Advanced perceptual systems are faced with the problem of securing a principled (ideally, veridical) relationship between the world and its internal representation. I propose a unified approach to visual representation, addressing the need for superordinate and basic-level categorization and for the identification of specific instances of familiar categories. According to the proposed theory, a shape is represented internally by the responses of a small number of tuned modules, each broadly selective for some reference shape, whose similarity to the stimulus it measures. This amounts to embedding the stimulus in a low-dimensional proximal shape space spanned by the outputs of the active modules. This shape space supports representations of distal shape similarities that are veridical as Shepard's (1968) second-order isomorphisms (i.e., correspondence between distal and proximal similarities among shapes, rather than between distal shapes and their proximal representations). Representation in terms of similarities to reference shapes supports processing (e.g., discrimination) of shapes that are radically different from the reference ones, without the need for the computationally problematic decomposition into parts required by other theories. Furthermore, a general expression for similarity between two stimuli, based on comparisons to reference shapes, can be used to derive models of perceived similarity ranging from continuous, symmetric, and hierarchical ones, as in multidimensional scaling (Shepard 1980), to discrete and nonhierarchical ones, as in the general contrast models (Shepard & Arabie 1979; Tversky 1977).

Failure to take note of distinctive attributes in the distal stimulus leads to an inadequate proximal encoding. Representation of similarities in Chorus suffers in this regard. Distinctive qualities may require additional complex representation (e.g., reference to linguistic terms) in order to facilitate discrimination. Additional semantic information, which configures proximal attributes, permits accurate identification of true veridical stimuli.

The human visual system is capable of learning both abstract and specific mappings to underlie shape recognition. How could dissimilar shapes be mapped to the same location in visual representation space, yet similar shapes be mapped to different locations? Without fundamental changes, Chorus, like other single-system models, could not accomplish both mappings in a manner that accounts for recent evidence.

The concept of distal similarity that plays a crucial role in Edelman's theory of representation is called into question in this commentary on theoretical as well as empirical grounds. A possible confusion between shape and (knowledge of) its referent, the problem of the subjective world, redundancy, and large individual differences in subjective space encountered in contrived universes are discussed.

Under shift, caused for example by eye movement, or by relative movement of the subject or object of perception, the cortical representation undergoes very large changes in “size” and “shape.” Space-variance of cortical representation rules out models that fundamentally require linear interpolation between shifted patterns (e.g., Edelman's model) or rigid shift of an invariant retinal stimulus corresponding to shift at the cortex (e.g., the shifter theory of van Essen). Recently, a computational solution of “quasi-shift” invariance for space-variant mappings has been constructed (Bonmassar & Schwartz 1997a; 1997b).

Although we find the idea of representation by similarities attractive as such, we have two main objections to the specific proposal of Edelman. First, he does not consider complexity issues in terms of storage and speed of recall for recognition. Related to this, the appearance of objects depends on far more factors than just shape, illumination, and pose. This requires an intermediate shape abstraction process that extracts category-specific shape properties from the mixed appearance of images.

Representing objects and concepts as points in low-dimensional shape space defined by distances to other complete object exemplars or prototypes, expressed as single numbers, misses the key advantages of representation in terms of hierarchically constructed, meaningful features of the environment. Generalisation along statistically significant, near-independent, sparse, cooperative features that stand directly for various aspects of a concept is essential.

The holistic representation of objects as coordinates in a psychological space should be supplemented with decompositional processes that break objects down into components. There is strong psychological evidence for object decomposition, and structured representations are also needed because of their computational efficiency. Structured and unstructured representations can be unified by a process that extracts regularities at multiple levels of an object.

Alternative models of similarity judgments that do not rest on metric space assumptions are known to be better descriptions of actual human behaviour but are ignored by Edelman. The internal spaces he postulates are a convenient fiction for artificial intelligence, but not compatible with what is now known about psychophysics at both behavioural and neurological levels of perceptual processing.

“Chorus embodies an attempt to find out how far a mostly bottom-up approach to representation can be taken.” Models that embody both bottom-up and top-down learning have stronger computational properties and explain more data about representation than feedforward models do.

Apart from the computationally appealing properties of representation by similarities, it is possible to extend this form of representation when needed to include object parts as well as the correspondence between subobject parts.

We argue that the notion of distal similarity on which Edelman's reconstruction of the process of perception and the nature of representation rests is ill defined. As a consequence, the mapping between world and description that is supposedly at stake is, in fact, a mapping between two different descriptions or “representations.”

The representation of similarities is a viable concept for a cognitive extension of visual psychophysics to the recognition of shapes, bringing issues such as similarity and categorization back into that field. However, as a framework it appears too general to place constraints on a particular process model for categorization. In particular, a preference for Chorus-like schemes with respect to structure-oriented approaches is unwarranted.

The Chorus scheme could be an important step in the search for solutions to the symbol grounding problem (Harnad 1990), but Edelman does not address the potential difficulties inherent in downgrading differences in favor of similarities in a categorization device. Isomorphism rather than representation is a more coherent way of thinking about Chorus whose modules are probably analytic rather than holistic.

Multidimensional space representations like those posited in Edelman's target article are not sufficient to capture all similarity phenomena. We discuss phenomena that are compatible with models of similarity that assume structured relational representations. An adequate model of similarity and perception will require multiple approaches to representation.

The Chorus representation is a sparse, similarity-preserving representation achieved by a feedforward neural network. Hence it is probably better suited for interpolation than for categorization. This commentary raises the question of how to combine categorization with interpolation, whether feedforward networks can be reasonable models for parts of the cerebral cortex, and whether people can perform more than one interpolation at a time.

This commentary discusses three main requirements for models of vision, namely, translation and scale invariance, scalability, and hierarchy. Edelman's Chorus model falls short of fulfilling these requirements because it ignores the highly dynamic nature of vision. Incorporating an attentional mechanism and assuming geon-like prototype representations may enhance Chorus's plausibility as a model of human object recognition.

Representation of similarities is not sufficient for most visual tasks. The proposed framework collapses useful dimensions such as position and pose for the sake of naming the object. Collapsing these dimensions leaves no representation of the object itself, but only an internal name that cannot be meaningfully manipulated.

Edelman suggests that any shape is encoded by an excitation vector with components corresponding to excitations of corresponding neuronal modules. This results in discrimination of stimuli in a shape space of low dimensionality. Similar vector encoding is present in color vision. Red-green, blue-yellow, bright and dark neurons are modules that represent a number of different color stimuli in color space of low dimensionality. Vector encoding allows effective computation of color differences and color similarities. Such a neuronal vector-encoding approach has also been applied to the perception of visual movement, line orientation, and stereopsis.

The neural basis of the Chorus model has been cast in terms of the visual alphabet theory, but the neural evidence can also be interpreted as supporting a theory of higher level representation in which neurons are responsive to complex 3D stimuli. These neurons, functioning as a population, could also form the basis of a representation such as envisaged by the Chorus model.