In order to compare the results of different works in the area, a group of tools that allows evaluation of different content image retrieval systems was proposed by Müller et al. [48]. This is a group of performance measures that have been adapted from the discipline of textual information retrieval.
3.3.1 Performance measures
Mainly there are two statistical measures: precision and recall. When it has com- pleted a consultation process the entire set of images belonging to the system is divided into two groups, which are the group of recovered images and the image group omitted. In turn, the images of each group are divided into a group of images that are relevant as the search criteria above and that do not meet the criteria. Therefore:
For a given query topic, the precision is defined as the ratio between the number of retrieved images that are really relevant to the total retrieved images in a query.
P recision = |{relevant documents} \ {retrieved documents}|
|{retrieved documents}| (3.5)
And recall, is the ratio of relevant images that were correctly recovered, with respect to the total relevant images that should be recovered.
Recall = |{relevant documents} \ {retrieved documents}|
|{relevant documents}| (3.6)
Therefore, a good information retrieval system seeks to maximize both values. Precision and recall values can be plotted to give a precision-recall curve, as shown
3 Basic Notions and Definitions 24
Figure 3.2: Precision-recall Curve
in the figure 3.2. In which an ideal result is that the precision value starts with a value of 1 and it remains even when the values of recall increases.
As we can see in figure 3.2 we can graph all values of precision in function of recall. Average precision (AveP) computes the average value of precision over the interval from recall = 0 to recall = 1 Mean average precision (MAP) for a set of queries is the mean of the average precision scores for each query.
M AP = Q P q=1 AveP (q) Q (3.7)
where Q is the number of queries.
The MAP value is one of the most important measures to consider, because it summarizes the overall behavior of a retrieval system, and this is the principal evaluation parameter in the most important benchmarking [29].
Chapter 4
Image Indexing using a Non-negative
Semantic Embedding
This chapter presents a new method for indexing histology images using multimodal information, taking advantage of two kinds of data: visual data extracted directly from images and available text data from annotations performed by experts. The new strategy called Non-negative Semantic Embedding that extends the NMF al- gorithm, defines a mapping between visual and text data assuming that the space spanned by the text is a good enough representation of the images semantics.
The results presented in this chapter were published in Workshop on Medical Content-Based Retrieval for Clinical Decision Support. MICCAI 2011 [49].
4.1 Non-negative semantic embedding
The methods based in NMF are oriented to model latent factors for multimodal data, that is, to find the hidden structure of the collection, which is assumed to be common between the two data modalities. We propose a simplified strategy that extends the NMF-asymmetric algorithm [46] to a setting in which the semantic encoding is already known.
NSE method is used when we assume that the semantic encoding is already known, i.e., in this model we assume that the space spanned by text terms is a good enough representation of image semantics, and we use it to index and represent all images in the collection. Then, we want to find a way to embed visual features in this semantic space, to index images with or without annotations. We formulate this problem as finding a linear transformation of the visual data imposing a non negativity constraint on the solution, as follows:
4 Image Indexing using a Non-negative Semantic Embedding 26
V = ST ; S 0 (4.1)
Where, S 2 Rm⇥n is the transformation matrix representing the relationships
between the visual and text modalities. n is the number of visual features and m is the number of text terms. The non-negativity constraint in this case enforces an additive reconstruction of visual features, since vectors in the matrix S can be thought of as parts of images that are combined according to the presence of associ- ated labels. Notice that the encoding matrix, T , is the matrix of text annotations, and the vectors in S can also be directly interpreted as the visual features related to each text term.
Finding the matrix S when V and T are known is a convex problem under the divergence or euclidean criteria in the related minimization problem. However, we approximate the solution to this problem using the NMF updating rule for the matrix S. Instead of requiring a global optimum for this problem, which might result in overfitting to the training data, we accept a good approximate solution obtained from the Lee and Seung’s approach [45]. The updating rule usually converges to a local minimum, but it may result in a better generalization with some robustness to intrinsic noise in the training data. Updating rule for S:
Sia Sia
P
µTaµViµ/(ST )iµ
P
Tav (4.2)
We call this approach the Non-negative Semantic Embedding (NSE) taking into account that the semantic space is known in the problem and the resulting solution to embed image features on it is non-negative. It also differs from the Gonzalez et al. [22] approach in the sense that no latent factors are herein modeled, but instead, a semantic space is assumed from the given text terms space.