Lovely Cat stocks something useful!

Before entering the topic, let's type 'Necker Cube' to the google search engine.  Then you can see following result.

If you are a quick witted, you already know what it is.

The Necker cube is kind of an optical illusion named by Louis Albert Necker (1786-1861). It is a simple wire-frame drawing of a cube, but interpreted differently for different users. People could perceive either the cube as a simple 2D image, 3D cube with the lower-left square as a frontal face, or 3D cube with the right-upper square as a frontal face.  

Measuring Presence in Virtual Environments: A Presence Questionnaire  (1998)

  Presence is defined as the subjective experience of being in one place or environment, even when one is physically situated in another. As applied to a virtual environment (VE), presence refers to experiencing the computer-generated environment rather than the actual physical locale. Then, what factors influence presence? what aspects of the VE or remote environment affect how much presence is experienced?  

  Presence in a VE depends on one's attention shifting from the physical environment to the VE, but does not require the total displacement of attention from the physical locale. Humans experience varying degrees of presence in a physical locale since the human attention is divided between the physical world and the mental world. How sharply users focus their attention on the VE partially determines the extent to which they will become involved in that environment and how much presence they will report. 

1. Attention

  According to Fountaine (The experience of a sense of presence in intercultural and international encounters, 1992), presence depends on a matter of focus. When experiencing a novel environment, people are generally more aroused and broadly focused on the tasks to be performed or the situation to be experienced. Fountaine (1992) claims that this broad focus enables the individual to be broadly aware of the entire task environment and argue that the broad focus is necessary for a high level of presence in VEs. 

  An alternate view is that the experience of presence in a VE may have aspects similar to the concept of selective attention. Selective attention refers to the tendency to focus on selected information that is meaningful and of particular interest to the individual. 

2. Involvement

  Involvement is a psychological state experienced as a consequence of focusing one's energy and attention on a coherent set of stimuli or meaningfully related activities and events. In general, as users focus more attention on the VE stimuli, they become more involved in the VE experience. 

3. Immersion 

  Immersion is a psychological state characterized by perceiving oneself to be enveloped by, included in, and interacting with an environment that provides a continuous stream of stimuli and experiences. Factors that affect immersion include isolation from the physical environment, the perception of self-inclusion in the VE, natural modes of interaction and control, and perception of self-movement. A VE that effectively isolates users from their physical environment, thus depriving them of sensations provided by that environment, will increase the degree to which they feel immersed in the VE.

4. Presence 

  Both involvement and immersion are necessary for experiencing presence, and involvement in a VE depends on focusing one's attention and energy on a coherent set of VE stimuli. Fully immersed observers perceive that they are interacting directly, not indirectly or remotely, with the environment.
 

What is cervico-ocular reflex?

   The cervico-ocular reflex (COR) is an ocular stabilization reflex that is elicited by rotation of the neck. It works in conjunction with the vestibulo-ocular reflex (VOR) and the optokinetic reflex (OKR) in order to prevent visual slip over the retina due to self-motion.

   The ocular stabilization reflexes serve to stabilize the visual image on the retina during head movements. Several sensory systems contribute to this process. The vestibulo-ocular reflex (VOR) moves the eyes on the basis of vestibular information opposite to the direction of head movement. It is mainly responsive to head movements with a high frequency. The optokinetic reflex (OKR) responds to visual motion stimulation. It directs the eyes in the same direction as the visual slip on the retina. The cervico-ocular reflex (COR) is a reflexive eye response that is elicited by rotation of the neck. The proprioception of muscles and the facet joints of the cervical spine form the receptor part of this reflex. In contrast to the VOR, both the OKR and COR respond optimally to head movements with a low velocity. In an optimal situation these stabilization reflexes work in conjunction at all head velocities in order to optimize the ocular response.

Does the COR change with age?

  The VOR and the OKR decrease with old age whereas the COR increases with age. 

Does the COR strength is influenced by the strength of the VOR or OKR?

  In order to investigate whether the COR strength is influenced by the strength of the other stabilization reflexes (VOR, OKR), an experiment was conducted. The experimental result found that there appeared to be a link between the properties of the COR and the VOR, but not between the OKR and the other reflexes (COR, VOR). 

  Let's take a look at the result more in detail. In the experiment, both the VOR and the COR correlated with age. The VOR decreases, and the COR increases. Their relationship seems to a negative relation: the higher the VOR, the lower the COR. Therefore, the strength of the COR can be partially predicted by the strength of the VOR. 

  In other words, the COR can compensate for loss of vestibular function.  When the gain of the VOR is lower than desired, the COR can be upregulated. The COR is most responsive at low velocities, whereas the VOR is responsive at high frequencies. However, even at low velocities the VOR often has a higher gain than the COR. Such a compensation can obviously only be effective in the range where the COR is active, and will therefore not influence performance at high frequencies. 

Reference

Kelders, W. P. A., et al. "Compensatory increase of the cervico‐ocular reflex with age in healthy humans." The Journal of physiology 553.1 (2003): 311-317.

Classification of Eye Movements based on their functions

Introduction

Our eyes move due to following reasons:

- To keep visual images as stable as possible on the retina.

- To change the direction of gaze.

- To prevent the fading of retinal images.

Stabilization of images 

  If our eyes fail to keep stable the visual images on the retina, it leads a motion smear. With the motion smear, we often fail to judge object location in space since the images we accepted become a blur. Vestibular-Ocular Reflex (VOR) and Optokinetic Nystagmus (OKN) are representative eye movements to stabilize images on the retinas.

 - Vestibular-Ocular Reflex (VOR): This reflex is to stabilize the gaze during head or body movement by producing eye movements in the direction opposite to head or body movement, thus preserving the image on the center of the retina. VOR can be classified into two phases: slow phases and fast phases. Most of VOR in natural cases is a slow phase which cancels the head rotation to keep the gaze steady. When a head movement carries the eye too far to handle with only slow phase, a fast phase which is a saccade recenters the eye past primary position to anticipate continued motion. (*Comatoes patients show slow phase but fast phase; eye travels to an edge and stays there.)

- Opto-Kinetic Nystagmus (OKN): This is also called the Opto-Kinetic Reflex (OKR), or Parade nystagmus, or Railway Nystagmus. OKN is elicited by periodic visual stimuli drifting across the subject's visual field. When we ride on a train, we can observe objects like trees coming closer to us. To preserve stable image on a retina, the eye tracks the objects in the direction of their movement until the eye at an extreme position in orbit (slow pursuit, Ocular-Following Response (OFR)). Then, the eye rapidly moves in opposite direction to look at a new object (fast, saccades movement). 

Changes in gaze direction

 If our interest moves from one to another, we also move our fovea to the new object of interest. In order to move and fixate the eye to a new target, we often use Saccades, Pursuits, and Vergences. 

- Saccade: This means a quick, simultaneous movement of both eyes from one to another position. (It also serve as a mechanism for the fast phase of optokinetic nystagmus as referred above.)

- Pursuit: This is also called smooth pursuit which allows the eyes to follow a moving object. Most people are not able to initiate the pursuit without a target. If a target moves greater than 30˚/s, catch-up saccades are often required in pursuit movement. Smooth pursuit is asymmetric: most humans tend to be better at horizontal than vertical pursuit and better at downward than upward pursuit. 

- Vergence: A vergence is the simultaneous movement of both eyes in opposite directions to obtain or maintain single binocular vision. To look at the nearby object, the eyes rotate towards each other (convergence), whereas to look at the object far away, the eyes rotate from each other (divergence). As opposed to the 500˚/s velocity of saccade movements, vergence movements are far slower, around 25˚/s.

Preventing the fading of retinal images

  When an image is stabilized on the retina by one means or another, it soon faded and disappears. A similar fading phenomenon is the Troxler's fading.  When you fixate your eyes to a particular point for a while, unchanging nearby images will fade away and disappear.  This fading phenomenon has been attributed to the adaptation of visual neurons. To avoid such disappearance, the nervous system carries out a mechanism called fixational eye movement, which continuously stimulates neurons in the early visual areas of the brain responding to transient stimuli. Miniature ocular movements are as follows:  

- Drift: Ocular drift is the fixational eye movement characterized by a smoother, slower, roaming motion of the eye when fixed on an object. The exact movement of ocular drift is often compared to Brownian motion, which is the random motion of a particle suspended in fluid as a result of its collision with the atoms and molecules that comprise that fluid. Ocular drifts occur incessantly during intersaccadic fixation. The frequency of ocular drifts is a range of 20 to 40 Hz. 

- Ocular Micro-Tremor (OMT): OMT is a constant, high frequency, low amplitude eye tremor occurring at frequencies in a range of 40 to 100 Hz. In a coma, there is a loss of high-frequency components of tremor and the extent of this reduction is related to the patient's prognosis. 

- Microsaccade: This is also known as "flicks" which is saccades, involuntarily, produced during the fixation periods.  It is the largest and fastest within the fixational eye movements. Like saccades, microsaccades are usually binocular, and conjugate movements with comparable amplitudes and directions in both eyes. The only way to distinguish microsaccades from saccades is by the time in which they happen: during fixation. Regular saccades are produced during the active exploration of the eye, during non-fixation tasks whereas microsaccades are only produced during fixation tasks. 

  Note that the existence of these movements has been known since the 1950s, only recently their functions have started to become clear. 

References

https://www.dartmouth.edu/~rswenson/NeuroSci/chapter_8D.html

https://en.wikipedia.org/wiki/Saccade

https://en.wikipedia.org/wiki/Nystagmus

http://schorlab.berkeley.edu/passpro/Gaze%20STABILIZAT4.pdf

https://en.wikipedia.org/wiki/Vestibulo%E2%80%93ocular_reflex

https://www.slideshare.net/GauriSShrestha/gaze-shifting-gaze-holding-ocular-motor-functions

https://www.dartmouth.edu/~rswenson/NeuroSci/chapter_8D.html

This posting introduces various methods for measuring stochastic similarity between two groups A and B. 

1. Goodness-of-fit

   Goodness-of-fit is widely used to test whether two samples have identical (or similar) distribution. The goodness-of-fit of a statistical model describes how well it fits a set of observations. Measures of goodness-of-fit summarize the discrepancy between observed values and the values expected under the model in question. A goodness-of-fit statistic tests the following hypothesis:

   H_0: the model M_0 fits

   H_A: the model M_0 does not fit(or, some other model M_A fits)

We call H_0 as a null hypothesis and H_A as a alternative hypothesis. 

  In assessing, there are two cases :

1. when the distribution of sample B is known, and

2. when the distribution of sample B is unknown. 

At first, let's assume that group B has known distribution, Gaussian(normal) distribution. 

1-1. Normality Test

 In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed. For this, following tests are available.

- D'agostin's K-squared test

- Jarque-Bera test

- Anderson-Darling test

- Cramer-von Mises criterion

- Lilliefors test

- Kolmogorov-Smirnov test

- Shapiro-Wilk test

- Pearson's chi-squared test

In [Razali et.al. 2011: "Power comparisons of Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors and Anderson–Darling tests"], Shapiro-Wilk has the best power for a given significance, followed closely by Anderson-Darling when comparing the Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors, and Anderson-Darling tests. Therefore, we will check those four tests. 

Shafiro test

Anderson-darling test

ANOVA?

Null hypothesis?

K-test?

Difference between One-way ANOVA & Two-way ANOVA

One-Way ANOVA: An ANOVA hypothesis tests the difference in population means based on one characteristic or factor. a----->b "An example of when a one-way ANOVA could be used is if you want to determine if there is a difference in the mean height of stalks of three different types of seeds. Since there is more than one mean, you can use a one-way ANOVA since there is only one factor that could be making the heights different. " Two-Way ANOVA: An ANOVA hypothesis tests comparisons between populations based on multiple characteristics. a---->c<----b "Suppose that there are three different types of seeds, and the possibility that four different types of fertilizer is used, then you would want to use a two-way ANOVA. The mean height of the stalks could be different for a combination of several reasons" Multivariate analysis of variance (MANOVA): it is simply an ANOVA with several dependent variables. That is to say, ANOVA tests for the difference in means between two or more groups, while MANOVA tests for the difference in two or more vectors of means. a----->c, b------>d, a----->d, b----->c 

Phase & Magnitude analysis in Fourier Transform

  The purpose of this post is to observe differences between textures which are quite similar but have slight differences. Here shows the texture samples. 

 Five samples are used for the experiment. The first sample is a grass texture, and we call it as an original sample. Rest four samples are variation of the original one. Long black rectangular is used for making variations. If it lies on top of the original sample, we call it as a 'Top'. In the same manner, 'Cen', 'Bot', and 'Right' are generated. 

 Now let's convert spatial data into frequency data using Fourier Transform. (For the convenience, we only examine R channel of samples - presented textures have three channels, RGB.) In the frequency domain, we can observe texture characteristics from two major components: magnitude and phase. Therefore, plotting those components is helpful to investigate differences  between those samples. Let's plot original one first. 

  then, let's plot rest four samples. 

 In terms of magnitude spectrum, we can find obvious differences. 'Top', 'Cen', 'Bot', and 'Right' samples have long huge white line at the center. 'Top', 'Cen', and 'Bot' have long vertical white line and 'right' sample has long white horizontal line. It represents the long black rectangle in the spatial domain. We can also observe that the white line lies on the same position in 'Top', 'Cen,' and 'Bot'. Since the frequency domain represents the data into signals, it is natural. 

 On the other hand, we cannot observe any significant differences from phase spectrum. They still seem mere random. MAYBE, since the phase have no locality (the data have similar phase distribution in all coordinates), we cannot find the obvious changes in the phase spectrum. Following graph shows the phase data is spread widely. 

(For the visualization purpose, we used log function to plot magnitude spectrum. Mat2gray normalization was also used for both magnitude and phase spectrum. Magnitude spectrum is the result of abs() function and phase spectrum is the result of angle() function of MATLAB) 

https://fgiesen.wordpress.com/2011/09/06/a-trip-through-the-graphics-pipeline-2011-part-12/

 Likert developed the principle of measuring attitudes by asking people to respond to a series of statements about a topic, in terms of the extent to which they agree with them, and so tapping into the cognitive and affective components of attitudes. A Likert scale assumes that the strength/intensity of experience is linear, i.e. on a continuum from strongly agree to strongly disagree, and makes the assumption that attitudes can be measured. 

 A scale can be created as the simple sum of questionnaire responses over the full range of the scale. In so doing, following characteristics should be considered. 

 - Symmetry: They contain equal numbers of positive and negative positions whose respective distances apart are bilaterally symmetric about the "neutral" value

- Balance: The distance between each candidate value is the same, allowing for quantitative comparisons such as averaging to be valid across items containing more than two candidate values. The format of a typical five-level Likert item could be

   strongly disagree / disagree / neutral / agree / strongly agree

Likert scaling is a bipolar scaling method, measuring either positive or negative response to a statement. Sometimes an even-point scale is used, where the middle option of "neutral" is not available. This is sometimes called a "forced choice" method, since the neutral option is removed. 

 In illustration, the diverging stacked bar charts is highly recommended [Plotting Likert and Other Rating Scales - 2011]. Diverging stacked bar charts make it easier to compare the attitudes of respondents in different demographic categories or who differ on the importance of increasing professional recognition than do any other figures discussed.