The computational magic of the ventral stream

I argue that the sample complexity of (biological, feedforward) object recognition is mostly due to geometric image transformations and conjecture that a main goal of the ventral stream – V1, V2, V4 and IT – is to learn-and-discount image transformations.

In the first part of the paper I describe a class of simple and biologically plausible memory-based modules that learn transformations from unsupervised visual experience. The main theorems show that these modules provide (for every object) a signature which is invariant to local affine transformations and approximately invariant for other transformations. I also prove that,
in a broad class of hierarchical architectures, signatures remain invariant from layer to layer. The identification of these memory-based modules with complex (and simple) cells in visual areas leads to a theory of invariant recognition for the ventral stream.

In the second part, I outline a theory about hierarchical architectures that can learn invariance to transformations. I show that the memory complexity of learning affine transformations is drastically reduced in a hierarchical architecture that factorizes transformations in terms of the subgroup of translations and the subgroups of rotations and scalings. I then show how translations are automatically selected as the only learnable transformations during development by enforcing small apertures – eg small receptive fields – in the first layer.

In a third part I show that the transformations represented in each area can be optimized in terms of storage and robustness, as a consequence determining the tuning of the neurons in the area, rather independently (under normal conditions) of the statistics of natural images. I describe a model of learning that can be proved to have this property, linking in an elegant way the spectral properties of the signatures with the tuning of receptive fields in different areas. A surprising implication of these theoretical results is that the computational goals and some of the tuning properties of cells in the ventral stream may follow from symmetry properties (in the sense of physics) of the visual world through a process of unsupervised correlational learning, based on Hebbian synapses. In particular, simple and complex cells do not directly care about oriented bars: their tuning is a side effect of their role in translation invariance. Across the whole ventral stream the preferred features reported for neurons in different areas are only a symptom of the invariances computed and represented.

The results of each of the three parts stand on their own independently of each other. Together this theory-in-fieri makes several broad predictions, some of which are:

-invariance to small transformations in early areas (eg translations in V1) may underly stability of visual perception (suggested by Stu Geman);

-each cell’s tuning properties are shaped by visual experience of image transformations during developmental and adult plasticity;

-simple cells are likely to be the same population as complex cells, arising from different convergence of the Hebbian learning rule. The input to complex “complex” cells are dendritic branches with simple cell properties;

-class-specific transformations are learned and represented at the top of the ventral stream hierarchy; thus class-specific modules such as faces, places and possibly body areas should exist in IT;

-the type of transformations that are learned from visual experience depend on the size of the receptive fields and thus on the area (layer in the models) – assuming that the size increases with layers;

-the mix of transformations learned in each area influences the tuning properties of the cells oriented bars in V1+V2, radial and spiral patterns in V4 up to class specific tuning in AIT (eg face tuned cells);

-features must be discriminative and invariant: invariance to transformations is the primary determinant of the tuning of cortical neurons rather than statistics of natural images.

The theory is broadly consistent with the current version of HMAX. It explains it and extend it in terms of unsupervised learning, a broader class of transformation invariance and higher level modules. The goal of this paper is to sketch a comprehensive theory with little regard for mathematical niceties. If the theory turns out to be useful there will be scope for deep mathematics, ranging from group representation tools to wavelet theory to dynamics of learning

The Computational Magic of the Ventral Stream: Towards a Theory

I conjecture that the sample complexity of object recognition is mostly due to geometric image transformations and that a main goal of the ventral stream – V1, V2, V4 and IT – is to learn-and-discount image transformations. The most surprising implication of the theory emerging from these assumptions is that the computational goals and detailed properties of cells in the ventral stream follow from symmetry properties of the visual world through a process of unsupervised correlational learning.

From the assumption of a hierarchy of areas with receptive fields of increasing size the theory predicts that the size of the receptive fields determines which transformations are learned during development and then factored out during normal processing; that the transformation represented in each area determines the tuning of the neurons in the aerea, independently of the statistics of natural images; and that class-specific transformations are learned and represented at the top of the ventral stream hierarchy.

Some of the main predictions of this theory-in-fieri are:
1. the type of transformation that are learned from visual experience depend on the size (measured in terms of wavelength) and thus on the area (layer in the models) – assuming that the aperture size increases with layers;
2. the mix of transformations learned determine the properties of the receptive fields – oriented bars in V1+V2, radial and spiral patterns in V4 up to class specific tuning in AIT (eg face tuned cells);
3. invariance to small translations in V1 may underly stability of visual perception
4. class-specific modules – such as faces, places and possibly body areas – should exist in IT to process images of object classes

The computational magic of the ventral stream: sketch of a theory (and why some deep architectures work).

This paper explores the theoretical consequences of a simple assumption: the computational goal of the feedforward path in the ventral stream -- from V1, V2, V4 and to IT -- is to discount image transformations, after learning them during development

Block-level discrete cosine transform coefficients for autonomic face recognition

This dissertation presents a novel method of autonomic face recognition based on the recently proposed biologically plausible network of networks (NoN) model of information processing. The NoN model is based on locally parallel and globally coordinated transformations. In the NoN architecture, the neurons or computational units form distributed networks, which themselves link to form larger networks. In the general case, an n-level hierarchy of nested distributed networks is constructed. This models the structures in the cerebral cortex described by Mountcastle and the architecture based on that proposed for information processing by Sutton. In the implementation proposed in the dissertation, the image is processed by a nested family of locally operating networks along with a hierarchically superior network that classifies the information from each of the local networks. The implementation of this approach helps obtain sensitivity to the contrast sensitivity function (CSF) in the middle of the spectrum, as is true for the human vision system. The input images are divided into blocks to define the local regions of processing. The two-dimensional Discrete Cosine Transform (DCT), a spatial frequency transform, is used to transform the data into the frequency domain. Thereafter, statistical operators that calculate various functions of spatial frequency in the block are used to produce a block-level DCT coefficient. The image is now transformed into a variable length vector that is trained with respect to the data set. The classification was done by the use of a backpropagation neural network. The proposed method yields excellent results on a benchmark database. The results of the experiments yielded a maximum of 98.5% recognition accuracy and an average of 97.4% recognition accuracy. An advanced version of the method where the local processing is done on offset blocks has also been developed. This has validated the NoN approach and further research using local processing as well as more advanced global operators is likely to yield even better results

Incremental object matching with probabilistic methods

This thesis deals with object matching, that is, the problem of locating the corresponding points of an object in an image. Conventional approaches to object matching are batch methods, meaning that the methods first learn the object model from a training set of example images that contain instances of the object, and then use the learned object model to match instances of the same object (or object class) in unseen test images. In matching the object in a test image, the visual correspondence of the points as well as their spatial layout is usually considered simultaneously. Typically the corresponding points of the object are manually pre-annotated in the training images which facilitates the learning process. In this thesis, a novel approach is taken: The object matching is incremental. This means that the system is given images one at the time, and the images are matched by updating the object model after each processed image. In addition, the methods presented in this thesis use images as such, without utilizing any pre-annotation or pre-segmentation information, so the task can be considered of being extremely difficult. Although an incremental learning procedure has been presented before that learns an object model incrementally and detects whether the object appears in a test image or not, the proposed methods are the first ones that try to locate the corresponding points of the object by handling images one by one. Like in the traditional object matching methods, the object model of the proposed methods also consists of spatially distributed local features. The adopted approach to the incremental matching is Bayesian; the likelihood corresponds to the appearance of the features and the prior distribution to the spatial layout. Recursive Bayesian formulas are utilized in updating the object model after each processed image and particle Monte Carlo methods are used to sample the posterior distribution. Results show that the methods are able to locate the corresponding points with similar accuracy as the batch matching methods. The learned object model can also be used in detection tasks, and according to the results, the detection capabilities of the presented methods are (almost) on a par with the batch detection methods, and superior to the reference incremental detection method

Mitigating the effect of covariates in face recognition

Current face recognition systems capture faces of cooperative individuals in controlled environment as part of the face recognition process. It is therefore possible to control lighting, pose, background, and quality of images. However, in a real world application, we have to deal with both ideal and imperfect data. Performance of current face recognition systems is affected for such non-ideal and challenging cases. This research focuses on designing algorithms to mitigate the effect of covariates in face recognition.;To address the challenge of facial aging, an age transformation algorithm is proposed that registers two face images and minimizes the aging variations. Unlike the conventional method, the gallery face image is transformed with respect to the probe face image and facial features are extracted from the registered gallery and probe face images. The variations due to disguises cause change in visual perception, alter actual data, make pertinent facial information disappear, mask features to varying degrees, or introduce extraneous artifacts in the face image. To recognize face images with variations due to age progression and disguises, a granular face verification approach is designed which uses dynamic feed-forward neural architecture to extract 2D log polar Gabor phase features at different granularity levels. The granular levels provide non-disjoint spatial information which is combined using the proposed likelihood ratio based Support Vector Machine match score fusion algorithm. The face verification algorithm is validated using five face databases including the Notre Dame face database, FG-Net face database and three disguise face databases.;The information in visible spectrum images is compromised due to improper illumination whereas infrared images provide invariance to illumination and expression. A multispectral face image fusion algorithm is proposed to address the variations in illumination. The Support Vector Machine based image fusion algorithm learns the properties of the multispectral face images at different resolution and granularity levels to determine optimal information and combines them to generate a fused image. Experiments on the Equinox and Notre Dame multispectral face databases show that the proposed algorithm outperforms existing algorithms. We next propose a face mosaicing algorithm to address the challenge due to pose variations. The mosaicing algorithm generates a composite face image during enrollment using the evidence provided by frontal and semiprofile face images of an individual. Face mosaicing obviates the need to store multiple face templates representing multiple poses of a users face image. Experiments conducted on three different databases indicate that face mosaicing offers significant benefits by accounting for the pose variations that are commonly observed in face images.;Finally, the concept of online learning is introduced to address the problem of classifier re-training and update. A learning scheme for Support Vector Machine is designed to train the classifier in online mode. This enables the classifier to update the decision hyperplane in order to account for the newly enrolled subjects. On a heterogeneous near infrared face database, the case study using Principal Component Analysis and C2 feature algorithms shows that the proposed online classifier significantly improves the verification performance both in terms of accuracy and computational time

Pattern Recognition

Pattern recognition is a very wide research field. It involves factors as diverse as sensors, feature extraction, pattern classification, decision fusion, applications and others. The signals processed are commonly one, two or three dimensional, the processing is done in real- time or takes hours and days, some systems look for one narrow object class, others search huge databases for entries with at least a small amount of similarity. No single person can claim expertise across the whole field, which develops rapidly, updates its paradigms and comprehends several philosophical approaches. This book reflects this diversity by presenting a selection of recent developments within the area of pattern recognition and related fields. It covers theoretical advances in classification and feature extraction as well as application-oriented works. Authors of these 25 works present and advocate recent achievements of their research related to the field of pattern recognition

I-theory on depth vs width: hierarchical function composition

Deep learning networks with convolution, pooling and subsampling are a special case of hierar- chical architectures, which can be represented by trees (such as binary trees). Hierarchical as well as shallow networks can approximate functions of several variables, in particular those that are com- positions of low dimensional functions. We show that the power of a deep network architecture with respect to a shallow network is rather independent of the specific nonlinear operations in the network and depends instead on the the behavior of the VC-dimension. A shallow network can approximate compositional functions with the same error of a deep network but at the cost of a VC-dimension that is exponential instead than quadratic in the dimensionality of the function. To complete the argument we argue that there exist visual computations that are intrinsically compositional. In particular, we prove that recognition invariant to translation cannot be computed by shallow networks in the presence of clutter. Finally, a general framework that includes the compositional case is sketched. The key con- dition that allows tall, thin networks to be nicer that short, fat networks is that the target input-output function must be sparse in a certain technical sense.This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF - 1231216

State of the Art in Face Recognition

Notwithstanding the tremendous effort to solve the face recognition problem, it is not possible yet to design a face recognition system with a potential close to human performance. New computer vision and pattern recognition approaches need to be investigated. Even new knowledge and perspectives from different fields like, psychology and neuroscience must be incorporated into the current field of face recognition to design a robust face recognition system. Indeed, many more efforts are required to end up with a human like face recognition system. This book tries to make an effort to reduce the gap between the previous face recognition research state and the future state