden layers. The first hidden layer has 50 neurons followed by a hidden layer
with 20 neurons. The classifier maps inputs into 10 classes. Determine the number of
parameters (wights and biases) in the network.
(ii) In a CNN, the input to a convolutional layer has width 30, height 40, and depth 20.
The convolutional layer uses 10 filters of size 5× 5 with a stride of 2 and zero padding
of P = 2 on all sides of the image.
(a) Determine the width, height, and depth, of the output of the convolutional layer.
(b) What is the depth of each of the filters used in this convolutional layer
3. This is a simple exercise in computing the output in a binary classifier that contains
convluition, max-pooling, and fully connected (neural network) layers. The image shown
below is applied to a filter with impulse response (kernel) 0 1 01 0 1
0 1 0