Learning Active Basis Model for Object Detection and Recognition

Abstract

This article proposes an active basis model, a shared sketch algorithm, and a computational architecture of sum-max maps for representing, learning, and recognizing deformable templates. In our generative model, a deformable template is in the form of an active basis, which consists of a small number of Gabor wavelet elements at selected locations and orientations. These elements are allowed to slightly perturb their locations and orientations before they are linearly combined to generate the observed image. The active basis model, in particular, the locations and the orientations of the basis elements, can be learned from training images by the shared sketch algorithm. The algorithm selects the elements of the active basis sequentially from a dictionary of Gabor wavelets.When an element is selected at each step, the element is shared by all the training images, and the element is perturbed to encode or sketch a nearby edge segment in each training image. The recognition of the deformable template from an image can be accomplished by a computational architecture that alternates the sum maps and the max maps. The computation of the max maps deforms the active basis to match the image data, and the computation of the sum maps scores the template matching by the log-likelihood of the deformed active basis.

Learning a probabilistic model mixing 3D and 2D primitives for view invariant object recognition

“…For log linear model, it has been proved that this term is an increasing function ofμ r . The second observation is proved in [25], and here we just show the corresponding curve in Fig.3 as a validation. According to these two observations, in a group of Ω i s having t views, optimal Ω i must be the one that leads to largestμ r , which should be the mean of the t largest of totally M responses.…”

“…Following the derivation of Active Basis model [25], the target image distribution can be written as:…”

“…Specifically, we compute responses of these filters centered at each pixel of an image, and at 15 equally spaced orientations. Following [25], we call these filtered responses together as SUM1 maps. For each Gabor filter, we compute its maximum responses in neighboring locations and orientations, and save these maximized responses in so called MAX1 maps.…”

“…As the same with learning tasks in [25,16], this primitive selection problem can be solved under the matching pursuit framework, which incrementally select primitives from a large set of candidates to approximate the target distribution. We will first explain the key steps of this learning algorithm and then list all steps later.…”

“…Inspired by active basis model [25] and recent work on learning both object texture and structure [18], we use template containing both 3D and 2D primitives to represent images of an object category from different views. The 3D and 2D primitives are stick-like elements defined in 3D and 2D spaces.…”