Polygon-Based Drawing Accuracy Analysis and Positive/Negative Space

in Art & Perception
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The study of drawing generally depends on ratings by human critics and self-reported expertise of the drawers. To complement those approaches, we developed an objective continuous performance-based measure of drawing accuracy. This measure represents drawings as sets of landmark points and analyses features of particular research interest by comparing polygons of those features’ landmark points with their counterpart polygons in a veridical image. This approach produces local accuracy measures (for each polygon), a global accuracy measure (the mean across several polygons), and four distinct properties of a polygon for analysis: its size, its position, its orientation and the proportionality of its shape. We briefly describe the method and its potential research applications in drawing education and visual perception, then apply it to a specific research question: Are we more accurate when drawing in the so-calledpositive space’ (or figure)? In a polygon-based accuracy analysis of 34 representational drawings, expert drawers outperformed less experienced participants on overall accuracy and every dimension of polygon error. Comparing polygons in the positive and negative space revealed an apparent trade-off on the different dimensions of polygon error. People were more accurate at proportionality and position in the positive space than in the negative space, but more accurate at orientation in the negative space. The contribution is the use of an objective, performance-based analysis of geometric deformations to study the accuracy of drawings at different levels of organization, here, in the positive and negative space.

Polygon-Based Drawing Accuracy Analysis and Positive/Negative Space

in Art & Perception

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References

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Figures

  • View in gallery

    The ground truth photograph (centre) is bracketed by examples of a novice drawing (left: one year of drawing experience; overall polygon error G=0.70) and an expert drawing (right: 17 years of drawing experience; overall polygon error G=0.16), each marked with their Regions of Interest (Q1,,4), the reference ROI (Q5), and the angle of interest (β1).

  • View in gallery

    In the model, the j Regions Of Interest (ROIs) in each drawing are described by j polygons (Qj), one of which is designated as the reference ROI (polygon QR). The orientation (α), area (A), centroid (C), side lengths (L), and the ray lengths (distance from the centroid to each corner, R) are used to compare the proportionality, scaling, orientation and positions of the polygons in the ith drawing to their counterparts in a ground truth photograph. Polygon properties such as Lj,k represent the kth L of the jth polygonal ROI.

  • View in gallery

    When we compare the orientation of the polygon Q1 in drawing n7 to the orientation of its reference polygon, QR, we can see that it is rotated clockwise more than Q1 is in the ground truth photograph. Informally, we measure the orientation error of polygon Q1 in a drawing such as n7 by: 1. Reorienting the drawing to match the angle of the minor principal axis of its reference polygon, QR, to that of the ground truth photograph (middle figures); 2. Taking the angle — in the ground truth photograph — of the minor principal axis of Q1 to the minor principal axis of QR (lower left figure); 3. Taking the angle — in the drawing — of the minor principal axis of Q1 to the minor principal axis of QR (lower right figure); and then 4. Taking the magnitude of the difference between those two angles. In the ground truth photograph, the angle of Q1 (αphoto,1) is −1.4816 radians. In drawing n7, the angle of Q1 (αn7,1) is −1.1214 radians. The orientation error of Q1 in drawing n7 is |αphoto,1αn7,1|=0.36886 radians (21°).

  • View in gallery

    In the ground truth photograph, polygon Q1 is nearly rectangular and roughly three times as wide as it is tall. In drawing n7, polygon Q1 is longer and skinnier, roughly four times as wide as it is tall, and less rectangular in shape. Informally, we measure the proportionality error of polygon Q1 by measuring side lengths — to capture shrinkage or stretch — and ray lengths from the centroid — to capture shear. For example, in the ground truth photograph, the left side of Q1, Lphoto,4, is 14% of the total perimeter (left figure) but in drawing n7, Ln7,4, is only 11% of the total perimeter (right figure), so the side Ln7,4 contributes an error of 3% to the total perimeter error. Similarly, the ray Rphoto,3 is 26% of the total of the ray lengths (left figure), but in drawing n7, ray Rn7,3 is 28% of the total (right figure), so the ray Rn7,3 contributes an error of 2% to the total ray length error. We calculate the proportionality error of polygon Q1 by halving the sum of all these side length and ray length errors. The proportionality error of Q1 in drawing n7 is 0.085369, or 8.5%.

  • View in gallery

    In the ground truth photograph, the area of Q1 is virtually identical to the area of its reference polygon, QR. In drawing n7, the area of Q1 is too large, roughly 124% of the area of its reference polygon, QR, while in drawing j4, the area of Q1 is too small, roughly 41% of the area of its reference polygon QR. Informally, we measure the scaling error of polygon Q1 in a drawing by: 1. Taking the ratio — in that drawing — of the area of Q1 to the area of its reference polygon, QR; 2. Taking the ratio — in the ground truth photograph — of the area of Q1 to the area of its reference polygon, QR; 3. Taking the magnitude of the difference between those ratios; and then 4. To keep the scaling error proportional to the true size of Q1, dividing by the ratio — in the ground truth photograph — of the area of Q1 to QR. The scaling error of Q1 in drawing n7 is |124%100%|100%=24%. The scaling error of Q1 in drawing j4 is |41%100%|100%=59%.

  • View in gallery

    When we resize, reorient and align drawing n7 to match its reference polygon, QR, to that of the ground truth photograph, we can see that — in drawing n7 — polygon Q1 is lower and to the left of where the ground truth photograph shows it should be. Informally, we measure the positioning error of polygon Q1 in a drawing such as n7 by: 1. Resizing the drawing to match the area (AR) of its reference polygon, QR, to that of the ground truth photograph (upper figures); 2. Reorienting the drawing to match the angle of the minor principal axis of its reference polygon, QR, to that of the ground truth photograph (middle figures); 3. Aligning the drawing to the ground truth photograph by aligning the centroids of their respective reference polygons, QR (lower figures); 4. Taking the distance, Doffset, between the centroids of polygon Q1 in the drawing and in the ground truth photograph (lower figures); and then 5. To keep the positioning error proportional to the true distance from Q1 to QR, dividing Doffset by the distance DQ1 — in the ground truth photograph — from the centroid of Q1 to the centroid of QR (lower figures). Position is the distance from the centroid of the reference polygon, and it is not given in absolute units, e.g., inches or pixels. It is measured in multiples (or fractions) of the square root of the area of the reference polygon, AR, which would be the height of a square of equal area. This reference length is intentionally dependent on the area of the reference polygon — rather than its height — to make position measurement less sensitive to deformations of the shape of the reference polygon. In the ground truth photograph, the centroid of polygon Q1 is 2.4286AR from the centroid of its reference polygon, QR. In drawing n7 — resized — the centroid of Q1 is 3.0685AR from the centroid of its reference polygon, QR. The offset Doffset between the centroids of Q1 in the ground truth and in drawing n7 is 0.68011AR. The positioning error of Q1 in drawing n7 is DoffsetDQ1=0.28005, or 28%.

  • View in gallery

    The still life Alpha, direct view, i.e., as seen from the participant’s viewpoint.

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    Overall polygon error measure, Gi, as a function of a participant’s years of drawing training and experience.

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    Experts made smaller polygon-wise errors than novices. Error bars represent ±one standard deviation.

  • View in gallery

    Polygons Q1 and Q6 describe objects, or positive space. Polygons Q3 and Q4 describe regions between objects, or negative space.

  • View in gallery

    Proportionality and position error were higher for negative space polygons than for positive space polygons. Orientation error was lower in the negative space. Error bars represent ±one standard deviation.

  • View in gallery

    Lunia Czechowska, 1919, by Amedeo Modigliani (left) and Mystery and Melancholy of a Street, 1914, by Giorgio de Chirico (right).

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    The table and chessboard in this medieval illustration (artist unknown, from Caxton, 1474) show divergent perspective.

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