Visual Invariance in Children: Understanding Early Vision

Christopher Wetzel and Alex Bäcker

Sandia National Labs & California Institute of Technology

When children begin to write, some have difficulty correctly reproducing letters; often, they sketch the reflection of a letter or number.  We hypothesized that the problem lies not in their writing skills, but in their perception: that children perceive a symbol or picture as the set of visual features in the images they see, and that, early in development, a child does not perceive the relationships between visual features that differentiates a symbol from its reflection or rotation. This hypothesis is inspired by the hierarchical nature of visual processing: assuming that elements higher in the visual hierarchy, which detect confluences of sets of elements lower in the hierarchy, can only properly develop after their component elements lower in the hierarchy have been formed, one should be able to find a developmental stage at which the features represented by the lower echelons of the hierarchy are represented, but their higher-order combinations are not.  To test this hypothesis, children from Caltech’s Children’s Center were shown a series of sets of three cards: first a reference card, bearing a symbol or picture, and then two other cards, one bearing the exact same symbol, and the other bearing a different symbol, or a reflection or rotation of the reference symbol.  The children were asked to point to the symbol which was the same as the reference symbol.  The data collected show that children have difficulty distinguishing reflections, and, to a lesser degree, rotations of symbols, supporting our hypothesis.

Examining the development of drawing skills in young children provides insight into and raises questions concerning the development of child vision.  Generally, children begin to scribble around age two.  At this time, a child may have developed the motor skills necessary to hold a crayon or other drawing instrument, but will generally not have any purpose in drawing other than the enjoyment gained from motor movement and seeing marks appear on paper (Crosser).  After about three years, however, children discover symbolism and begin to associate symbols, often very simple ones, like circles, with objects in their environment.  Soon, children begin to draw simple shapes—lines, circles, squares, etc.  Initially, children will notice that a scribble resembles an object without first intending to symbolically represent the object (Crosser).  At some point children begin to recognize other symbols shown to them and begin to copy them.  Here something interesting happens.  Consider the following drawing:

Here, the child, a two-year-old, has responded to the text already present (Veronica) by inversion of the characters over a horizontal axis.  This raises an interesting question: how are visual symbols, such as the letters of the alphabet, represented in a child’s brain?  We know that the brain can break down an image by component shapes.  A certain neuron may fire when a series of photoreceptors in a vertical line all fire, thus detecting a vertical line.  Another neuron may fire when a series of photoreceptors in an L shape all fire, thus detecting a right angle.  We know that this information is given to the brain because of the hierarchical arrangement of neurons in the brain; we don’t know exactly how the information processed by this system is translated into vision, especially in children.  Consider the symbols L and Γ.  Both have two lines and a right angle.  It is possible that the similarity in representation of both L and Γ account for drawings like the one above.  Each symbol has the same relative relationships (angles and distances) between each of its key features.  In these symbols are identical if thought of as three dimensional objects. 

Although vision is, to some extent, hard-wired into the brain at birth, children still must complete a journey of discovery that enables them to use their vision system.  Just as an infant waves its limbs randomly at first and then with increasing degrees of purpose later, so also does an infant explore and develop its sight.  We hypothesize that children perceive a symbol or picture as the set of relationships among the visual features in the images they see, and that, early in development, a child does not perceive the relationships between visual features that differentiates a symbol from its reflection or rotation.  This hypothesis is inspired by the hierarchical nature of visual processing. Assuming that elements higher in the visual hierarchy, which detect confluences of sets of elements lower in the hierarchy, can only properly develop after their component elements lower in the hierarchy have been formed, one should be able to find a stage of development at which the features represented by the lower echelons of the hierarchy are represented, but their higher-order combinations are not.  For example, while a developing brain may be able to detect right angles, it may not be able to distinguish between L and Γ. 

To test this hypothesis, we performed two experiments on 27 children from three to five years old from the Caltech Children’s Center.  In each experiment, children were shown sets of three cards.  Each set contained one reference card (the first card shown to the child) and two test cards, one of which was a copy of the reference card.  The other card contained a different symbol, a reflection of the reference symbol, or a rotation of the reference symbol.  The child, after briefly viewing the reference card, was required to choose which test card looked like the reference card.  We performed two experiments, the first using a combination of ASCII symbols and the second using combinations of only three simply figures (Figure 3).  We performed two versions of the second experiment, one “Card Up,” where the child could see the reference card while choosing between the test cards, and “Card Down,” where, as in the first experiment, the child could not see the reference card.

Results

The data collected from our experiments indicate that children have difficulty distinguishing between rotations and reflections and that this effect is not linked to memory.  On average the children scored 19.7% worse when asked to compare reflections of symbols and 15.6% worse when asked to compare rotations of symbols than when asked to compare different symbols.  Children scored 14% worse on average in the card down experiments compared to the card up experiments (Figures 5 and 6).  Because the card down experiment required the children to remember what the reference card looks like whereas the card up experiment did not, the fact that the results of both experiments are correlated (r² = .6328) indicates that memory is not a significant factor in the differences seen among “different,” “reflection,” and “rotation” scores (See Figure 7).

Further Work

In order to further understand the development of the vision system of the brain, it is important to demonstrate the physiological implications of our hypothesis, namely, that the neurons that are high in the visual hierarchy which detect confluences of sets of elements lower in the hierarchy should display less activity, or actively not correlated to visual discrimination tasks in developing brains when compared with developed brains performing the same tasks.  In addition, it is important to investigate the relationship between classes of visual elements and to correlate this with neural anatomy.  Given that lines are lower in the visual hierarchy than intersections, and that points are lowing than lines, figures composed of points should be easier to distinguish than figures composed of lines for a developing nervous system.  Finally, it is important to investigate this hypothesis in some way that does not involve children, as age could certainly be a confounding factor.

Methods

The first experiment consisted of 39 sets of 3 symbols, Each set contained a reference symbol and two test symbols, one which looked exactly like the reference symbol, and one which was a reflection of the reference symbol, a rotation of the reference symbol, or a completely different symbol.  Of these 39 sets, 6 are sets of pictures, 6 are simple figures created using four straight lines, and 27 are a mix of letters, numbers, Greek letters, and symbols such as &, ), and @.  I began by showing the child the first symbol from the reference deck for approximately five seconds, while telling the child to remember exactly what he or she sees.  I then put the first symbol face down and held up the first cards from the other two decks.  I then asked the child to point to the symbol that was the same as the first one.  I then recorded his or her selection and proceed with the next set of three symbols, repeating this procedure until I finished going through the set of cards.  After I finished with each child, I reordered the deck to prevent the experience the child gained during the experiment from biasing the results due to learning curve effects.

The second experiment contained two versions of the first experiment: “Card up” and “Card down”.  For each child, I would run through a new set of cards twice, first leaving the first card, the reference card, face up and then a second time, leaving the reference card face down.  The new deck contained only 18 sets of cards, with 6 sets of each type: different, reflection, and rotation.  Only the three symbols in Fig. 3 were used in creating these cards to reduce the influence of the symbols on the results of the experiments.  I encountered few problems in my research.  Most children were reasonably interested in the experiment and cooperated.  Some have even asked to play the “game” again.  A few children, however, left in the middle, telling me that they did not want to play anymore.

References

Sandra Crosser. “When Children Draw.”  Earlychildhood.com (2002).  1 March 2004 http://www.earlychildhood.com/Articles/index.cfm?A=130&FuseAction=Article.

Acknowledgements

We would like to thank the Caltech Children’s Center and the parents of the children who participated in my experiment for allowing me to work at the Center over the summer; and the SURF Program for providing this opportunity to participate in undergraduate research. 

An early version of this manuscript was presented in a 2005 Caltech SURF report.