A moment is defined as:

$$m_{p,q}(x,y) = \int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} x^p y^q f(x,y) dxdy$$

In other words, it is the summation of the figure with respect to the function $f$ for both axes.

Q: What are Zernike moments?

Zernike moments are complex polynomial functions used to sum the elements of a shape. They were first introduced in the 1930s. The higher the order, the more complex the shape that can be represented. Order 1 Zernike moments (ZMs) are ellipsoid planes where one side is higher than the other.

Q: What is the difference between Hu moments and Zernike moments?

The importance of Zernike moments lies in their rotational invariance. However, Hu moments are also said to have these properties. Thus, Hu moments appear to be simpler alternatives to Zernike moments.

Q: What are their properties?

Zernike moments use polar coordinates, making it easy to describe rotational invariance.

Keywords:

• Stereo image
• descriptor
• circle
• quantization
• formalization
• binary mask
• Depth estimation

Q1: How is depth estimation related to object recognition?

Objects are located in a 3D environment, and in order to recognize them correctly, we need to be able to recreate their layout in a scene. With such an aid, we can successfully determine the object boundaries.

Q2: What does the descriptor contain?

It is a concatenation of vectors. The first vector is the Gaussian of the center point with a $\Sigma_0$, the second set of vectors are circles lying on circle $R_1$, the third set of vectors are circles lying on circle $R_2$… Each vector contains orientation maps after a Gaussian convolution.

Q3: On which datasets did the authors try the technique?

As far as I can tell, it is a custom dataset that contains the view of the same scene from many perspectives.

Q4: What is the salience criterion for keypoints?

The aim of the technique is not matching these keypoints to each other by selecting the most appropriate ones. The computation is done on all pixels/keypoints. Hence, no criterion for keypoint filtering is reported.

Authors: Alexandre Alahi, Raphael Ortiz, Pierre Vandergheynst

Keywords:

• Keypoint
• Binary descriptor
• Retina
• Sampling
• Saccadic
• Coarse-to-fine
• Orientation

Q1: What is the formula for the retina pattern?

The one difference from BRISK is that the pattern has overlapping circles. In BRISK, they were tangential. Redundancy increases recognition.

The circles are log-polar. In this case, it is similar to Shape Context descriptors, but we do not divide into regions; we create increasingly larger circles on polar lines.

Q2: What do the descriptors contain?

A binary descriptor is a string of bits. A bit corresponds to a pair of receptive fields. If the intensity of the first receptive field is larger than the second, the bit is set to 1; otherwise, it is zero.

Q3: How does the sampling work?

Each circle in the pattern is called a receptive field. A Gaussian kernel is applied to these fields, and their intensities are calculated.

Q4: Is there scale invariance? How?

There is no discussion of scale invariance, but scale invariance seems to arise from the building of the descriptor. Since the circles are created in log-polar orbits and bits are put into the descriptor according to their contribution to recognition, scale invariance follows these.

Q5: How is rotation invariance achieved?

Orientation is calculated using 45 symmetric pairs from the center. It has larger steps than those of BRISK and thus needs lower memory.