Q2: (Easy Questions)

a.    Network Forward Propagation [3 marks].

Given below is asingle node in a neural network. Supposing that d is 4, x={1,3,2,7},   and w={0.6,0.2,0.4,-0.4}, b=0.3, and that the activation function is a standard ReLU,  that is =max(0,x), where x is the input to the activation function.  What is the output of this network?

a.   Suppose that the input to a 2x2, stride 2 max pooling layer has the following input in a neural network.  What would be the output? [ 4 marks]

b.   Suppose that the output vector of the last layer of neural network is [0.1, 0.5, 0.7,

0.9], then a softmax function is applied. What would be the resulting output vector? [ 3 marks]

Q3: (Medium difficulty)

a. Optical Flow [5 Marks]

Optical flow defines the dense motion field of pixels across two image frames. Lucas &

Kanade (1981) proposed a solution to solve the optical flow of all pixels by enforcing the

local patch constant motion constraint, which is known as Lucas-Kanade algorithm. Please   answer the following question based on your understanding of the algorithm. What are the conditions the optical flow for that patch can be calculated correctly and accurately?

b. Shape from Shading [5 Marks]

Shape from Shading methods aim to predict the geometric information such as the surface normal from an intensity image. Assume we can capture animage of a planar surface

(Lambertian surface) illuminated by apoint light source at infinity, that is, light rays are all  parallel. Suppose that we have used other methods to know the brightness of the lighting, its direction and the reflectance properties of the surface in the above scenario.

We also have the image intensity information for this plane. Describe the distribution of the intensity values on this plane surface. Can the surface normals be obtained from this image  given all this information? Please provide the analysis to your answers.

Q4: (Medium difficulty)

a.    Homography Matrix VS Fundamental Matrix [5 Marks]

What is the difference between a homography matrix and a fundamental matrix? Explain the answer in one sentence.

b. Stereo [5 Marks]

Assume we have a stereo setup where two cameras are set so that the images are coplanar, and the optical axes are parallel with the camera centres are lying at the same height.  One   pixel in one view (image) represents a ray that passes through this pixel and the camera

centre. The projection of this ray in the other view defines an epipolar line. Describe the properties of epipolar lines for this stereo setup. Please provide a short answer to your   analysis.

Q5: (10 marks) (algorithm design) (Challenging)

Suppose that you have been asked to write software for a camera product: astereo camera rig to obtain dense depth values for all the pixels. The stereo camera rig has been

constructed so that two cameras that are rigidly mounted, pointing with their optical axes in parallel, with their image planes coplanar. The cameras have lenses that can be accurately

modelled as a pinhole. The rig comes with a large dice for which we know the centre

coordinates of each dot on each side as a calibration device.

You are asked to write software for the camera rig.

Firstly, design an algorithm for the configuration software, to calibrate the camera rig as required.

Secondly, design an algorithm that takes parameters which are the output of the camera calibration process. You need to specify these parameters. The algorithm returns dense   depth values for all the pixels that are overlapping in the camera views. Your algorithm    should be efficient and accurate.

Please clearly state any reasonable assumptions that you need to make to solve the problem.