Specification of Primitives and Relations

A second way in which various object perception models differ is in the elementary units, or primitives, that make up object representations. Again, Marr set the agenda by proposing a different set of primitives for each of the four stages in his object perception theory. In this framework, the image initially is represented by pixel intensity values, then the contours of the object are represented by oriented line segments, then the "2.5D" structure of the object is represented by surface patches, and finally the 3D structure is represented by a collection of volumetric primitives called generalized cylinders (which include such shapes as bricks, pyramids, and tubes).

Representations made up of simple primitives such as pixel intensity values have the advantage of describing an object with great precision. For example, in Fig. 4A, we see a close-up of the image pixels in a portion of Fig. 1A. A great deal of information is derivable from this simple representation, e.g., the various surfaces making up the object's "head" and "neck," the amount of light reflected by the surfaces, the precise curve of the neck, and the fact that the head is above the neck. Though not explicitly stated, these details nevertheless are implicit in the collection of pixel intensity values.

If we transform this representation into one using more sophisticated primitives, such as the oriented line segments illustrated in Fig. 4B, we lose some information but gain the advantage of explicitly representing certain properties of the object. Here, the oriented lines explicitly specify the boundary between the object and the background but do not code anything about surface lightness either explicitly or implicitly. In Fig. 4C, we see a further transformation from contours to a structural description with high-level primitives. Here, we explicitly represent the facts that there are two distinct parts and that one has the shape of a curved tube, whereas the other is wedge-shaped. But now we have lost the information about exactly how much the neck is curved.

Along with the set of primitives, an object perception model must also specify how the relationships between primitives are coded in a representation. Structural descriptions generally use high-level primitives (e.g., generalized cylinders) and specify relations

Figure 4 (A)-(C) illustrate three representations of a portion of the SOGI object using increasingly complex primitives. (A) simply includes the pixel intensity values of the image, (B) codes the orientations of the object's edges, and (C) is a structural description that explicitly denotes the shapes and relations between the two parts of the object. The latter representation is stable across the viewpoint shift that produces the image in (D) but is not sensitive enough to represent the difference between the objects depicted in (A) and (E).

Figure 4 (A)-(C) illustrate three representations of a portion of the SOGI object using increasingly complex primitives. (A) simply includes the pixel intensity values of the image, (B) codes the orientations of the object's edges, and (C) is a structural description that explicitly denotes the shapes and relations between the two parts of the object. The latter representation is stable across the viewpoint shift that produces the image in (D) but is not sensitive enough to represent the difference between the objects depicted in (A) and (E).

explicitly—for example, the representation in Fig. 4C makes explicit the fact that the wedge is ABOVE the curved tube. Indeed, explicit specification of the relations between primitives is, for many theorists, the defining property of a structural description. View-based theories, on the other hand, generally use low-level primitives and represent relations between them only implicitly. That is, Fig. 4A includes the information that the head is above the neck only because the gray pixels of the head part have X-coordinates that are smaller than the coordinates of the pixels composing the neck part.

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