Which explanation of the müller lyer illusion is offered by the text

For the L condition, the top line had randomised line length between and pixels. For the S condition, the bottom line length was randomised also between and pixels.

The comparator line length was randomised to be between 2 and 62 pixels shorter than the top or bottom line for the L or S condition. The vertical position of the top line was randomised between 48 and pixels from the top of the image while bottom line's vertical position was randomly placed between and pixels.

This forced the machine learner to rely on invariant properties rather than on absolute positional information for classification. Column 1 : Cross Fin XF images are used for training in all experiments. Column 2 : Control LR images are used to test accuracy levels for a standard stimulus. Column 3 : Illusion ML images are used to test performance levels for images that induce human perceptual error. We ran each experiment in two stages: a training stage and a test stage.

The model consisted of interleaved S and C layers, with a support vector machine SVM on top to perform final classification see Methods Section for details. For the training period, we exposed the network to a set of images to learn features at different positions and scales. Features were only learnt in the S2 and C2 cell layers; S1 and C1 have a fixed set of features refer to Methods Section.

For the test phase, C2 vectors were built for the test set of images which were then classified using the SVM. Cross Fin XF images Fig. Fin lengths were randomised between 15 and 40 pixels measured from the end of the shaft to the tip of the fin. Fin angles were randomised between 10 and 90 degrees for both top and bottom lines. This was to prevent the classifier from relying on the end positions of fins or on bounding box information to make a length judgment.

Essentially, we wanted to confirm that the machine learner was making its decision based only on the length of the inside lines shafts while also allowing it to be exposed to other irrelevant features.

The first experiment we ran was to ensure that the classifier was able to distinguish long from short images at an acceptable level of accuracy and precision for a set of control stimuli.

The control stimuli we used are illustrated in Fig. Fin angles were randomised between 10 and 70 degrees. We selected these control stimuli annotated LR because they contain the same number of features as those present in our illusion test stimuli. As expected, performance results for the experiment were affected by the size of the network.

Figure 4 illustrates these results, with error bars marking standard error of the mean between runs. With network sizes larger than , performance did not substantially improve. We therefore chose to use this network size for all subsequent experiments so as to achieve high accuracy while minimising computational expense. For our following experiments, the critical comparison was between our control and illusion conditions. Accuracy for the control condition versus the network size of S2 units.

Values shown are the average of 10 runs. Error bars show standard error of the mean. With a network size of S2 cells, we achieved an overall accuracy of We noticed a slight bias between our LONG category The ML images we tested are shown in Figure 2 Column 3, where the top line always has arrowtails and the bottom line always has arrowheads.

The fin length and fin angle were varied in the same way as for the control images. If the top line always has arrowtails for every single test image, the top line will appear perceptually elongated. The bottom line always having arrowheads will appear contracted. For a human observer, this means that when the two lines are objectively of equal length, the top line will appear longer. If the model is not susceptible to the illusion, accuracy levels should be similar to those shown in Experiment I.

However, if the model is susceptible to the illusion, then we should expect to see two effects. Firstly, for the LONG category, we would expect to see the model classifying these above the accuracy level in the control condition Secondly, for the SHORT category, we expect to see the classifier perform worse than the control condition Values displayed are the average of 10 runs for test images per category and error bars indicate standard error.

S2 network size was set to as in the control condition. The inverse effect is shown in the SHORT category, where the ML condition performs under the classification accuracy of the control condition. This indicates that the model is indeed susceptible to the MLI. Error bars indicate standard error of the mean. The results shown in Experiment II demonstrate errors consistent with an illusory effect; however they do not provide a detailed picture of classification performance using HMAX for control versus illusory data.

We can obtain a better picture of the illusory effect within HMAX by measuring classification across incremental line length differences.

By plotting classification results as a psychometric function, we are able to extract information such as the Point of Subjective Equality PSE , for the illusory stimulus.

Furthermore, we can separate out factors known to affect the strength of the illusion, such as the fin angle size or fin length, and observe consequent changes in the PSE. Figure 6 shows results for the control condition versus illusion conditions with three separate fin angles, plotted as psychometric functions.

The y-axis indicates the percentage of images classified as LONG. Instead, what we see is a series of sigmoid functions indicating that when line length difference is large in either negative or positive direction , it is easier for the system make a correct classification judgement.

Sigmoid curves such as these are typical when mapping human psychophysical responses. The control condition with all angles collapsed shows no bias. For illusory lines with 40 degree fins we see a PSE of approximately 12 pixels. Illusory lines with 20 degree fins show a larger PSE, congruent with human data. We first plotted the control condition with all angles collapsed. This indicates that with 40 degree fins, the top line must be For our lines of to pixels, this would create an average PSE of Illusory lines with 60 degree angle fins no longer demonstrated an illusory effect, indicated by a PSE of zero.

For 20 degree data, HMAX performance matched human performance closely. However, as fin angles were increased, the illusory effect tapered off earlier in HMAX compared with human data. So although we observed an overall illusory effect and a degradation of illusory strength with an increase in fin angles, the illusory effect decreased faster for HMAX compared to humans.

In this paper, we devised a set of experiments to measure the classification performance for an ML stimulus versus a control, in a biologically plausible model of object recognition. We trained the model using a set of cross fin images that do not induce any illusion in humans and that contain all features present in test stimuli.

We then compared these results to an illusory stimulus in Experiment II, where we observed a respective increase and decrease in classification accuracy for the long and short conditions. In Experiment III, we further investigated the strength of the illusion within the model by manipulating fin angle. The salient percepts that visual illusions create, along with the fact that they arise from internal processing, constantly stimulates researchers to search for the mechanism and the location within the brain where illusions originate.

However, illusions have proven as difficult to explain as any other perceptual phenomena. The physiological origins of some illusions have been investigated in animals, some of which are known to perceive them similarly to humans Tudusciuc and Nieder, This research shows that perceptual phenomena such as visual masking, flash suppression, filling-in, motion-induced depth, and cyclopean perception random dot stereograms are present in early stages of the visual processing in structures such as the thalamus, and the primary and secondary visual cortices Carney et al.

In an effort to understand the neuronal mechanisms behind the illusion previous work by Zeman et al. The authors first trained the network to categorize images of short and long horizontal shafts, presented in configurations that do not evoke the illusion in humans.

After this training they asked the network to classify the shaft lengths of images containing the classical MLI. The results show that the HMAX network showed a bias in the classification of the horizontal shafts, classifying the ones with arrowheads as shorter than actually were. Interestingly, the magnitude of the bias was similar to that measured in humans, and this effect was also modulated by the angle of the fins, with smaller angles closer to the horizontal shaft producing a larger bias.

Importantly, the authors demonstrated that the final classification layer, i. This result fails to support the low-level explanation of the illusion stating the low-pass characteristics of the center-surround and simple cells might be the principal cause of the illusion Figure 1F. The new work of Zeman et al. The reduction of the illusion by complex cells suggests that the property of positional invariance the ability to respond to a stimulus despite its spatial location could make those neurons less sensitive to the bias induced by the illusion.

These new results indicate that the magnitude of the MLI might be represented differently across different neuronal populations, and that more abstract representations of the images might be less sensitive to the illusory effects. The mechanisms behind the illusion are still elusive. As Zeman and colleagues show, the low-level explanation, despite its attractive simplicity, might not be the complete story. As has been shown with random dots stereograms and other binocular versions of the illusion Figure 1E , the MLI can be generated at a processing level beyond those of simple center-surround receptive fields, even in the absence of luminance contrast Julesz, It is clear that the visual system is comparing something else across the drawings, and it might be related to complete visual objects, not to local information.

Eye and brain: The psychology of seeing , 5th edition. Princeton University Press. Jahoda, G. Retinal pigmentation, illusion susceptibility and space perception. International Journal of Psychology , 6 3. Macpherson, F. Cognitive penetration of colour experience: Rethinking the issue in light of an indirect mechanism. Philosophy and Phenomenological Research , 84 1 , pp. McCauley, R. Philosophical Psychology , 19 1 , pp. Pollack, R. Contour detectability thresholds as a function of chronological age.

Perceptual and Motor Skills , 17, pp. Psychonomic Science , 8, pp. While there are no depth cues, the illusion still occurs. It has also been demonstrated that the illusion can even occur when viewing three-dimensional objects. Depth plays an important role in our ability to judge distance. One explanation of the Muller-Lyer illusion is that our brains perceive the depths of the two shafts based upon depth cues.

When the fins are pointing in toward the shaft of the line, we perceive it as sloping away much like the corner of a building. This depth cue leads us to see that line as further away and therefore shorter. When the fins are pointing outward away from the line, it looks more like the corner of a room sloping toward the viewer.

This depth cue leads us to believe that this line is closer and therefore longer. An alternative explanation proposed by R. Day suggests that the Muller-Lyer illusion occurs because of conflicting cues. Our ability to perceive the length of the lines depends on the actual length of the line itself and the overall length of the figure. Researchers from the University of London suggest that the illusion demonstrates how the brain reflexively judges information about length and size before anything else.

If an illusion can capture attention in this way, then this suggests that the brain processes these visual clues rapidly and unconsciously. This also suggests that perhaps optical illusions represent what our brains like to see," explained researcher Dr. Michael Proulx. Ever wonder what your personality type means? Sign up to find out more in our Healthy Mind newsletter.

Ninio J. Geometrical illusions are not always where you think they are: a review of some classical and less classical illusions, and ways to describe them.