ImageView's scale type centerCrop
was what I wanted. Unfortunately I couldn't specify this property for bitmaps. I changed my splash screen layout to FrameLayout and added an ImageView and TextView overlapping each other. This way I was able to achieve what I wanted.
<FrameLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent"
tools:context=".SplashScreen"
android:orientation="vertical" >
<ImageView
android:id="@+id/imageView1"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:src="@drawable/splash2"
android:scaleType="centerCrop" />
<RelativeLayout
android:layout_width="match_parent"
android:layout_height="match_parent" >
<TextView
android:id="@+id/roadSignName"
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:layout_marginLeft="20dp"
android:layout_marginRight="20dp"
android:layout_centerHorizontal="true"
android:layout_centerVertical="true"
android:background="#FFF"
android:gravity="center_vertical|center_horizontal"
android:padding="10dp"
android:text="My program"
android:textAppearance="?android:attr/textAppearanceLarge"
android:textColor="#000000"
android:textSize="40sp" />
</RelativeLayout>
</FrameLayout>