Monte Carlo simulation of track reconstruction and pattern filtering in a HEP particle detector.

<p><b>a</b>, Schematic representation of a sector of a four-layers tracking detector, with simulated data (see Methods). Black dots represent measured positions where flying particles cross the detector layers - they can also be produced by random noise. Each layer is subdivided into a finite number of intervals (<i>bins</i>), delimited here by vertical bars. Every possible combination of bins (one on each layer) defines a <i>pattern</i> (grey line example). Only a small fraction of the patterns are compatible with the presence of a real particle (red line example), <b>b</b>, Probability distribution of the frequency of patterns (<i>δ(p)</i>) produced by a sample of simulated events of the type shown in (a) (grey histogram). The distribution of the sub-sample of patterns corresponding to valid particle trajectories is shown as a red histogram. The red curve is the function of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069154#pone.0069154.e001" target="_blank">eq. 1</a>, with N = 50 and W = 0.15. The vertical red lines indicate the probability range selected by our model, using the constraint ∫_{<i>f(p)>c</i>}<i>pδ(p)</i>d<i>p.</i></p

Human contrast sensitivity to visual patterns vs. model predictions.

<p><b>a,</b> Probability distribution of the 512 possible 3×3 1-bit pixel patterns (grey histogram). The curves are the model selection functions (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069154#pone.0069154.e001" target="_blank">eq. 1</a>) for W = 0.05 and two different values of N.(green: N = 50; blue: N = 15). Green and blue histograms are the probability distributions of corresponding selected patterns. Their actual bandwidth occupancies (∫_{<i>f(p)>c</i>}<i>pδ(p)</i>d<i>p</i>) turn out to be slightly lower (respectively 0.025 and 0.015) than the imposed limit W. Cyan and yellow histograms are the distributions of low-probability patterns used in our measurements. <b>b,c,</b> Visualization of the pattern sets shown in (a), in green and blue respectively. <b>d,</b> Visualization of the lowest-probability patterns (discarded by our approach due to large storage occupation). <b>e,</b> Visualization of the highest-probability patterns (discarded due to large bandwidth occupation). <b>f,</b> Averaged sensitivity for detection of the patterns as a function of their probability, measured on three human subjects (different colors). Errors are determined by the fit (see Methods). The results of pairwise statistical comparisons (z tests, N = 100) amongst sensitivities plotted in (f) are: </p

Examples of images from the database and sketches used.

<p><b>a</b> Examples of full color natural images extracted from the database <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069154#pone.0069154-Olmos1" target="_blank">[23]</a>, available at: <a href="http://tabby.vision.mcgill.ca/html/browsedownload.html" target="_blank">http://tabby.vision.mcgill.ca/html/browsedownload.html</a>. <b>b</b> Digitized versions of images in (a). <b>c</b> Sketches obtained from the images in (b), by using the optimal pattern set of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069154#pone-0069154-g003" target="_blank">fig. 3b</a>.</p

Entropy yield per unit cost, plotted as a function of the pattern probability (eq. 1).

<p>Blue curve: limited bandwidth and unlimited pattern storage capacity (W = 0.001, N = ∞); green curve: limited storage and unlimited bandwidth (N = 100, W = ∞); Red curve: limited bandwidth and storage (N = 100, W = 0.001)). Parameter values and the vertical scale are arbitrarily chosen for illustration.</p

Effect of local features.

<p>Discrimination of sketches obtained with optimal patterns (left) and of sketches where optimal patterns were replaced by randomly chosen non-optimal patterns (right). Each color represents a different subject.</p

Patterns selection.

<p>The gray histogram represents the probability distribution, in natural log scale, of the 2²⁷ possible 3x3 patterns, extracted from the dataset of RGB images used in this study [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159898#pone.0159898.ref016" target="_blank">16</a>]. The green curve is the model selection function with N = 500, W = 0.08. The green histogram is the probability distribution of corresponding selected patterns. The red histogram is the probability distribution of equiluminant patterns.</p

Percentage of correct discrimination, averaged over all subjects, plotted as a function of the number of matched patterns, for the same data as in fig. 5c and 5d.

<p>Percentage of correct discrimination, averaged over all subjects, plotted as a function of the number of matched patterns, for the same data as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069154#pone-0069154-g005" target="_blank">fig. 5c and 5d</a>.</p

Examples of sketches obtained from different pattern sets.

<p><b>a,</b> Original 256 grey-levels image. <b>b</b>, Sketch obtained from the optimal pattern set of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069154#pone-0069154-g003" target="_blank">fig. 3b</a>. The corresponding compression factor is 40, and its information content is 9.8% of the original. <b>c,</b> Sketch obtained from the optimal pattern set of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069154#pone-0069154-g003" target="_blank">fig 3c</a>. The corresponding compression factor is 67 and its information content is 5.5% of the original. <b>d,</b> Sketch obtained from the 244 low-probability pattern set (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069154#pone-0069154-g003" target="_blank">fig. 3d</a> shows a sub-sample); information (5.5%) and compression (factor 90) are similar to (c). <b>e,</b> Percentage of correct discrimination for sketches obtained as in (b), (c), (d) (green, blue, yellow bars respectively) and 256 grey-levels images as controls (red bars), for four subjects. The striped blue bar represents results obtained from the same dataset shown in blue, after reweighting the data to match the distribution of the number of patterns of the yellow dataset. <b>f,</b> Distributions of the number of points found in the sketches for the two sets in (c) and (d), shown with the same color code. The distributions are taken over the entire image database of our study. Each data point represents 300 trials. The black dashed line indicates chance performance. Error bars are s.d. The results of pairwise statistical comparisons (binomial tests) amongst performances plotted in (f) are: red vs. green: D.B. p = 0.96, V.B. p = 0.06, G.M. p = 0.16, F.C. p = 0.13; red vs. blue: D.B. p = 0.48, V.B. p = 0.009, G.M. p = 0.003, F.C. p = 0.08; blue vs. green: D.B. p = 0.3, V.B. p = 0.7,G.M. p = 0.3, F.C. p = 0.9; blue vs. yellow: D.B. p = 9.8*10⁻¹², V.B. p = 2*10⁻⁵, G.M. p = 0.002, F.C. p = 1.1*10⁻⁷. </p

Discrimination of images based on luminance and color sketches.

<p>Percentage of correct discrimination of three subjects in four different conditions tested: 1bit luminance-only sketches (2 gray-levels bars), 1 bit equiluminant sketches (2 red/green-levels bars), 2 bit luminance-only sketches (4 gray-levels bars) and 1 bit equi-luminance + 1 bit luminance sketches (4 red/green-levels bars). Values correspond to averages over different sessions (300 trials) of the same condition. Errors are binomial s.d. The dashed line represents chance performance. <i>Statistical binomial tests</i>. 1bit <i>luminance</i> vs. 1bit <i>equiluminance</i>: <i>p<0</i>.<i>0001</i> for each subject; <i>equiluminance</i> vs. <i>chance p>0</i>.<i>1</i>; 1 bit <i>luminance</i> vs. 1 bit <i>equiluminance +</i>1 bit <i>luminance</i>: N.T and L.S <i>p>0</i>.<i>05</i>, M.D <i>p = 0</i>.<i>048</i>;1 bit <i>luminance</i> vs. 2 bits <i>luminance</i>: and L.S <i>p<0</i>.<i>0001</i>, N.T and M.D <i>p>0</i>.<i>1</i>.</p

Stimuli and visual filters.

<p>a) Examples of RGB natural color images from the database. b) Set of N = 50 filters obtained after digitizing to 1 bit the <i>luminance</i> (L+M) coordinate. The actual bandwidth occupancy of the set () turns out to be slightly higher (0.06) than the imposed limit W (0.05). c) Set of N = 50 filters obtained after digitizing to one bit the <i>l</i> (L/(L+M)) coordinate. The actual bandwidth occupancy of the set out to be slightly higher (0.06) than the imposed limit W (0.05), but is still the same as the actual bandwidth of the 1 bit luminance set. d) Two gray-levels luminance sketches obtained with the filters in (b). e) Color-only sketches obtained with the filters in (c). f) Set of N = 50 filters obtained after digitizing to 2 bit the <i>luminance</i> coordinate. The actual bandwidth occupancy of the set turns out to be slightly higher (0.07) than the imposed limit W (0.05). g) Set of N = 50 filters obtained after digitizing to 1 bit both <i>l</i> (L/(L+M)) and <i>luminance</i> (L+M) coordinates. The actual bandwidth occupancy of the set turns out to be slightly higher (0.07) than the imposed limit W (0.05), but is still the same as the actual bandwidth of the 2 bits luminance set. h) Four gray-levels luminance sketches obtained the set of filters in (f). i) Color sketches obtained with the set of filters in (<b>g</b>).</p